Dissertations / Theses on the topic 'Interest rate and volatility risk'

lnterest rate risk is one of the most important types of risk to which banks are inherently exposed. lnterest rates determine a bank's profitability and have an effect on a bank's liquidity and investment portfolio. It is, therefore, extremely important to be able to predict interest rates accurately and manage interest rate risk effectively. In trying to manage interest rate risk, banks rely on Asset and Liability Committees (ALCOs). They also make use of several strategies, which are described (Gap, Earnings Sensitivity Analysis, Duration Gap and Market Value of Equity sensitivity analysis). The first step for these strategies, on which later steps depend, is to make interest rate forecasts. Forecasting plays such a crucial role because many significant decisions depend on the anticipated future values of specific variables. Forecasts may be produced in various different ways. The method chosen depends on the reason for and the importance of the forecasts as well as on the costs of alternative forecasting methods. In an attempt to manage interest rate risk by being able to predict the next rates correctly, several different models are used to try and predict interest rates for two data sets, namely: BA (Bankers' Acceptances, which is money market data) and Esc (Eskom, which is capital market data). They each have their place in the South African financial system, which is described in general. The chosen simple forecasting models that are used are: naive, moving average and exponential smoothing models. The aim is to try to predict the direction of the next interest rate (UP, CONSTANT, or DOWN) while supplying a point prediction of the next rate (one-step ahead). The "best" simple forecasting models are determined by specific set criteria (percentage of correct direction predictions, mean squared error and tracking signals). For the same time series, more advanced models are taken into account where the aim is to try to find an interval wherein the future interest rates (not only in the short-term but in the longer-term as well) are most likely to lie, using models based on the data, as well as first differences. For the long-term forecasts, two types of more advanced models are used, namely: Box-Jenkins models (where, specifically, nonseasonal second-order autoregressive or AR(2) models are examined); and volatility models that are found using a new technique that creates an interval by using different volatility estimates. The word 'volatility' used throughout the study refers to models with a fixed volatility function and not dynamic volatility as in models such as the ARCH and GARCH types. In this study, the range from simple to more complex time series models with constant volatility are considered. The former, simple models and AR(2) models are referred to as forecasting models, the latter more advanced models are referred to as volatility estimates. Short- and long-term predictions are, thus, made for each time series, at different specifically chosen points. A comparison of the effectiveness of the forecasting and volatility models is made.
Thesis (M.Sc. (Information Technology))--North-West University, Vaal Triangle Campus, 2006.

This thesis presents the modeling of credit risk by using structural approach. Three fundamental questions of credit risk literature are analyzed throughout the research: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric brownian motion assumption in explaining empirical properties of real data. Then we propose a new extended model in which asset value, volatility and interest rates follow affine jump diffusion processes. In our extended model volatility is stochastic, asset value and volatility has correlated jumps and interest rates are stochastic and have jumps. Finally, we analyze the modeling of single firm credit risk and credit risk pricing by using our extended model and show how our model can be used as a solution for the problems we encounter with simple models.

Esta Dissertação apresenta um modelo para extrair fatores capazes de prever a volatilidade do índice de ações IBOVESPA, representativo do mercado de ações brasileiro. Esta metodologia é diferenciada por utilizar fatores que não incluem ativos da classe de ações. São utilizados fatores extraídos de classes de ativos de crédito, taxas de juros, moedas e commodities para precificar a volatilidade de um índice de ações. Além disso, os fatores são extraídos de painéis de volatilidades filtradas por modelos do tipo GARCH.
It will be presented a model that is able to extract factors capable of predicting the volatility of IBOVESPA market index, which is representative of Brazilian equity market. This methodology is different from others because it won t use any inputs from equity asset classes. It will be used factors extracted from credit risk, interest rates, exchange rates and commodities data for pricing the volatility of an equity index. Besides that, those factors will be extracted from panels of volatility filtered by GARCH models.

Equity Risk Premium (ERP) is the cornerstone in Financial Economics. It is a basic requirement in stock valuation, evaluation of portfolio performance and asset allocation. For the last decades, several studies have attempted to investigate the relationship between macroeconomic drivers of ERP. In this work, I empirically investigate the macroeconomic determinants of UK ERP. For this I parsimoniously cover a large body of literature stemming from ERP puzzle. I motivate the empirical investigation based on three mutually exclusive theoretical lenses. The thesis is organised in the journal paper format. In the first paper I review the literature on ERP over the past twenty-eight years. In particular, the aim of the paper is three fold. First, to review the methods and techniques, proposed by the literature to estimate ERP. Second, to review the literature that attempts to resolve the ERP puzzle, first coined by Mehra and Prescott (1985), by exploring five different types of modifications to the standard utility framework. And third, to review the literature that investigates and develops relationship between ERP and various macroeconomic and market factors in domestic and international context. I find that ERP puzzle is still a puzzle, within the universe of standard power utility framework and Consumption Capital Asset Pricing Model, a conclusion which is in line with Kocherlakota (1996) and Mehra (2003). In the second paper, I investigate the impact of structural monetary policy shocks on ex-post ERP. More specifically, the aim of this paper is to investigate the whether the response of UK ERP is different to the structural monetary policy shocks, before and after the implementation of Quantitative Easing in the UK. I find that monetary policy shocks negatively affect the ERP at aggregate level. However, at the sectoral level, the magnitude of the response is heterogeneous. Further, monetary policy shocks have a significant negative (positive) impact on the ERP before (after) the implementation of Quantitative Easing (QE). The empirical evidence provided in the paper sheds light on the equity market’s asymmetric response to the Bank of England’s monetary policy before and after the monetary stimulus. In the third paper I examine the impact of aggregate and disaggregate consumption shocks on the ex-post ERP of various FTSE indices and the 25 Fama-French style value-weighted portfolios, constructed on the basis of size and book-to-market characteristics. I extract consumption shocks using Structural Vector Autoregression (SVAR) and investigate its time-series and cross-sectional implications for ERP in the UK. These structural consumption shocks represent deviation of agent’s actual consumption path from its theoretically expected path. Aggregate consumption shocks seem to explain significant time variation in the ERP. At disaggregated level, when the actual consumption is less than expected, the ERP rises. Durable and Semi-durable consumption shocks have a greater impact on the ERP than non-durable consumption shocks. In the fourth and final paper I investigate the impact of short and long term market implied volatility on the UK ERP. I also examine the pricing implications of innovations to short and long term implied market volatility in the cross-section of stocks returns. I find that both the short and the long term implied volatility have significant negative impact on the aggregate ERP, while at sectoral level the impact is heterogeneous. I find both short and long term volatility is priced negatively indicating that (i) investors care both short and long term market implied volatility (ii) investors are ready to pay for insurance against these risks.

Mestrado em Finanças
Este trabalho tem o objectivo de facilitar a previsão para investidores em mercados financeiros. Embora possa ser usado em acções e futuros de petróleo, o principal objectivo é o mercado cambial, mais especificamente, opções de moeda, extraindo com risco neutro a densidade de probabilidade da função através de uma abordagem paramétrica e não paramétrica. Consequentemente, tal foi aplicado a um caso muito recente, em 2019, entre o dólar Norte americano e a libra inglesa, tornando assim mais atractiva a leitura do comportamento da densidade, especialmente com a saída do Reino unido da União Europeia.
This work has the purpose of easing the forecast for financial market investors. Although it can be used on equities and oil futures, the main aim is the Foreign exchange. More so, it is specialized on currency options, extracting then the closer Risk Neutral Probability Density Function through a parametric approach and a nonparametric approach. Subsequently, this was applied to a very recent case, in 2019, between the United States of America dollar and United Kingdom pound, making it more attractive to assess the behaviour of the density, specially linked to the withdrawal of United Kingdom from the European Union.
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Stocks, Bonds, and Long-Run Consumption Risks. Bansal and Yaron (2004) show that long-run consumption risks and time-varying economic uncertainty in conjunction with recursive preferences can account for important features of equity markets. I bring the model to the term structure of interest rates and show that a calibrated version of the model can simultaneously explain properties of bonds and equities. Specifically, the model accounts for deviations from the expectations hypothesis, the upward sloping nominal yield curve, and the predictive power of the nominal yield spread. However, an estimation of the model using Simulated Method of Moments yields less convincing results and illustrates the difficulty of precisely estimating parameters of the model. Real (nominal) interest rates in the model are positively (negatively) correlated with consumption growth and real stock returns move inversely with inflation. The cyclicality of nominal interest rates and yield spreads is shown to depend on the relative values of the elasticity of intertemporal substitution and the correlation between real consumption growth and inflation. The “Fed-model” and the Changing Correlation of Stock and Bond Returns: An Equilibrium Approach. This paper presents an equilibrium model that provides a rational explanation for two features of data that have been considered puzzling: The positive relation between US dividend yields and nominal interest rates, often called the Fed-model, and the time-varying correlation of US stock and bond returns. Key ingredients are time-varying first and second moments of consumption growth, inflation, and dividend growth in conjunction with Epstein-Zin and Weil recursive preferences. Historically in the US, inflation has signaled low future consumption growth. The representative agent therefore dislikes positive inflation shocks and demands a positive risk premium for holding assets that are poor inflation hedges, such as equity and nominal bonds. As a result, risk premiums on equity and nominal bonds comove positively through their exposure to macroeconomic volatility. This generates a positive correlation between dividend yields and nominal yields and between stock and bond returns. High levels of macro volatility in the late 1970s and early 1980s caused stock and bond returns to comove strongly. The subsequent moderation in aggregate economic risk has brought correlations lower. The model is able to produce correlations that can switch sign by including the covariances between consumption growth, inflation, and dividend growth as state variables. International Bond Risk Premia. We extend Cochrane and Piazzesi (2005, CP) to international bond markets by constructing forecasting factors for bond excess returns across different countries. While the international evidence for predictability is weak using Fama and Bliss (1987) regressions, we document that local CP factors have significant predictive power. We also construct a global CP factor and provide evidence that it predicts bond returns with high R2 across countries. The local and global factors are jointly significant when included as regressors, which suggests that variation in bond excess returns are driven by country-specific factors and a common global factor. Shocks to US bond risk premia seem to be particularly important determinants for international bond premia. Motivated by these results, we estimate a parsimonious no-arbitrage affine term structure model in which risk premia are driven by one local and one global CP factor. We find that international bond risk premia are driven by a local slope factor and a world interest rate level factor.

The diploma thesis deals mostly with interest rate risk issue. It describes the basic methods of interest rate risk measurement with use of analyses executing by Asset Liability Management department in banks. Such analyses as repricing GAP, net interest income analysis, market value of equity and sensitivity analyses to interest rate movements. There is an analysis of Czech crown yield curve as well, in order to deeper insight of its probability behaviour. Results of this analysis are used for advanced techniques in ALM. Especially knowledge of volatilities of particular yield points and theirs relations is used in these methods. There was also a multi equation model for predictions of yield curve development created. One of the variables in the model there is the 2-week repo rate of Czech National Bank included.

2013/2014
The past twenty years have seen a massive proliferation in insurance-linked derivative products. The public, indeed, has become more aware of investment opportunities outside the insurance sector and is increasingly trying to seize all the benefits of equity investment in conjunction with mortality protection. The competition with alternative investment vehicles offered by the financial industry has generated substantial innovation in the design of life products and in the range of benefits provided. In particular, equity-linked policies have become ever more popular, exposing policyholders to financial markets and providing them with different ways to consolidate investment performance over time as well as protection against mortality-related risks. Interesting examples of such contracts are variable annuities (VAs). This kind of policies, first introduced in 1952 in the United States, experienced remarkable growth in Europe, especially during the last decade, characterized by “bearish” financial markets and relatively low interest rates. The success of these contracts is due to the presence of tax incentives, but mainly to the possibility of underwriting several rider benefits that provide protection of the policyholder’s savings for the period before and after retirement. In this thesis, we focus in particular on the Guaranteed Lifetime Withdrawal Benefit (GLWB) rider. This option meets medium to long-term investment needs, while providing adequate hedging against market volatility and longevity-related risks. Indeed, based on an initial capital investment, it guarantees the policyholder a stream of future payments, regardless of the performance of the underlying policy, for his/her whole life. In this work, we propose a valuation model for the policy using tractable financial and stochastic mortality processes in a continuous time framework. We have analyzed the policy considering two points of view, the policyholder’s and the insurer’s, and assuming a static approach, in which policyholders withdraw each year just the guaranteed amount. In particular, we have based ourselves on the model proposed in the paper “Systematic mortality risk: an analysis of guaranteed lifetime withdrawal benefits in variable annuities” by M. C. Fung, K. Ignatieva and M. Sherris (2014), with the aim of generalizing it later on. The valuation, indeed, has been performed in a Black and Scholes economy: the sub-account value has been assumed to follow a geometric Brownian motion, thus with a constant volatility, and the term structure of interest rates has been assumed to be constant. These hypotheses, however, do not reflect the situation of financial markets. In order to consider a more realistic model, we have sought to weaken these misconceptions. Specifically we have taken into account a CIR stochastic process for the term structure of interest rates and a Heston model for the volatility of the underlying account, analyzing their effect on the fair price of the contract. We have addressed these two hypotheses separately at first, and jointly afterwards. As part of our analysis, we have implemented the theoretical model using a Monte Carlo approach. To this end, we have created ad hoc codes based on the programming language MATLAB, exploiting its fast matrix-computation facilities. Sensitivity analyses have been conducted in order to investigate the relation between the fair price of the contract and important financial and demographic factors. Numerical results in the stochastic approach display greater fair fee rates compared to those obtained in the deterministic one. Therefore, a stochastic framework is necessary in order to avoid an underestimation of the policy. The work is organized as follows. Chapter 1. This chapter has an introductory purpose and aims at presenting the basic structures of annuities in general and of variable annuities in particular. We offer an historical review of the development of the VA contracts and describe the embedded guarantees. We examine the main life insurance markets in order to highlight the international developments of VAs and their growth potential. In the last part we retrace the main academic contributions on the topic. Chapter 2. Among the embedded guarantees, we focus in particular on the Guaranteed Lifetime Withdrawal Benefit (GLWB) rider. We analyze a valuation model for the policy basing ourselves on the one proposed by M. Sherris (2014). We introduce the two components of the model: the financial market, on the one hand, and the mortality intensity on the other. We first describe them separately, and subsequently we combine them into the insurance market model. In the second part of the chapter we describe the valuation formula considering the GLWB from two perspectives, the policyholder’s and the insurer’s. Chapter 3. Here we implement the theoretical model creating ad hoc codes with the programming language MATLAB. Our numerical experiments use a Monte Carlo approach: random variables have been simulated by MATLAB high level random number generator, whereas concerning the approximation of expected values, scenario- based averages have been evaluated by exploiting MATLAB fast matrix-computation facilities. Sensitivity analyses are conducted in order to investigate the relation between the fair fee rate and important financial and demographic factors. Chapter 4. The assumption of deterministic interest rates, which can be acceptable for short-term options, is not realistic for medium or long-term contracts such as life insurance products. GLWB contracts are investment vehicles with a long-term horizon and, as such, they are very sensitive to interest rate movements, which are uncertain by nature. A stochastic modeling of the term structure is thus appropriate. In this chapter, therefore, we propose a generalization of the deterministic model allowing interest rates to vary randomly. A Cox-Ingersoll-Ross model is introduced. Sensitivity analyses have been conducted. Chapter 5. Empirical studies of stock price returns show that volatility exhibits “random” characteristics. Consequently, the hypothesis of a constant volatility is rather “counterfactual”. In order to consider a more realistic model, we introduce the stochastic Heston process for the volatility. Sensitivity analyses have been con- ducted. Chapter 6. In this chapter we price the GLWB option considering a stochastic process for both the interest rate and the volatility. We present a numerical comparison with the deterministic model. Chapter 7. Conclusions are drawn. Appendix. This section presents a quick survey of the most fundamental concepts from stochastic calculus that are needed to proceed with the description of the GLWB’s valuation model.
Negli ultimi venti anni si `e assistito ad una massiccia proliferazione di prodotti de- rivati di tipo finanziario-assicurativo. Gli individui, infatti, sono diventati sempre piu` consapevoli delle opportunita` di investimento esistenti al di fuori del settore as- sicurativo e pertanto richiedono all’impresa di assicurazione non solo la protezione contro il rischio di mortalit`a/longevit`a, ma anche tutti i benefici di un investimento di capitali. Ed `e proprio per soddisfare le esigenze del mercato e per fronteggiare la concorrenza alimentata da altri competitors (banche, ecc.) che il mercato assi- curativo sta cambiando ed ha iniziato a sviluppare nuovi prodotti assicurativi ad elevato contenuto finanziario. Nell’ambito di questi prodotti, particolare interesse rivestono le cosiddette polizze variable annuities. Introdotte per la prima volta negli Stati Uniti nel 1952, esse hanno raggiunto ben presto un notevole sviluppo anche in Europa, soprattutto nell’ultimo decennio caratterizzato da mercati finanziari bearish e da tassi di interesse relativamente bassi. Il successo di questo tipo di contratti `e dovuto al favorevole trattamento fiscale di cui godono, ma soprattutto all’offerta di opzioni implicite che garantiscono una protezione dei risparmi degli investitori prima e dopo il pensionamento. In questo lavoro di tesi, ci siamo concentrati in particola- re sull’opzione Guaranteed Lifetime Withdrawal Benefit (GLWB). Essa permette di soddisfare esigenze di investimento di medio/lungo periodo e nello stesso tempo offre una discreta copertura al rischio dovuto alla volatilit`a dei mercati e al longevity risk. Infatti, a fronte di un capitale iniziale investito, garantisce all’assicurato un flusso di pagamenti futuri indipendente dalla performance della polizza sottostante per tutta la durata della sua vita. Piu` precisamente, in questo lavoro proponiamo un modello di valutazione per questo tipo di contratto, facendo ricorso a processi stocastici per descrivere la componente finanziaria e quella legata alla mortalità dell’assicurato. Analizziamo la polizza considerando sia il punto di vista del cliente che quello della compagnia di assicurazione. La nostra valutazione si è basata sul modello proposto da M. C. Fung, K. Ignatieva e M. Sherris nell’articolo “Systematic mortality risk: an analysis of guaranteed lifetime withdrawal benefits in variable annuities” (2014). Tuttavia le ipotesi alla base di questa analisi non trovano giustificazione nel mercato; in effetti, considerare un tasso di interesse ed una volatilità costanti sembra poco sensato. Proprio per proporre un modello più fedele al mercato, si è pensato di indebolire questi assunti, prendendo in considerazione un processo stocastico a sé stante per descrivere la dinamica del tasso di interesse e della volatilità. Dapprima abbiamo analizzato separatamente l’impatto dei due processi sul prezzo equo dell’opzione, per poi considerare anche il loro effetto congiunto. Come parte integrante del lavoro, abbiamo implementato il modello teorico proposto impiegando un approccio Monte Carlo. A questo scopo abbiamo creato codici ad hoc utilizzando il linguaggio di programmazione MATLAB, sfruttando al meglio tutte le sue potenzialità di calcolo matriciale. Sono state condotte analisi di sensitività per analizzare l’impatto sul prezzo equo dell’opzione di alcuni importanti parametri finanziari e demografici. I risultati numerici mostrano come effettivamente l’impiego di un approccio stocastico sia più capace di descrivere le fluttuazioni del mercato e quindi permetta di ottenere risultati più realistici. Il valore equo delle commissioni applicate dalla compagnia di assicurazione per l’attivazione della garanzia GLWB aumenta quando si passa da un approccio deterministico ad uno stocastico (soprattutto se quest’ultimo considera congiuntamente tassi di interesse e volatilità stocastici), rivelando come un adeguato modello stocastico sia necessario per evitare una sottovalutazione di tali polizze. Il lavoro è strutturato come segue: Capitolo 1. Questo capitolo ha un ruolo introduttivo e mira a fornire una descrizione delle caratteristiche principali delle polizze variable annuities. Si analizza l'evoluzione storica di tali polizze ed il loro sviluppo nei principali mercati internazionali. Segue una breve rassegna dei principali contributi accademici sulla valutazione di tali contratti e si spiegano le ragioni alla base di questo lavoro. Capitolo 2. Tra le varie garanzie implicite nei contratti variable annuity ci soffermiamo sull'opzione Guaranteed Lifetime Withdrawal Benefit. In questo capitolo analizziamo il modello di valutazione del contratto proposto da M. Sherris (2014); introduciamo le due componenti del modello (il mercato finanziario e l'intensità di mortalità) dapprima descrivendole separatamente, poi combinandole. Nella seconda parte del capitolo studiamo le formule per il calcolo del prezzo equo del contratto considerando due punti di vista, quello dell'assicurato e quello dell'assicuratore. Capitolo 3. In questo capitolo implementiamo il modello teorico creando codici ad hoc con il linguaggio di programmazione MATLAB. Le nostre valutazioni sono state realizzate utilizzando un approccio Monte Carlo. Diverse analisi di sensitività sono state condotte per analizzare l’impatto sul prezzo equo dell’opzione di alcuni importanti parametri finanziari e demografici. Capitolo 4. In questo capitolo si propone una generalizzazione del modello deterministico indebolendo l'ipotesi di struttura a termine dei tassi di interesse costante. Per descrivere la dinamica del tasso di interesse si introduce in particolare un processo Cox- Ingersoll- Ross. Capitolo 5. In questo capitolo si indebolisce l'ipotesi che considera costante la volatilità del fondo d'investimento prevedendo una dinamica descritta dal processo di Heston. Capitolo 6. Si descrive un modello che considera congiuntamente un processo stocastico per i tassi di interesse (CIR) e per la volatilità (Heston). Si conducono analisi di sensitività e si mostrano i risultati ottenuti. Capitolo 7. In questo capitolo traiamo le conclusioni del nostro lavoro. Appendice. Proponiamo una breve rassegna delle principali nozioni di calcolo stocastico necessarie per meglio comprendere la descrizione del modello di valutazione.
XXVII Ciclo
1986

The globilisation phenomena is causing an increasing interaction between different markets and sectors. This has led to the evolution of derivative instruments from ”single asset” instruments to complex derivatives that have underlying assets from different markets, sectors and sub-sectors. These are the so-called hybrid products that have multi-assets as underlying instruments. This article focuses on interest rate hybrid products. In this article an analysis of the application of stochastic interest rate models and stochastic volatility models in pricing and hedging interest rate hybrid products will be explored.

In this thesis, we consider some two-factor short rate models that incorporate stochastic volatility with jumps. The motivation for studying such kinds of model is to overcome the shortcomings of di usion-based stochastic models and to provide a more accurate description of the empirical characteristics of the short rates. In our rst model, a jump process for the short-rate volatility is described with jump times generated by a Poisson process and with jump sizes following exponential distribution. Secondly, we extend the volatility model further by taking a superposition of two independent jump processes. We present the corresponding Markov chain Monte Carlo estimation algorithm and provide estimation results of candidate model parameters, latent volatility processes and the jump processes using the 3- month U.S. Treasury Bill rates. Finally, we apply our models to price fixed-income products through Monte Carlo simulation.

This thesis analyses the link between interest rate risk faced by financial intermediaries in the G-10 countries, their balance sheet composition and national bank regulation. The regulatory authorities both in the US and in Europe increasingly emphasise the issue of bank interest rate exposure. The importance of this topic is also reasserted by recent developments in the monetary environment. The thesis offers three major contributions to the area. First, it empirically investigates the interest rate risk exposure of financial intermediaries across a large international data sample over the 1997 to 2009 time period. The results verify the importance of interest rate exposure for the majority of analysed institutions, with statistical inferences being robust to the choice of interest rate proxy, time period, and the adopted econometric methodology. Second, this research examines the underlying determinants of bank interest rate risk. Both company and market specific information is considered in the analysis. The findings suggest that national regulatory and supervisory characteristics, and notably international diversity among these provisions, are as important as firm-level accounting variables in explaining the interest rate exposures of individual banks. Finally, this work empirically addresses the impact of securitization on bank interest rate risk. In particular, the research questions whether securitization is conducive to the optimal hedging of bank interest rate risk, or is merely a funding source enabling these companies to pursue more profitable but riskier projects. The reported results imply that banks resorting to asset securitization do not, on average, achieve an unambiguous reduction in their exposure to the term structure developments.

Dans le Chapitre 1, nous présentons une nouvelle approche pour évaluer des options dites à barrières basée sur une méthode connue sous le nom de méthode Vanna-Volga. Cette nouvelle méthode nous permet une calibration simple et rapide sur le marché des options à barrières directement ce qui permet d'évaluer ces options avec un outil en accord avec le marché. Nous comparons également nos résultats avec ceux provenant d’autres modèles célèbres et nous étudions la sensibilité de cette méthode par rapport aux données du marché. Nous donnons une nouvelle justification théorique associée à la méthode Vanna-Volga comme étant une approximation de Taylor du premier ordre du prix de l'option autour de la volatilité dite à la monnaie.

Dans le Chapitre 2 de la thèse nous allons développer un modèle qui compte de la volatilité implicite du marché et de la variabilité des taux d'intérêts. Nous travaillons dans le marché particulier des taux de changes, avec un modèle à volatilité locale pour la dynamique du taux de change dans lequel les taux d'intérêts domestiques et étrangers sont également supposé stochastiques. Nous dérivons l'expression de la volatilité locale et dérivons divers résultats particulièrement utiles pour la calibration du modèle. Finalement, nous développons un nouveau modèle hybride où la volatilité du taux de change possède une composante locale et une composante stochastique et nous dérivons une méthode de calibration pour ce nouveau modèle.

Dans le Chapitre 3, nous allons appliquer le modèle à volatilité locale et taux d'intérêts stochastiques développé dans le précédent chapitre mais dans le cadre d'évaluation de produits dérivés associés aux assurances vie. Nous utilisons une méthode de calibration développée dans le Chapitre 2. Les produits étudiés étant exotiques, nous allons également comparer les prix obtenus dans différents modèles, à savoir le modèle à volatilité locale, à volatilité stochastique et enfin à volatilité constante pour le sous-jacent, les trois modèles étant combinés avec des taux d'intérêts stochastiques.

Finalement, dans le Chapitre 4 nous allons travailler avec un modèle dit de Lévy pour modéliser le sous-jacent. Nous nous intéressons à l'évaluation d'options Asiatiques arithmétiques. Comme de nombreuses options exotiques, il n'est pas possible d'obtenir un prix analytique et dans ce cas seules les méthodes numériques permettent de résoudre le problème. Dans ce Chapitre 4, nous développons une méthode basée sur la méthode de simulations de Monte Carlo et nous employons deux types de variables de contrôle permettant d'améliorer la convergence du programme. Nous développons également une méthode permettant d'obtenir une borne inférieure au prix de l'option avec une efficacité qui surpasse les autres méthodes.

Doctorat en Sciences
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Mestrado em Economia Monetária e Financeira
It's usually accepted that financial asset prices reflect market participants' expectations concerning the evolution of certain important economic and financial variables. In comparison with the majority of the other financial assets, in particular against the futures or forwards, option prices have an additional interest resulting from their ability to provide information, not only in terms of the expected future value of an asset, but also about the higher moments of the probability distribution perceived by economic agents. Regarding the relationship among option prices and their strike prices it's possible to estimate the risk-neutral probability density function (RNPDF), which allow us to characterise almost completely, market expectations regarding the price of the underlying asset at the maturity date of the option. In the Black-Sholes framework, RNPDF estimation would be a trivial issue only consisting in implied volatility estimation. However, the systematic differences observed between theoretical model prices and those observed in the market, raise some suspicions about the reality adjustment of some of its premises, namely the lognormality for the underlying price distribution and the constant volatility assumed across the time and different strike prices. In this work, a set of alternative approaches for the RNPDF estimation is presented, along with its advantages and drawbacks, as a way to characterise the current state of the art. Using EURIBOR 3-month interest rate future option prices, and considering a mixture of lognormal distributions, we estimate RNPDF for some days around ECB Council meetings, in order to analyse market views about possible changes in ECB reference interest rates in these meetings. We also study the impact in market expectations, regarding the evolution of shorter-term interest rates, from the events that occurred in the USA on the 11th of September 2001, and the "time-to-maturity" effect on RNPDF volatility.
É geralmente aceite que os preços dos activos financeiros reflectem as expectativas dos participantes nos mercados. Face à maioria dos activos financeiros, em particular aos futuros ou "forwards", os preços das opções possuem um interesse adicional oriundo da capacidade que têm de fornecer informação relativa, não só, ao valor médio esperado pelo mercado para o preço futuro do activo subjacente, mas também, sobre os momentos de ordem mais elevada da distribuição de probabilidade percepcionada pelos agentes económicos. Com base na relação entre os preços das opções e respectivos preços de exercício é possível estimar a função de densidade de probabilidade neutra ao risco (FDPNR) que permite caracterizar, de uma forma quase completa, o perfil de expectativas dos agentes relativamente ao preço do activo subjacente na maturidade opção. No universo do modelo Black-Sholes, a estimação da FDPNR seria um assunto trivial consistindo apenas na estimação da volatilidade implícita. Porém, as diferenças sistemáticas observadas, entre os preços gerados pelo modelo e os observados no mercado, levantam a suspeita que algumas das suas hipóteses são pouco realísticas, nomeadamente a lognormalidade para a distribuição do preço do activo subjacente e a volatilidade constante assumida para os diferentes preços de exercício e ao longo do tempo. Neste trabalho é apresentado um conjunto de abordagens alternativas para a estimação de FDPNR, suas vantagens e desvantagens relativas, procurando-se caracterizar o actual estado da arte. Recorrendo aos preços de opções sobre futuros da taxa de juro EURIBOR a três meses e com base numa mistura de distribuições lognormais, estimamos as FDPNR para algumas datas em torno das reuniões do Conselho do BCE, utilizando-as na análise das expectativas do mercado relativamente a possíveis alterações das taxas de juro directoras nessas reuniões. Analisamos ainda o impacto nas expectativas dos agentes, relativamente à evolução das taxas de juro, dos acontecimentos ocorridos nos EUA, em 11 de Setembro de 2001 e o efeito "time-to-maturity" na volatilidade das FDPNR.

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Com o objetivo de analisar o impacto na Estrutura a Termos de Volatilidade (ETV) das taxas de juros utilizando dois diferentes modelos na estimação da Estrutura a Termo das Taxas de Juros (ETTJ) e a suposição em relação a estrutura heterocedástica dos erros (MQO e MQG ponderado pela duration), a técnica procede em estimar a ETV utilizando-se da volatilidade histórica por desvio padrão e pelo modelo auto-regressivo Exponentially Weighted Moving Average (EWMA). Por meio do teste de backtesting proposto por Kupiec para o VaR paramétrico obtido com as volatilidades das ETV´s estimadas, concluí-se que há uma grande diferença na aderência que dependem da combinação dos modelos utilizados para as ETV´s. Além disso, há diferenças estatisticamente significantes entre as ETV´s estimadas em todo os pontos da curva, particularmente maiores no curto prazo (até 1 ano) e nos prazos mais longos (acima de 10 anos).
For the purpose of analyzing the impact in Volatility Term Structure (VTS) of interest rate using two different models in the estimation of the Term Structure of Interest Rates (TSIR) and the assumption regarding the heterocedastic structure of errors (OLS and GLS weighted by duration), the technique proceeds in estimating the VTS using the historical volatility by the standard deviation and autoregressive model Exponentially Weighted Moving Average (EWMA). Through the backtesting test proposed by Kupiec for parametric VaR obtained with the volatilities of VTS’s estimate, conclude that there is a big difference in adherence that depend on the combination of the models used for VTS’s. In addition, there is statistically significant differences between the VTS’s estimated around the points of the curve, specially higher in the short term (less than 1 year) and long term (over 10 years).

This thesis studies the pricing of Treasury bonds, the pricing of corporate bonds and the modelling of portfolios of defaultable debt. By drawing on the related literature, Chapter 1 provides economic background and motivation for the study of each of these topics. Chapter 2 studies the use of Gaussian affine dynamic term structure models (GDTSMs) for forming forecasts of Treasury yields and conditional decompositions of the yield curve into expectation and risk premium components. Specifically, it proposes market prices of risk that can generate bond price time series that are consistent with the important empirical result of Cochrane and Piazzesi (2005), that a linear combination of forward rates can forecast excess returns to bonds. Since the GDTSM here falls into the essentially affine class (Duffee (2002)), it is analytically tractable. Chapter 3 studies conditional risk premia in a commonly applied default intensity based model for pricing corporate bonds. Here, I refer to such models as completely affine defaultable dynamic term structure models (DDTSMs). There are two main contributions. First, I show that completely affine DDTSMs imply that the compensation for the risk associated with shocks to default intensities (the credit spread risk premium) is related to the volatility of default intensities. Second, I run regressions to show that this relationship holds in a set of corporate bond data. Finally, Chapter 4 proposes a new dynamic model for default rates in large debt port- folios. The model is similar in principle to Duffie, Saita, and Wang (2007) and Duffie, Eckner, Horel, and Saita (2009) in that the default intensity depends on the observed macroeconomic state and unobserved frailty variables. However, the model is designed for use with more commonly available aggregate, rather than individual, default data. Fitting the model to aggregate charge-off rates in US corporate, real-estate and non- mortgage retail sectors, it is found that interest rates, industrial production and unemployment rates have quantitatively plausible effects on aggregate default rates.

The technological development of recent years has allowed a revolution in the financial sector with the introduction of new financing methods including Peer to Peer Lending. In this study it will be discussed the business model of Prosper, which is a Peer to Peer Lending platform that aims to facilitate the connection between borrowers and creditors by implementing the disintermediation process. To get a general idea of the theme that will be discussed later, the most discussed topics in recent literature regarding P2P platforms have been reported. In particular, it will be analysed the topics of the relationship with the banks, the importance of the information related to the users of the platform, the credit risk and the interest rate. Subsequently, the Prosper database will be studied in order to understand the real advantages of this platform. In particular, from the data provided by Prosper will be studied the various information concerning the borrowers and creditors. Then, the loans provided by the platform will be examined, and the risk adjusted interest rate will be calculated from their interest rate and credit risk. The objective of this document is to determine the adequacy of the interest rates proposed by Prosper and to establish the variables that influence them.

I study, develop and implement selected interest rate models. I begin with a simple categorization of interest rate models and with an explanation why interest rate models are useful. I explain and discuss the notion of arbitrage. I use Oldrich Vasicek's seminal model (Vasicek; 1977) to develop the idea of no-arbitrage term structure modeling. I introduce both the partial di erential equation and the risk-neutral approach to zero-coupon bond pricing. I briefly comment on affine term structure models, a general equilibrium term structure model, and HJM framework. I present the Czech Treasury yield curve estimates at a daily frequency from 1999 to the present. I use the parsimonious Nelson-Siegel model (Nelson and Siegel; 1987), for which I suggest a parameter restriction that avoids abrupt changes in parameter estimates and thus allows for the economic interpretation of the model to hold. The Nelson-Siegel model is shown to fit the Czech bond price data well without being over-parameterized. Thus, the model provides an accurate and consistent picture of the Czech Treasury yield curve evolution. The estimated parameters can be used to calculate spot rates and hence par rates, forward rates or discount function for practically any maturity. To my knowledge, consistent time series of spot rates are not available for the Czech economy. I introduce two estimation techniques of the short-rate process. I begin with the maximum likelihood estimator of a square root diff usion. A square root di usion serves as the short rate process in the famous CIR model (Cox, Ingersoll and Ross; 1985b). I develop and analyze two Matlab implementations of the estimation routine and test them on a three-month PRIBOR time series. A square root diff usion is a restricted version of, so called, CKLS di ffusion (Chan, Karolyi, Longsta and Sanders; 1992). I use the CKLS short-rate process to introduce the General Method of Moments as the second estimation technique. I discuss the numerical implementation of this method. I show the importance of the estimator of the GMM weighting matrix and question the famous empirical result about the volatility speci cation of the short-rate process. Finally, I develop a novel yield curve model, which is based on principal component analysis and nonlinear stochastic di erential equations. The model, which is not a no-arbitrage model, can be used in areas, where quantification of interest rate dynamics is needed. Examples, of such areas, are interest rate risk management, or the pro tability and risk evaluation of interest rate contingent claims, or di erent investment strategies. The model is validated by Monte Carlo simulations.

This thesis studies the estimation of credit exposure arising from a portfolio of interest rate derivatives. The estimation is performed using a Monte Carlo simulation. The results are compared to the exposure obtained under the current exposure method provided by the Bank for International Settlements (BIS). We show that the simulation method provides a much richer set of information for credit risk managers. Also, depending on the current exposure and the nature of the transactions, the BIS method can fail to account for potential exposure. All test portfolios benefit significantly from a netting agreement, but the BIS approach tends to overestimate the risk reduction due to netting. In addition we examine the impact of antithetic variates and different time-discretizations. We find that a discretization based on derivatives' start and maturity dates may reduce simulation time significantly without loosing generality in exposure profiles. Antithetic variates have a small effect.

Cette thèse traite de plusieurs sujets en mathématiques financières: risque de crédit, optimisation de portefeuille et modélisation des taux d’intérêts. Le chapitre 1 consiste en trois études dans le domaine du risque de crédit. La plus innovante est la première dans laquel nous construisons un modèle tel que la propriété d’immersion n’est vérifiée sous aucune mesure martingale équivalente. Le chapitre 2 étudie le problème de maximisation de la somme d’une utilité de la richesse terminale et d’une utilité de la consommation. Le chapitre 3 étudie l’évaluation des produits dérivés de taux d’intérêt dans un cadre multicourbe, qui prend en compte la différence entre une courbe de taux sans risque et des courbes de taux Libor de différents tenors
This thesis deals with several topics in mathematical finance: credit risk, portfolio optimization and interest rate modeling. Chapter 1 consists of three studies in the field of credit risk. The most innovative is the first one, where we construct a model such that the immersion property does not hold under any equivalent martingale measure. Chapter 2 studies the problem of maximization of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where a sudden jump in the risk-free interest rate induces market incompleteness. Chapter 3 studies the valuation of Libor interest rate derivatives in a multiple-curve setup, which accounts for the spreads between a risk-free discount curve and Libor curves of different tenors

In the aftermath of the financial crisis of 2008, regulatory authorities have implemented stricter policies to ensure more prudent risk management practices among banks. Despite the growing importance of demand deposits for banks, no policies for how to adequately account for the inherent interest rate risk have been introduced. Demand deposits are associated with two sources of uncertainties which make it difficult to assess its risks using standardized models: they lack a predetermined maturity and the deposit rate may be changed at the bank’s discretion. In light of this gap, this study aims to empirically investigate the modeling of the valuation and interest rate risk of demand deposits with two different frameworks: the Economic Value Model Framework (EVM) and the Replicating Portfolio Model Framework (RPM). To analyze the two frameworks, models for the demand deposit rate and demand deposit volume are developed using a comprehensive and novel dataset provided by one the biggest commercial banks in Sweden. The findings indicate that including macroeconomic variables in the modeling of the deposit rate and deposit volume do not improve the modeling accuracy. This is in contrast to what has been suggested by previous studies. The findings also indicate that there are modeling differences between demand deposit categories. Finally, the EVM is found to produce interest rate risks with less variability compared to the RPM.
Till foljd av nanskrisen 2008 har regulatoriska myndigheter infort mer strikta regelverk for att framja en sund nansiell riskhantering hos banker. Trots avistakontons okade betydelse for banker har inga regulatoriska riktlinjer introducerats for hur den associerade ranterisken ska hanteras ur ett riskperspektiv. Avistakonton ar forknippade med tva faktorer som forsvarar utvarderingen av dess ranterisk med traditionella ranteriskmetoder: de saknar en forutbestamd loptid och avistarantan kan andras nar sa banken onskar. Med hansyn till detta gap fokuserar denna studie pa att empiriskt analysera tva modelleringsramverk for att vardera och mata ranterisken hos avistakonton: Economic Value Model Framework (EVM) and Replicating Portfolio Model Framework (RPM). Analysen genomfors genom att initialt ta fram modeller for hur avistarantan och volymen pa avistakonton utvecklas over tid med hjalp av ett modernt och unikt dataset fran en av Sveriges storsta kommersiella banker. Studiens resultat indikerar att modellerna for avistarantan och avistavolymen inte forbattras nar makroekonomiska variabler ar inkluderade. Detta ar i kontrast till vad tidigare studier har oreslagit. Vidare visar studiens resultat att det modellerna skiljer sig nar avistakontona ar egmenterade pa en mer granular niva. Slutligen pavisar resultatet att EVM producerar ranteriskestimat som ar mindre kansliga for antanganden an RPM.

Financial institutions are exposed to several different types of risk. One of the risks that can have a significant impact is the interest rate risk in the bank book (IRRBB). In 2018, the European Banking Authority (EBA) released a regulation on IRRBB to ensure that institutions make adequate risk calculations. This article proposes an IRRBB model that follows EBA's regulations. Among other things, this framework contains a deterministic stress test of the risk-free yield curve, in addition to this, two different types of stochastic stress tests of the yield curve were made. The results show that the deterministic stress tests give the highest risk, but that the outcomes are considered less likely to occur compared to the outcomes generated by the stochastic models. It is also demonstrated that EBA's proposal for a stress model could be better adapted to the low interest rate environment that we experience now. Furthermore, a discussion is held on the need for a more standardized framework to clarify, both for the institutions themselves and the supervisory authorities, the risks that institutes are exposed to.
Finansiella institutioner är exponerade mot flera olika typer av risker. En av de risker som kan ha en stor påverkan är ränterisk i bankboken (IRRBB). 2018 släppte European Banking Authority (EBA) ett regelverk gällande IRRBB som ska se till att institutioner gör tillräckliga riskberäkningar. Detta papper föreslår en IRRBB modell som följer EBAs regelverk. Detta regelverk innehåller bland annat ett deterministiskt stresstest av den riskfria avkastningskurvan, utöver detta så gjordes två olika typer av stokastiska stresstest av avkastningskurvan. Resultatet visar att de deterministiska stresstesten ger högst riskutslag men att utfallen anses vara mindre sannolika att inträffa jämfört med utfallen som de stokastiska modellera genererade. Det påvisas även att EBAs förslag på stressmodell skulle kunna anpassas bättre mot den lågräntemiljö som vi för tillfället befinner oss i. Vidare förs en diskussion gällande ett behov av ett mer standardiserat ramverk för att tydliggöra, både för institutioner själva och samt övervakande myndigheter, vilka risker institutioner utsätts för.

This paper examines how the level and volatility of interest rates affect the stock return of banks using a GARCH-M model. Data is collected for Swedish and Danish banks stock return and interest rates on monthly basis for the period January 2000 to April 2018. The effects of interest rates on banks stock return is tested by two hypotheses, if the volatility of interest rates affects the volatility of the stock returns and if the level of the interest rate affects the excess return. The excess returns are also tested for significance of its own conditional variance in form of the mean term in the GARCH-M model. The results show that the volatility of interest rates has a significant effect on the excess return of the bank stocks while the level of the interest rate does not have a significant effect, the mean term is not significant, implying that some of the risk is not priced by an increased risk premium. The paper also discusses how the quantitative easing activities that has been performed by central banks could affect the bank stocks sensitivity to interest rates changes.

Mestrado em Actuarial Science
Desde a crise financeira de 2008, fundos de pensões começaram a reconhecer, mais do que nunca, a necessidade de se protegerem contra o risco da taxa de juro. Este risco é o mais significativo e volátil para os fundos de pensões pois uma mudança nas condições do mercado pode ter um grande impacto tanto nos ativos como nos passivos do fundo, afetando o seu nível de financiamento. Estratégias de remoção do risco são críticas à luz dos planos de benefícios definidos (BD) estarem cada vez mais insustentáveis. Fundos de pensões estão a considerar várias estratégias de remoção do risco e a reavaliar as suas estratégias de investimento com o objetivo de garantirem, com elevado nível de confiança, os pagamentos aos seus participantes e beneficiários. Este relatório irá discutir como é que planos BD são afetados pelo risco da taxa de juro, como é que esse risco é refletido no relatório da avaliação e que estratégias e ferramentas são usadas para mitigar este risco. Este relatório é o resultado de um de um estágio de cinco meses na Willis Towers Watson. O foco do estágio foi em avaliações de fundos de pensões do Reino Unido em que eu trabalhei nos cálculos do passivo e na análise dos resultados apresentados no relatório da avaliação. O estágio providenciou-me a oportunidade de aplicar o conhecimento atuarial que desenvolvi durante o Mestrado num ambiente empresarial.
Since the financial crisis of 2008, pension schemes began recognizing more than ever that they need to protect against interest rate risk. Interest rate risk is the most significant and volatile risk to pension schemes because a change in market conditions can have a big impact on both the assets and the liabilities of the pension scheme, affecting the funding level of the scheme. De-risking strategies are critical in light of defined benefit pension schemes becoming increasingly unsustainable. Pension schemes are putting many de-risking strategies into place and reevaluating their investment strategies to get to a position to reliably pay their members. This paper discusses how DB pension schemes are affected by interest rate risk, how the risk is reflected in the actuarial valuation report, and what strategies and tools are used to mitigate interest rate risk. This paper is the result of my five-month curricular internship at Willis Towers Watson. The focus of the internship was UK pension scheme valuations in which I worked with the liability calculations and analysis associated with the actuarial valuation report. The internship gave me the opportunity to apply the actuarial knowledge that I developed in the master to a real work environment. In this paper I show an example of one client who uses de-risking strategies against interest rate risk.
info:eu-repo/semantics/publishedVersion

Syfte: Syftet är att undersöka svenska storföretags användande av derivatet ränteswap (svensk benämning för interest rate swap) för år 2012 och 2013 samt att undersöka skillnader utifrån tidigare funna bakomliggande faktorer mellan företag som använder olika typer av ränteswaps och företag som inte använder ränteswap. Metod: Studien tillämpade en empirisk totalundersökning gällande de icke-finansiella företagen noterade på Nasdaq OMX Stockholm Large Cap för slutet på år 2012 respektive år 2013. Utifrån företagens årsredovisningar kategoriserades företagen i fyra grupper baserat på företagets användande av ränteswap. Fem tidigare funna bakomliggande faktorer för användandet av ränteswap sammanställdes genomsnittligt per kategori och jämfördes därefter kategorierna emellan. Resultat: Av de största noterade börsföretagen använde 29 av 40 stycken företag ränteswap år 2012 och 29 av 42 företag år 2013. Företag som använde rörlig ränteswap var signifikant större än de företag som inte använde ränteswap för år 2012 och 2013. År 2013 hade de företag som använde fast och båda typer av ränteswaps högre andel kortfristiga lån i jämförelse med de företag som inte använde ränteswap. Uppmätta skillnader kategorierna emellan för de resterande tre undersökta faktorerna; andel långfristiga lån, löptiden på företagens lån liksom företagens förväntade obeståndskostnader var inte signifikanta vilket innebar att de uppmätta skillnaderna inte kunde hänföras till svenska storföretag. Slutsatser: Över två tredjedelar av de undersökta företagen använde ränteswap. Storleken för företag som använde ränteswap var en urskiljande faktor i jämförelse med företag som inte använde ränteswap. För svenska storföretags andel kortfristiga lån för ett av de undersökta åren talar det mesta för att företag som använde ränteswap hade högre andel kortfristiga lån än företag som inte använde ränteswap. Skillnader i andel långfristiga lån, löptid på lån liksom förväntade obeståndskostnader kategorierna emellan kunde inte hänföras till svenska storföretag och därmed inte ses som urskiljande faktorer för användande av ränteswap.
Purpose: The purpose is to investigate the largest Swedish companies utilization of interest rate swap (afterwards referred to as IRS), as well as variations in the underlying factors between companies who use IRS and companies who do not. Methodology: The study applied an empirical investigation about the non-financial companies noted on Nasdaq OMX Stockholm Large Cap for the end of year 2012 and year 2013. By their annual reports, companies where divided into four categories based on their usage of IRS. Five earlier factors for the use of IRS were compiled per category and were then compared between the categories. Findings: 29 out of the 40 largest listed companies used IRS 2012, and 29 out of 42 companies 2013. The companies who used variable IRS were significantly larger than the ones who didn't use IRS. Companies who used fixed, and both types of IRS year 2013, had a higher proportion of short-term loans compared to the companies which didn't use IRS. Measured differences between the categories for the remaining three factors; proportion of long-term loans, duration on the companies loans as well as their expected distress costs was not significant which implicates that the measured differences could not be assigned to Swedish corporations. Conclusions: Over two thirds of the investigated companies used IRS. The size of the companies that used IRS was a factor which differed between companies who used IRS and the companies that didn't. The proportion of short-term loans showed a significant disparity for one of the investigated years indicated that the companies who used IRS have a larger proportion of short-term loans than the ones who don't. Differences in the proportion of long-term loans, duration on loans and expected distress costs between the categories could not be assigned to Swedish corporations.

In this companion paper to Broll and Mukherjee (2017), we empirically analyse how exchange rate volatilities affect firms optimal production and exporting decisions. The firms elasticity of risk aversion determines the direction of the impact of exchange rate risk on exports. Based on a flexible utility function that incorporates all possible risk preferences, a unique structurally estimable equation is used to estimate the risk aversion elasticities for a panel of Indian service sector (non-financial) firms over 2004-2015, using the quantile regression method.

Starting from basic financial mathematics, we cover the mathematics of pricing swaptions, options on interest rate swaps. We then continue to the topic of obtaining an approximately pure volatility exposure. This exposure to volatility, which in practice enables us to trade volatility according to our perceptions of the market, is obtained by buying or selling swaptions and appropriate amounts of the underlying interest rate swap contract. Taking offsetting positions in the underlying contract is called hedging and is covered in depth. We note that hedging can primarily be done in two ways, and discuss the advantages and disadvantages of each of them. After deriving the value formulas for such a swaption strategy aimed at isolating volatility exposure we end with a discussion on the transition from theory to practice.We find that this way of trading volatility is conceptually simple, but that pre-trade profitability analysis is difficult due to the sometimes poor availability of the sophisticated data needed to simulate such a swaption strategy. Despite the possible limitations in the data necessary to translate this theory into an experimental setup, this thesis serves as a good basis for further research on the profitability of a volatility trading strategy using interest rate swaptions.

Fixed income markets are vast markets, involving a large number of actors including financial institutions, state actors, asset managers and corporations. An import part of these markets are contracts written on the xIBOR rates. This report is concerned with the trying to provide prices for options written on these rates, in particular for swaptions that are not at-the-money (atm) utilizing prices in the cap market. Different methods have been suggested in the literature for solving this problem. In particular we study the method suggested by Hagan et al where one calibrates a SABR model to the caplet surface with the same expiry as the swaption. One then assumes that the swaption contract with the same expiry follows the same SABR dynamics as the caplet, but with a recalibrated initial volatility to fit the atm point. We also study the approach suggested by Rebonato and Jäckel. They derive a model for swaption prices based on the individual volatilities of the forward rates that the underlying interest rate swap consists of, as well as the correlation between the forward rates.  Both of these approaches are studied empirically for the STIBOR market. The data set span between 2016 and 2021 and consists of the yield curve, flat cap volatilities and swaption volatilities. We use the 1Y1Y and 5Y5Y swaption surfaces, where the prices are not only quoted atm, to verify our model. We conclude that despite the SABR model being able to fit the caplet prices well, the method suggested by Hagan does not capture the swaption smile. The Rebonato and Jäckel approach also falls short of capturing the smile and produces similar results as the Hagan et al method. This is suggested to be due to the Hagan method capturing the caplet smile well, and the constant correlation assumption made in this thesis.

In this thesis we establish a relationship between the Potential Approach to interest rates and the Market Models. This relationship allows us to derive the dynamics of forward LIBOR rates and forward swap rates by modelling the state price density. It means that we are able to secure the arbitrage-free condition and positive interest rate feature when we model the volatility drifts of those dynamics. On the other hand, we develop the Potential Approach, particularly the Hughston-Rafailidis Chaotic Interest Rate Model. The early argument enables us to infer that the Chaos Models belong to the Stochastic Volatility Market Models. In particular, we propose One-variable Chaos Models with the application of exponential polynomials. This maintains the generality of the Chaos Models and performs well for yield curves comparing with the Nelson-Siegel Form and the Svensson Form. Moreover, we calibrate the One-variable Chaos Model to European Caplets and European Swaptions. We show that the One-variable Chaos Models can reproduce the humped shape of the term structure of caplet volatility and also the volatility smile/skew curve. The calibration errors are small compared with the Lognormal Forward LIBOR Model, the SABR Model, traditional Short Rate Models, and other models under the Potential Approach. After the calibration, we introduce some new interest rate models under the Potential Approach. In particular, we suggest a new framework where the volatility drifts can be indirectly modelled from the short rate via the state price density.

博士
國立中山大學
財務管理學系研究所
99
This dissertation investigates the volatility of the relationships between exchange rates and interest rates. The first part of the paper explores the transmission relationship between these two markets using a time-series model. Previous studies have assumed that covariance was constant in both markets. However, if the volatilities of the exchange rate and interest rate markets are correlated over time, the interaction and spillover effects between the two markets may be affected by time-varying covariance. Hence, this paper utilizes the BEKK-GARCH model developed by Engle and Kroner (1995) to capture the dynamic relationship between the exchange rates and interest rates. This study uses the returns data for G7 members’ exchange rates and interest rates to test whether these markets exhibited volatilities spillover from 1978 to 2009. The results show bi-directional volatility spillovers in the markets of the UK, the Euro countries, and Canada, where the volatilities of the two markets were interrelated. The second part of the paper explores the relationship between exchange rates and interest rates using a jump diffusion model. Previous studies assumed that the dynamic processes of exchange rates and interest rates follow a diffusion process with a continuous time path, but an increasing number of empirical studies have shown that a continuous diffusion stochastic model does not capture the dynamic process of these variables. Thus, this paper investigates the discontinuous variables of exchange rates and interest rates and assumes that these variables follow a jump diffusion process. The UIRP model is employed to explore the relationship between both variables and to divide the systematic risk into systematic continuous risk and systematic jump risk. The returns data for G7 members’ exchange rates and interest rates from 2005 to 2010 were analyzed to test whether the expected exchange rate is affected by jump components when the interest rate market experiences a jump. The results show that the jump diffusion model has more explanatory power than the pure diffusion model does, and, when the interest rate market experiences a jump risk, the systematic jump risk has a significant relationship with the expected exchange rates in some G7 countries.

碩士
東吳大學
財務工程與精算數學系
102
The Basel III Accord will counterparty credit risk (CCR) to adjust the value called credit valuation adjustment (CVA). Recent literatures suggest that investor and counterparty may default, and therefore the bilateral counterparty credit risk (BCCR) is proposed. Under the base of BCCR, the adjustment to the net present value is called bilateral credit valuation adjustment (BCVA). This article consider a constant elasticity of variance (CEV) of the LM model which is proposed by Andersen and Andreasen (2000), and is called CEV-LM model. In this article, the value of the credit valuation adjustment for IRS with bilateral counterparty credit risk in the CEV-LM model. The situational analysis, default correlation, different contract maturities and the beginning of the volatility will affect bilateral credit valuation adjustment for interest rate swap. However, when the beginning of the volatility about the same, bilateral credit valuation adjustment for interest rate swap in different local volatility model is not affected.

碩士
國立臺灣科技大學
財務金融研究所
103
The paper develops a stochastic interest rate and volatility model. The short rates follow CIR model and the volatility of exchange rate follow Heston model. Discuss the pricing and the risk value of foreign currency derivative on the stochastic model. With the case study, the Chunghwa Telecom Co. event occurred 4 billion Taiwan dollars unrealized loss in 2008. We will discuss in the perspective of Chunghwa Telecom Co. and try to find a better way to hedge foreign exchange rate. Because of the flexibility to adjust the conditions of contract, we provide some way to change the conditions of contract. However, we also advise to buy forward for hedge. Then, use Monte-Carlo method to evaluate the value and the risk of all the contract. Compare each value and risk of contract. The model we use is more difficult to estimate the parameters, but the results have shown that stochastic volatility model will facilitate the evaluation of foreign exchange option. The condition of contract change to reduce the down side risk will help to gain the value of contract.

The main objective of the study was to determine the exchange rate volatility regime for carry trade profitability when using the South African Rand as the target currency. The study used the Logistic Smooth Transition Regression (LSTR) model to test the uncovered interest rate parity (UIP). The Sharpe ratio and the risk adjusted forward premium were used as the transition variables. The transition variable is a function of the transition function, which is used to determine the regime for the UIP. The LSTR model is characterised by three regimes, i.e. the lower regime, the middle regime and the upper regime. The LSTR model was tested for the short-term forward rate maturity of less than one year. The results show that the UIP hypothesis holds in the middle regime for the Rand/USD and the Rand/GBP when using the Sharpe ratio as the transition variable. Meanwhile, the UIP hypothesis does not hold for the Rand/Yen when using the Sharpe ratio as the transition variable for the forward rate maturity of one month, and it does hold for other short-term forward rate maturity of less than one year. The results for the risk adjusted forward premium as the transition variable show that the UIP hypothesis does not hold for all three currencies at various short-term forward rate maturities of less than one year. The research provides the following contributions to new knowledge: (1) Uncovered interest parity hypothesis holds in the middle regime for all periods for the Rand/USD and the Rand/GBP when using the Sharpe ratio as the transition variable with a short-term forward rate maturity of less than one year. (2) Currency carry trade profit taking for the Rand/USD and the Rand/GBP can be achieved in the upper regime. (3) The results for the Rand/Yen are mixed, in that the UIP hypothesis does not hold for other crisis periods as a result of negative Sharpe ratios. However, for the calm periods, UIP hypothesis holds in the middle regime for the Rand/Yen for short-term forward rate maturity of more than one month but less than one year when using the Sharpe ratio as the transition variable. The overall contribution of this study is that for the South African Rand as the target currency, the UIP hypothesis holds for the short-term horizon when using the Sharpe ratio as the transition variable and that this mostly depends more on currency than on horizon. Contrary to other researchers who found that the UIP holds in the long-term maturity with higher Sharpe ratios in the upper regime, this study proved that the UIP holds in the short-term maturity horizon.
Business Management
D.B.L.

Орєхов О. А. Управління фінансовою стійкістю комерційного банку в умовах ризикової діяльності : кваліфікаційна робота магістра спеціальності 072 «Фінанси, банківська справа та страхування» / наук. керівник О. О. Шапуров. Запоріжжя : ЗНУ, 2021. 122 с.
UA : В кваліфікаційній роботі сформовано теоретичні аспекти управління фінансовою стійкістю комерційного банку в умовах ризикової діяльності; проаналізовано результатів діяльності комерційного банку; удосконалено управління фінансовою стійкістю комерційного банку в умовах ризикової діяльності.
EN : The qualifying final work has outlined and described management of financial stability of a commercial bank in terms of risky activities; financial results of commercial bank are analyzed; improve the financial stability management of a commercial bank in the context of risky activities was proposed.

Since the financial crisis, risk based portfolio allocations have gained a great deal in popularity. This increase in popularity is primarily due to the fact that they make no assumptions as to the expected return of the assets in the portfolio. These portfolios implicitly put risk management at the heart of asset allocation and thus their recent appeal. This paper will serve as a comparison of four well-known risk based portfolio allocation methods; minimum variance, maximum diversification, inverse volatility and equally weighted risk contribution. Empirical backtests will be performed throughout rising interest rate periods from 1953 to 2015. Additionally, I will compare these portfolios to more simple allocation methods, such as equally weighted and a 60/40 asset-allocation mix. This paper will help to answer the question if these portfolios can survive in a rising interest rate environment.

碩士
元智大學
財務金融研究所
92
A procedure is provide a framework of interest rate pricing to extend the Ho and Lee model allowing stochastic volatility. In our framework, we illustrate the discount bond with stochastic volatility, and then illustrate the call option of the discount bond with stochastic volatility. Finally, we also illustrate the put option of the discount bond with stochastic volatility. The result of the first illustrate, we find that the extend Ho and Lee model can be use to pricing the discount bond with stochastic volatility, and the price of the discount bond with stochastic volatility is lower than the price of the discount bond with constant volatility. The result of the second illustrate, we find that the extend Ho and Lee model can be use to pricing any European call option of the discount bond with stochastic volatility. The last result of our study, we find that the extend Ho and Lee model can be use to pricing the at-the-money put and in-the-money put. According to the result of this paper, we find that the extend Ho and Lee model can be use to pricing the asset with stochastic volatility even if we doesn’t know the correct volatility. Hence the important contribution of this paper is providing a process and idea to extend the original pricing model of interest rate contingent claim. Additional, we also using this model to price the discount bond option that has stochastic volatility successful.

碩士
國立暨南國際大學
經濟學系
92
This article presents several alternative models of the short-term interest rate volatility that must capture well-known empirical features, including mean-reverting and level effect, and therefore uses Chan, Karolyi, Longstaff, and Sanders（1992）’s level model as our baseline model. Furthermore, we will extend previous level model in three directions. First, we consider a version of short-term interest rate volatility being a function of the news arrival process, and use the GARCH model to capture this feature. Second, We introduce the possibility of an asymmetric volatility effect as modeled in Glosten, Jagannathan and Runkle (1993). Finally, we consider a new class of different economic regimes which are likely to appear to govern interest rate volatility, and use the Markov-Switching to account for this explicitly. The other objective of this article is to compare the out-of-sample forecasting performance of models of the spot interest rate volatility using Taiwan, America and Hong Kong short-term interest rates, 1986-2002. For a one-week horizon, the volatility forecasts evaluation shows that the best in-sample model does not necessarily have the highest forecasting power.