Dissertations / Theses: 'Interest rate models – Mathematical models'

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Ziervogel, Graham. "Hedging performance of interest-rate models." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20482.

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This dissertation is a hedging back-study which assesses the effectiveness of interest- rate modelling and the hedging of interest-rate derivatives. Caps that trade in the Johannesburg swap market are hedged using two short-rate models, namely the Hull and White (1990) one-factor model and the subsequent Hull and White (1994) two-factor extension. This is achieved by using the equivalent Gaussian additive-factor models (G1++ and G2++) outlined by Brigo and Mercurio (2007). The hedges are constructed using different combinations of theoretical zero-coupon bonds. A flexible factor hedging method is proposed by the author and the bucket hedging technique detailed by Driessen, Klaasen and Melenberg (2003) is tested. The results obtained support the claims made by Gupta and Subrahmanyam (2005), Fan, Gupta and Ritchken (2007) and others in the literature that multi-factor models outperform one-factor models in hedging interest-rate derivatives. It is also shown that the choice of hedge instruments can significantly influence hedge performance. Notably, a larger set of hedge instruments and the use of hedge instruments with the same maturity as the derivative improve hedging accuracy. However, no evidence to support the finding of Driessen et al. (2003) that a larger set of hedge instruments can remove the need for a multi-factor model is found.

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Mbongo, Nkounga Jeffrey Ted Johnattan. "Building Interest Rate Curves and SABR Model Calibration." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96965.

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Thesis (MSc)--Stellenbosch University
ENGLISH ABSTRACT : In this thesis, we first review the traditional pre-credit crunch approach that considers a single curve to consistently price all instruments. We review the theoretical pricing framework and introduce pricing formulas for plain vanilla interest rate derivatives. We then review the curve construction methodologies (bootstrapping and global methods) to build an interest rate curve using the instruments described previously as inputs. Second, we extend this work in the modern post-credit framework. Third, we review the calibration of the SABR model. Finally we present applications that use interest rate curves and SABR model: stripping implied volatilities, transforming the market observed smile (given quotes for standard tenors) to non-standard tenors (or inversely) and calibrating the market volatility smile coherently with the new market evidences.
AFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nie

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Luo, Xingguo, and 骆兴国. "Two essays on interest rate and volatility term structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44921251.

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O???Brien, Peter Banking &amp Finance Australian School of Business UNSW. "Term structure modelling and the dynamics of Australian interest rates." Awarded by:University of New South Wales. School of Banking and Finance, 2006. http://handle.unsw.edu.au/1959.4/28283.

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This thesis consists of two related parts. In the first part we conduct an empirical examination of the dynamics of Australian interest rates of six different maturities, covering the whole yield curve. This direct study of the long rates is quite novel. We use maximum likelihood estimation on a variety of models and find some results that are in stark contrast to previous studies. We estimate Poisson-jump diffusion (PJD) models and find very strong evidence for the existence of jumps in all daily interest rate series. We find that the PJD model fits short-rate data significantly better than a Bernoulli-jump diffusion model. We also estimate the CKLS model for our data and find that the only model not rejected for all six maturities is the CEV model in stark contrast to previous findings. Also, we find that the elasticity of variance estimate in the CKLS model is much higher for the short-rates than for the longer rates where the estimate is only about 0.25, indicating that different dynamics seem to be at work for different maturities. We also found that adding jumps to the simple diffusion model gives a larger improvement than comes from going from the simple diffusion to the CKLS model. In the second part of the thesis we examine the Flesaker and Hughston (FH) term structure model. We derive the dynamics of the short rate under both the original measure and the risk-neutral measure, and show that some criticisms of the bounds for the short rate may not be significant in actual applications. We also derive the dynamics of bond prices in the FH model and compare them to the HJM model. We also extend the FH model by allowing the martingale to follow a jump-diffusion process, rather than just a diffusion process. We derive the unique change of measure that guarantees the family of bond prices is arbitrage-free. We derive prices for caps and swaptions, and extend the results to include Bermudan swaptions and show how to price options with the jump-diffusion version of the FH model.

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Zhang, Hua 1962. "The dynamic behaviour of the term structure of interest rates and its implication for interest-rate sensitive asset pricing." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41168.

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This thesis investigates the fundamental assumptions made in recent continuous-time equilibrium models of the term structure of interest rates. It finds that the number and the stochastic processes of state variables are strikingly different from those assumed in the literature. It develops a three-factor empirical term structure model, based on 22 years of cross-maturity time series data. The results show that the price differences, between the well-known Vasicek, and Cox, Ingersoll and Ross models and the three-factor empirical model, for interest-rate sensitive securities are of substantial economic significance.

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Ezzine, Ahmed. "Some topics in mathematical finance. Non-affine stochastic volatility jump diffusion models. Stochastic interest rate VaR models." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211156.

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Tsujimoto, Tsunehiro. "Calibration of the chaotic interest rate model." Thesis, University of St Andrews, 2010. http://hdl.handle.net/10023/2568.

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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.

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Mutengwa, Tafadzwa Isaac. "An analysis of the Libor and Swap market models for pricing interest-rate derivatives." Thesis, Rhodes University, 2012. http://hdl.handle.net/10962/d1005535.

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This thesis focuses on the non-arbitrage (fair) pricing of interest rate derivatives, in particular caplets and swaptions using the LIBOR market model (LMM) developed by Brace, Gatarek, and Musiela (1997) and Swap market model (SMM) developed Jamshidan (1997), respectively. Today, in most financial markets, interest rate derivatives are priced using the renowned Black-Scholes formula developed by Black and Scholes (1973). We present new pricing models for caplets and swaptions, which can be implemented in the financial market other than the Black-Scholes model. We theoretically construct these "new market models" and then test their practical aspects. We show that the dynamics of the LMM imply a pricing formula for caplets that has the same structure as the Black-Scholes pricing formula for a caplet that is used by market practitioners. For the SMM we also theoretically construct an arbitrage-free interest rate model that implies a pricing formula for swaptions that has the same structure as the Black-Scholes pricing formula for swaptions. We empirically compare the pricing performance of the LMM against the Black-Scholes for pricing caplets using Monte Carlo methods.

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9

Alfeus, Mesias. "Heath–Jarrow–Morton models with jumps." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96783.

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Thesis (MSc)--Stellenbosch University, 2015.
ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by Eberlein and Raible (1999), in which a Brownian motion (BM) is replaced by a wide class of processes with jumps. In particular, the HJM driven by the generalised hyperbolic processes was studied. This approach was motivated by empirical evidence proving that models driven by a Brownian motion have several shortcomings, such as inability to incorporate jumps and leptokurticity into the price dynamics. Non-homogeneous Lévy processes and the change of measure techniques necessary for simplification and derivation of pricing formulae were also investigated. For robustness in numerical valuation, several transform methods were investigated and compared in terms of speed and accuracy. The models were calibrated to liquid South African data (ATM) interest rate caps using two methods of optimisation, namely the simulated annealing and secant-Levenberg–Marquardt methods. Two numerical valuation approaches had been implemented in this study, the COS method and the fractional fast Fourier transform (FrFT), and were compared to the existing methods in the context. Our numerical results showed that these two methods are quite efficient and very competitive. We have chose the COS method for calibration due to its rapidly speed and we have suggested a suitable approach for truncating the integration range to address the problems it has with short-maturity options. Our calibration results provided a nearly perfect fit, such that it was difficult to decide which model has a better fit to the current market state. Finally, all the implementations were done in MATLAB and the codes included in appendices.
AFRIKAANSE OPSOMMING : Die standaard-Heath–Jarrow–Morton-raamwerk (kortom die HJM-raamwerk) is daarvoor bekend dat dit op die prysbepaling en verskansing van afgeleide finansiële instrumente vir rentekoerse toegepas kan word. Hierdie studie het die uitgebreide HJM-raamwerk geïmplementeer wat deur Eberlein en Raible (1999) bekendgestel is en waarin ’n Brown-beweging deur ’n breë klas prosesse met spronge vervang word. In die besonder is die HJM wat deur veralgemeende hiperboliese prosesse gedryf word ondersoek. Hierdie benadering is gemotiveer deur empiriese bewyse dat modelle wat deur ’n Brown-beweging gedryf word verskeie tekortkominge het, soos die onvermoë om spronge en leptokurtose in prysdinamika te inkorporeer. Nie-homogene Lévy-prosesse en die maatveranderingstegnieke wat vir die vereenvoudiging en afleiding van prysbepalingsformules nodig is, is ook ondersoek. Vir robuustheid in numeriese waardasie is verskeie transformmetodes ondersoek en ten opsigte van spoed en akkuraatheid vergelyk. Die modelle is vir likiede Suid-Afrikaanse data vir boperke van rentekoerse sonder intrinsieke waarde gekalibreer deur twee optimiseringsmetodes te gebruik, naamlik die gesimuleerde uitgloeimetode en die sekans-Levenberg–Marquardt-metode. Twee benaderings tot numeriese waardasie is in hierdie studie gebruik, naamlik die kosinusmetode en die fraksionele vinnige Fourier-transform, en met bestaande metodes in die konteks vergelyk. Die numeriese resultate het getoon dat hierdie twee metodes redelik doeltreffend en uiters mededingend is. Ons het op grond van die motiveringspoed van die kosinus-metode daardie metode vir kalibrering gekies en ’n geskikte benadering tot die trunkering van die integrasiereeks voorgestel ten einde die probleem ten opsigte van opsies met kort uitkeringstermyne op te los. Die kalibreringsresultate het ’n byna perfekte passing gelewer, sodat dit moeilik was om te besluit watter model die huidige marksituasie die beste pas. Ten slotte is alle implementerings in MATLAB gedoen en die kodes in bylaes ingesluit.

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Nguyen, Hai Nam. "Contributions to credit risk and interest rate modeling." Thesis, Evry-Val d'Essonne, 2014. http://www.theses.fr/2013EVRY0038.

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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

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周抒思 and Shu-see Chow. "Intrinsic demands for borrowing and lending in primitive population models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31212219.

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Ye, Hui, and Anastasia Ellanskaya. "Arbitrage-free market models for interest rate options and future options: the multi-strike case." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-6220.

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This work mainly studies modeling and existence issues for martingale models of option markets with one stock and a collection of European call options for one fixed maturity and infinetely many strikes. In particular, we study Dupire's and Schweizer-Wissel's models, especially the latter one. These two types of models have two completely different pricing approachs, one of which is martingale approach (in Dupire's model), and other one is a market approach (in Schweizer-Wissel's model). After arguing that Dupire's model suffers from the several lacks comparing to Schweizer-Wissel's model, we extend the latter one to get the variations for the case of options on interest rate indexes and futures options. Our models are based on the newly introduced definitions of local implied volatilities and a price level proposed by Schweizer and Wissel. We get explicit expressions of option prices as functions of the local implied volatilities and the price levels in our variations of models. Afterwards, the absence of the dynamic arbitrage in the market for such models can be described in terms of the drift restrictions on the models' coefficients. Finally we demonstrate the application of such models by a simple example of an investment portfolio to show how Schweizer-Wissel's model works generally.

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13

Thafeni, Phumza. "A no-arbitrage macro finance approach to the term structure of interest rates." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96108.

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Thesis (MSc)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: This work analysis the main macro-finance models of the term structure of interest rates that determines the joint dynamics of the term structure and the macroeconomic fundamentals under no-arbitrage approach. There has been a long search during the past decades of trying to study the relationship between the term structure of interest rates and the economy, to the extent that much of recent research has combined elements of finance, monetary economics, and the macroeconomics to analyse the term structure. The central interest of the thesis is based on two important notions. Firstly, it is picking up from the important work of Ang and Piazzesi (2003) model who suggested a joint macro- finance strategy in a discrete time affine setting, by also imposing the classical Taylor (1993) rule to determine the association between yields and macroeconomic variables through monetary policy. There is a strong intuition from the Taylor rule literature that suggests that such macroeconomic variables as in inflation and real activity should matter for the interest rate, which is the monetary policy instrument. Since from this important framework, no-arbitrage macro-finance approach to the term structure of interest rates has become an active field of cross-disciplinary research between financial economics and macroeconomics. Secondly, the importance of forecasting the yield curve using the variations on the Nelson and Siegel (1987) exponential components framework to capture the dynamics of the entire yield curve into three dimensional parameters evolving dynamically. Nelson-Siegel approach is a convenient and parsimonious approximation method which has been trusted to work best for fitting and forecasting the yield curve. The work that has caught quite much of interest under this framework is the generalized arbitrage-free Nelson-Siegel macro- nance term structure model with macroeconomic fundamentals, (Li et al. (2012)), that characterises the joint dynamic interaction between yields and the macroeconomy and the dynamic relationship between bond risk-premia and the economy. According to Li et al. (2012), risk-premia is found to be closely linked to macroeconomic activities and its variations can be analysed. The approach improves the estimation and the challenges on identication of risk parameters that has been faced in recent macro-finance literature.
AFRIKAANSE OPSOMMING: Hierdie werk ontleed die makro- nansiese modelle van die term struktuur van rentekoers pryse wat die gesamentlike dinamika bepaal van die term struktuur en die makroekonomiese fundamentele faktore in 'n geen arbitrage wêreld. Daar was 'n lang gesoek in afgelope dekades gewees wat probeer om die verhouding tussen die term struktuur van rentekoerse en die ekonomie te bestudeer, tot die gevolg dat baie onlangse navorsing elemente van nansies, monetêre ekonomie en die makroekonomie gekombineer het om die term struktuur te analiseer. Die sentrale belang van hierdie proefskrif is gebaseer op twee belangrike begrippe. Eerstens, dit tel op by die belangrike werk van die Ang and Piazzesi (2003) model wat 'n gesamentlike makro- nansiering strategie voorstel in 'n diskrete tyd a ene ligging, deur ook die klassieke Taylor (1993) reël om assosiasie te bepaal tussen opbrengste en makroekonomiese veranderlikes deur middel van monetêre beleid te imposeer. Daar is 'n sterk aanvoeling van die Taylor reël literatuur wat daarop dui dat sodanige makroekonomiese veranderlikes soos in asie en die werklike aktiwiteit moet saak maak vir die rentekoers, wat die monetêre beleid instrument is. Sedert hierdie belangrike raamwerk, het geen-arbitrage makro- nansies benadering tot term struktuur van rentekoerse 'n aktiewe gebied van kruis-dissiplinêre navorsing tussen nansiële ekonomie en makroekonomie geword. Tweedens, die belangrikheid van voorspelling van opbrengskromme met behulp van variasies op die Nelson and Siegel (1987) eksponensiële komponente raamwerk om dinamika van die hele opbrengskromme te vang in drie dimensionele parameters wat dinamies ontwikkel. Die Nelson-Siegel benadering is 'n gerie ike en spaarsamige benaderingsmetode wat reeds vertrou word om die beste pas te bewerkstellig en voorspelling van die opbrengskromme. Die werk wat nogal baie belangstelling ontvang het onder hierdie raamwerk is die algemene arbitrage-vrye Nelson-Siegel makro- nansiele term struktuur model met makroekonomiese grondbeginsels, (Li et al. (2012)), wat kenmerkend van die gesamentlike dinamiese interaksie tussen die opbrengs en die makroekonomie en die dinamiese verhouding tussen band risiko-premies en die ekonomie is. Volgens Li et al. (2012), word risiko-premies bevind om nou gekoppel te wees aan makroekonomiese aktiwiteite en wat se variasies ontleed kan word. Die benadering verbeter die skatting en die uitdagings van identi- sering van risiko parameters wat teegekom is in die afgelope makro- nansiese literatuur.

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Van, Wijck Tjaart. "Interest rate model theory with reference to the South African market." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/3396.

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Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2006.
An overview of modern and historical interest rate model theory is given with the specific aim of derivative pricing. A variety of stochastic interest rate models are discussed within a South African market context. The various models are compared with respect to characteristics such as mean reversion, positivity of interest rates, the volatility structures they can represent, the yield curve shapes they can represent and weather analytical bond and derivative prices can be found. The distribution of the interest rates implied by some of these models is also found under various measures. The calibration of these models also receives attention with respect to instruments available in the South African market. Problems associated with the calibration of the modern models are also discussed.

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Rayée, Grégory. "Essays on pricing derivatives by taking into account volatility and interest rates risks." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209649.

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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
info:eu-repo/semantics/nonPublished

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Aleksa, Algiment. "Palūkanų normų dinamikos modeliai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2004. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2004~D_20040604_205640-67926.

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This paper concentrates on valuation of interest rate. Changes in the short rate captured in a stochastic model which generates a term structure of interest rates. Leading interest rate models are Vasicek model, Cox, Ingersoll & Ross model and Heath, Jarrow and Morton model. First two model are called mean reversion of the short rate, that is, a tendency for the short rate to drift back to some underlying rate. Both models assume that the process for the short rate r is stochastic with one source of uncertainty. The two models differ in the handling of volatility. The last one model describes the forward rate evolution. The dynamics of interest rate of Lithuania has changed apace in these latter years. This can be explained by spontaneous process of resurgent economics. Because Vasicek and Cox, Ingersoll & Ross models are similar in essence, dynamics of interest rate is also similar according to these models. The received results using separate algorithms fit laws of fluctuation in interest rates of Republic of Lithuania. Problem is realized with programme equipment Microsoft Visual Basic 6.3.

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Twarog, Marek B. "Pricing security derivatives under the forward measure." Link to electronic thesis, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-053007-142223/.

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Diallo, Ibrahima. "Some topics in mathematical finance: Asian basket option pricing, Optimal investment strategies." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210165.

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This thesis presents the main results of my research in the field of computational finance and portfolios optimization. We focus on pricing Asian basket options and portfolio problems in the presence of inflation with stochastic interest rates.

In Chapter 2, we concentrate upon the derivation of bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework.We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity

In Chapter 3, we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of Curran M. (1994) [Valuing Asian and portfolio by conditioning on the geometric mean price”, Management science, 40, 1705-1711] and of Deelstra G. Liinev J. and Vanmaele M. (2004) [Pricing of arithmetic basket options by conditioning”, Insurance: Mathematics & Economics] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of Deelstra G. Diallo I. and Vanmaele M. (2008). [Bounds for Asian basket options”, Journal of Computational and Applied Mathematics, 218, 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and

time-to-maturity.

In Chapter 4, we use the stochastic dynamic programming approach in order to extend

Brennan and Xia’s unconstrained optimal portfolio strategies by investigating the case in which interest rates and inflation rates follow affine dynamics which combine the model of Cox et al. (1985) [A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), 385-408] and the model of Vasicek (1977) [An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188]. We first derive the nominal price of a zero coupon bond by using the evolution PDE which can be solved by reducing the problem to the solution of three ordinary differential equations (ODE). To solve the corresponding control problems we apply a verification theorem without the usual Lipschitz assumption given in Korn R. and Kraft H.(2001)[A Stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269] or Kraft(2004)[Optimal Portfolio with Stochastic Interest Rates and Defaultable Assets, Springer, Berlin].

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19

Loulit, Ahmed. "Valuing credit risky bonds: generalizations of first passage models." Doctoral thesis, Universite Libre de Bruxelles, 2006. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210756.

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This work develops some simple models to study risky corporate debt using first passage-time approach. Analytical valuation expression derived from different models as functions of firm’s values and the short-term interest rate with time-dependent parameters governing the dynamics of the firm values and interest rate. We develop some numerical approximation of the analytical valuation, which is given implicitly through Voltera integral equation related to the density of the first-passage- time that a firm reaches some specified default barrier. For some appropriate default barrier arising from financial considerations we obtain a closed-form solution, which is more flexible for numerical calculation.
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20

Unal, Birol. "Interest rate term structure models." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.407078.

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21

Schumann, Gareth William. "Trolle-Schwartz HJM interest rate model." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/23030.

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The Trolle and Schwartz (2009) interest rate model prices interest rate derivatives in a generalised stochastic volatility framework. It is a reformulation of the multifactor Heath, Jarrow and Morton (1992) framework with stochastic volatility terms presented in an analogous fashion to the seminal Heston (1993) model. The Trolle and Schwartz (2009) model provides semi-analytical pricing formulas for zerocoupon bonds and zero-coupon bond options. These formulas are extended to price interest rate caplets, and therefore caps, as well as swaptions. These formulas are described as semi-analytical because of the use of numerical methods as well as their dependency on unobserved state variables. These state variables are estimated by applying an extended Kalman filter on a dataset of interest rates and interest rate derivative prices. Although Trolle and Schwartz (2009) confirm the accuracy of their model when testing against empirical prices, they do not provide an analysis of the consistency between the semi-analytical formulas and Monte Carlo pricing. Presenting this test for consistency seeks to confirm the validity of these pricing formulas. The aim of this dissertation is to implement the Trolle and Schwartz (2009) model and discuss the performance of the semi-analytical pricing formulas against a Monte Carlo simulation. Emphasis will be placed firstly on reviewing the derivations outlined in Trolle and Schwartz (2009) and secondly, building a Monte Carlo framework capable of comparing prices with the semi-analytical pricing formulas. Simulated data will be considered for the purpose of confirming that the estimation of the state vector is sufficiently accurate. Thereafter, an analysis on an empirical dataset can determine whether the results hold across different sets of data.

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22

Trovato, Manlio Battaglia. "Interest rate models with Markov chains." Thesis, Imperial College London, 2009. http://hdl.handle.net/10044/1/8805.

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23

Hansen, Oyvind Grande. "Multifactor Interest Rate Models in Low-Rate Environments." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22624.

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This thesis studies a multi-factor Heath-Jarrow-Morton model and a LIBOR mar-ket model on the Norwegian, European and US interest rate market. The mainconcerns are the low-rate environment and exposure to negative interest rates inthese models. We begin by introducing financial markets and the mathematicalmodels explaining them. Further we discuss the problem with the current low-rateenvironment and the historical market practice. The focuses are implementationsof two multi-factor interest rate models and the presence of negative interest rates.The historical data is provided by DNB and consists of zero coupon swap rates forseveral maturities in the period 2000-2012. The volatility factors are derived fromhistorical data using principal component analysis and covariance matrices. Withtoday?s yield curve the probability of negative rates is highly significant in the HJMmodel, whereas it is zero in LMM because of lognormality. Monte Carlo is used onthe models to compare prices of caps and floors. We show that the models do notproduce the same price especially around strikes near the current 3-month rates.Further we price long butterfly spreads to show the absence of arbitrage in bothmodels.

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Vocke, Carsten. "Hedging with multi-factor interest rate models /." [St. Gallen] : [s.n.], 2005. http://www.gbv.de/dms/zbw/503121223.pdf.

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25

Iqbal, Adam Saeed. "Dynamic interest rate and credit risk models." Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/6851.

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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.

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Zhao, Huimin. "Testing interest rate models for China's repo market /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?FINA%202005%20ZHAO.

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Pietersz, Raoul. "Pricing Models for Bermudan-Style Interest Rate Derivatives." [Rotterdam]: Erasmus Research Institute of Management (ERIM), Erasmus University Rotterdam ; Rotterdam : Erasmus University Rotterdam [Host], 2005. http://hdl.handle.net/1765/7122.

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Slinko, Irina. "Essays in option pricing and interest rate models." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögskolan i Stockholm] (EFI), 2006. http://www2.hhs.se/EFI/summary/706.htm.

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29

Klaassen, Pieter. "Stochastic programming models for interest-rate risk management." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/11913.

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30

Nyamai, Dayton. "Pricing of Interest Rate Derivatives under the Cheyette model." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-421201.

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31

Yolcu, Yeliz. "One Factor Interest Rate Models: Analytic Solutions And Approximations." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/2/12605863/index.pdf.

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The uncertainty attached to future movements of interest rates is an essential part of the Financial Decision Theory and requires an awareness of the stochastic movement of these rates. Several approaches have been proposed for modeling the one-factor short rate models where some lead to arbitrage-free term structures. However, no definite consensus has been reached with regard to the best approach for interest rate modeling. In this work, we briefly examine the existing one-factor interest rate models and calibrate Vasicek and Hull-White (Extended Vasicek) Models by using Turkey'
s term structure. Moreover, a trinomial interest rate tree is constructed to represent the evolution of Turkey&rsquo
s zero coupon rates.

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Ge, Zhong. "A numerical study of one-factor interest rate models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ34038.pdf.

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33

Bi, Jiangchun. "Interest rate models with non-gaussian driven stochastic volatility." Thesis, Heriot-Watt University, 2009. http://hdl.handle.net/10399/2313.

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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.

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34

Tan, David Kim Hong. "Mathematical models of rate control for communication networks." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624531.

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35

Rahantamialisoa, Tahirivonizaka Fanirisoa Zazaravaka. "Interest rates market and models after the 2007 credit crunch." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20413.

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Thesis (MSc)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: The interest rates market has changed dramatically since the 2007 credit crunch with the explosion of basis spreads between rates of different tenors and currencies. Consequently, the classical replication of FRA rates with spot LIBOR rates is no longer valid. Moreover, the 2007 credit crunch yields a separation between the curve used for discounting and the forward or projection curves that estimate all future cash-fl ows. Another impact of the credit crunch in risk management is that market participants have started to give more importance to the difference between collateralized and uncollateralized trades. Nowadays, the wide spread use of collateral, especially in swap contracts, has made the overnight index swap (OIS) rate the appropriate benchmark for discounting collateralized trades. Inspired by the seminal works of Mercurio (2010a,b), Kijima et al. (2008), Fujii et al. (2011), Bianchetti (2010b), with the contributions of other authors, and motivated by the evolution of the interest rates market and models, this thesis examines a new framework that uses multiple-curves to value interest rate derivatives which is compatible with the current market practice. Firstly, we discuss the roots of the 2007 credit crunch and its serious consequences for pricing interest rate derivatives. We underscore the necessity of a multiple-curve pricing framework for interest rate derivatives. This is followed by a discussion on the importance of collateralization and OIS discounting in pricing Over-The-Counter (OTC) derivatives. The central part of the thesis discusses the modern theoretical framework and the practical implementation of the multiple curve pricing method. We present a bootstrapping algorithm used to construct and fit the multiple-yield curves to market prices of plainvanilla contracts. Secondly, starting with the single-currency economy, the extended version of the LIBOR Market Model, developed by Mercurio (2010a,b), which proposes a joint model of FRA rates, implied forward rates and their corresponding spread is investigated. Analogously, the extended version of short-rate model in a multiple-curve setup and in the presence of basis spread, proposed by Kijima et al. (2008), is presented and discussed. This work provides a detailed analysis of these extensions and the corresponding closed formulae for liquid products such as caps and swaptions. Finally, in the multiple-currencies case, the HJM model with stochastic basis spreads, introduced by Fujii et al. (2011), consistent with the foreign exchange and cross-currency swaps markets that includes the effect of collateralization is examined thoroughly.
AFRIKAANSE OPSOMMING: Die rentekoers mark het dramaties verander sedert die 2007 krediet krisis met 'n ontplo ng van basisverspreidings tussen koerse van verskillende looptye ("tenor") en geldeenhede. As gevolg, is die klassieke replikasie van FRA koerse met LIBOR sigkoerse nie langer geldig nie. Verder het die 2007 kredietkrisis 'n skeiding veroorsaak tussen die kromme wat gebruik word vir diskontering en die voorwaardse of vooruitskattings krommes wat toekomstige kontantvloei voorspel. 'n Verdere impak van die kredietkrisis in risikobestuur is dat mark deelnemers begin het om meer klem te lê op verskille tussen aangevulde en onaangevulde handel. Deesdae, met die algemene gebruik van kollaterale sekuriteit, veral in ruiltransaksiekontrakte, is die oornagse indeks ruiltransaksie (overnight index swap, OIS) koers die geskikte maatstaf om aangevulde handel te diskonteer. Geïnspireer deur die gedagteryke werk van Mercurio (2010a,b), Kijima et al. (2008), Fujii et al. (2011), Bianchetti (2010b), met bydrae van menige outeurs, en gemotiveer deur die evolusie van die rentekoers markte en modelle, ondersoek hierdie tesis 'n nuwe raamwerk wat multikrommes gebruik om rentekoers afgeleide effekte te waardeer wat versoenbaar is met die lopende mark praktyk. Eerstens, bespreek ons die oorsake van die 2007 kredietkrisis en die ernstige nagevolge vir die waardering van rentekoers afgeleide effekte. Ons beklemtoon die noodsaaklikheid van 'n multikromme waarderings raamwerk vir rentekoers afgeleide effekte. Dit word gevolg deur 'n bespreking oor die belangrikheid van aanvulling en OIS diskontering in die waardering van oor-die-toonbank (over-the-counter, OTC) effekte. Die teoretiese raamwerk en die praktiese implimentering van die multikromme waarderings metode word bespreek. Ons stel ook ten toon 'n skoenlus ("bootstrapping") algoritme wat gebruik kan word om meervoudige opbrengs krommes saam te stel en die dan te pas op mark pryse van vanielje kontrakte. Tweedens, met 'n enkel geldeenheid ekonomie as beginpunt, word die uitgebreide weergawe van die LIBOR Mark Model (ontwikkel deur Mercurio (2010a,b), wat 'n gesamentlike model van FRA koerse voorstel), geïmpliseerde termyn koerse en hul ooreenstemmende verspreiding bestudeer. Ooreenkomstig word die uitgebreide weergawe van die kort koers model in 'n multikromme opset en in die aanwesigheid van basisspreiding (voorgestel deur Kijima et al. (2008)) uiteengesit en bespreek. Hierdie werk verskaf 'n uitvoerige analise van hierdie uitbreidings en die ooreenstemmende geslote formules vir vloeibare produkte soos perke en ruiltransaksie opsies. Ten slotte, in die multi-geldeenheid geval, word die HJM model met stogastiese basisverspreiding (voorgestel deur Fujii et al. (2011)), nie-strydig met buitelandse valuta en kruisvaluta ruiltransaksie markte wat die effekte van aanvulling insluit word deuglik bestudeer.

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36

Al-Zoubi, Haitham. "New Evidence on Interest Rate and Foreign Exchange Rate Modeling." ScholarWorks@UNO, 2003. http://scholarworks.uno.edu/td/467.

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This dissertation empirically and theoretically investigates three interrelated issues of market anomalies in interest rates derivatives and foreign exchange rates. The first essay models the spot exchange rate as a decomposition of permanent and transitory components. Unlike extant analysis, the transitory component could be stationary or explosive. The second essay examines the market efficiency hypothesis in the foreign exchange markets and relates the rejection of forward rate unbiasedness hypothesis to the existence of risk premium not to the failure of rational expectation. The third essay examines the behavior of short-term riskless rate and models the risk free rate as a nonlinear trend stationary process. While addressing these issues, these essays account for: (1) finite sample bias; (2) Unit root and other nonstationary behaviors; (3) the role of nonlinear trend; and (4) the interrelations between different behaviors. Several new results have been gleaned from our analysis; we find that: (1) the spot exchange rates display a very slow mean aversion behavior, which implies the failure of the purchasing power parity; (2) there are positive autocorrelations across the long horizons overlapping returns increases overtime and then begin to decline at a very long horizon period; (3) the short-term riskless rate displays a nonlinear trend stationary process which is closer to driftless random walk behavior; (4) modifying the mean reverting shortterm interest rates models to a nonlinear trend stationary shows an extreme improvement and outperforms all suggested models; (5) the traditional tests for rational expectations and market efficiency in the foreign exchange markets are subject to size distortions; (6) we relate the rejection of market efficiency in the foreign exchange markets documented across most currencies to the existence of risk premium not to the rejection of rational expectation hypothesis.

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Frota, Silvia Franciele Padilha. "Um estudo da estrutura a termo de taxas de juros de títulos públicos prefixados e o modelo de Svensson." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2576.

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A Estrutura a Termo de Taxas de Juros (ETTJ) é um elemento essencial para formulação da política monetária. Ela é capaz de indicar as expectativas do mercado financeiro em relação as taxas de juros futuras. Nesse trabalho estudamos a formação da ETTJ com enfoque maior na matemática envolvida, haja visto que na literatura esse assunto em geral é tratado apenas com foco na economia. Demonstramos as relações matemáticas entre as taxas de juros à vista, futuras e instantâneas. Estudamos também o modelo matemático empírico de previsão da curva de juros proposta por Lars E. O. Svensson (SVENSSON, 1994). Esse modelo é de fácil aplicação pois necessita de poucos parâmetros para se ajustar a curva de juros. Por esse motivo esse modelo tem sido amplamente usado em Bancos Centrais de diversos países inclusive pelo Banco Central do Brasil. Concluímos com uma aplicação do modelo de Svensson (SVENSSON, 1994) utilizando os preços dos títulos prefixados do Tesouro Direto.
The Term Structure of Interest Rates (TSIR) is an essential element for the formulation of monetary policy. It is able to indicate the expectations of the financial market in relation to future interest rates. In this work we study the formation of TSIR with a greater focus on the mathematics involved, since in the literature this subject is generally treated only with a focus on economics. We prove the mathematical relation between spot, future and instantaneous interest rates. We also study the empirical mathematical model of forecasting the interest curve proposed by Lars E. O. Svensson (SVENSSON, 1994). This model is easy to apply since it requires few parameters to adjust the interest curve. For this reason, this model has been widely used by Central Banks of several countries, including the Central Bank of Brazil. We conclude with an application of the Svensson (SVENSSON, 1994) model using the prices of fixed-rate Treasury Direct securities.

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38

Gathy, Maude. "On some damage processes in risk and epidemic theories." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210063.

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Cette thèse traite de processus de détérioration en théorie du risque et en biomathématique.

En théorie du risque, le processus de détérioration étudié est celui des sinistres supportés par une compagnie d'assurance.

Le premier chapitre examine la distribution de Markov-Polya comme loi possible pour modéliser le nombre de sinistres et établit certains liens avec la famille de lois de Katz/Panjer. Nous construisons la loi de Markov-Polya sur base d'un modèle de survenance des sinistres et nous montrons qu'elle satisfait une récurrence élégante. Celle-ci permet notamment de déduire un algorithme efficace pour la loi composée correspondante. Nous déduisons la famille de Katz/Panjer comme famille limite de la loi de Markov-Polya.

Le second chapitre traite de la famille dite "Lagrangian Katz" qui étend celle de Katz/Panjer. Nous motivons par un problème de premier passage son utilisation comme loi du nombre de sinistres. Nous caractérisons toutes les lois qui en font partie et nous déduisons un algorithme efficace pour la loi composée. Nous examinons également son indice de dispersion ainsi que son comportement asymptotique.

Dans le troisième chapitre, nous étudions la probabilité de ruine sur horizon fini dans un modèle discret avec taux d'intérêt positifs. Nous déterminons un algorithme ainsi que différentes bornes pour cette probabilité. Une borne particulière nous permet de construire deux mesures de risque. Nous examinons également la possibilité de faire appel à de la réassurance proportionelle avec des niveaux de rétention égaux ou différents sur les périodes successives.

Dans le cadre de processus épidémiques, la détérioration étudiée consiste en la propagation d'une maladie de type SIE (susceptible - infecté - éliminé). La manière dont un infecté contamine les susceptibles est décrite par des distributions de survie particulières. Nous en déduisons la distribution du nombre total de personnes infectées à la fin de l'épidémie. Nous examinons en détails les épidémies dites de type Markov-Polya et hypergéométrique. Nous approximons ensuite cette loi par un processus de branchement. Nous étudions également un processus de détérioration similaire en théorie de la fiabilité où le processus de détérioration consiste en la propagation de pannes en cascade dans un système de composantes interconnectées.

Doctorat en Sciences
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39

Kim, Myung Suk. "Statistical testing and estimation in continuous time interest rate models." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/4189.

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The shape of drift function in continuous time interest rate models has been investigated by many authors during the past decade. The main concerns have been whether the drift function is linear or nonlinear, but no convincing conclusions have been seen. In this dissertation, we investigate the reason for this problem and test several models of the drift function using a nonparametric test. Furthermore, we study some related problems, including the empirical properties of the nonparametric test. First, we propose regression models for the estimation of the drift function in some continuous time models. The limiting distribution of the parameter estimator in the proposed regression model is derived under certain conditions. Based on our analyses, we conclude that the effect of drift function for some U.S. Treasury Bill yields data is negligible. Therefore, neither linear nor nonlinear modeling has a significant effect. Second, parametric linear and nonlinear proposed regression models are applied and the correctness of those models is examined using the consistent nonparametric model specification test introduced by Li (1994) and Zheng (1996), henceforth the Jn test. The test results indicate that there is no strong statistical evidence against the assumed drift models. Furthermore, the constant drift model is not rejected either. Third, we compare the Jn and generalized likelihood ratio (GLR) tests through Monte Carlo simulation studies concerning whether the sizes of tests are stable over a range of bandwidth values, which is an important indicator to measure the usefulness of nonparametric tests. The GLR test was applied to testing the linear drift function in continuous time models by Fan and Zhang (2003). Our simulation study shows that the GLR test does not provide stable sizes over a grid of bandwidth values in testing the drift function of some continuous time models, whereas the Jn test usually does.

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40

Pang, Kin. "Calibration of interest rate term structure and derivative pricing models." Thesis, University of Warwick, 1997. http://wrap.warwick.ac.uk/36270/.

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We argue interest rate derivative pricing models are misspecified so that when they are fitted to historical data they do not produce prices consistently with the market. Interest rate models have to be calibrated to prices to ensure consistency. There are few published works on calibration to derivatives prices and we make this the focus of our thesis. We show how short rate models can be calibrated to derivatives prices accurately with a second time dependent parameter. We analyse the misspecification of the fitted models and their implications for other models. We examine the Duffle and Kan Affine Yield Model, a class of short rate models, that appears to allow easier calibration. We show that, in fact, a direct calibration of Duffle and Kan Affine Yield Models is exceedingly difficult. We show the non-negative subclass is equivalent to generalised Cox, Ingersoll and Ross models that facilitate an indirect calibration of nonnegative Duffle and Kan Affine Yield Models. We examine calibration of Heath, Jarrow and Morton models. We show, using some experiments, Heath, Jarrow and Morton models cannot be calibrated quickly to be of practical use unless we restrict to special subclasses. We introduce the Martingale Variance Technique for improving the accuracy of Monte Carlo simulations. We examine calibration of Gaussian Heath Jarrow and Morton models. We provide a new non-parametric calibration using the Gaussian Random Field Model of Kennedy as an intermediate step. We derive new approximate swaption pricing formulae for the calibration. We examine how to price resettable caps and floors with the market- Libor model. We derive a new relationship between resettable caplets and floorlets prices. We provide accurate approximations for the prices. We provide practical approximations to price resettable caplets and floorlets directly from quotes on standard caps and floors. We examine how to calibrate the market-Libor model.

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41

Parker, Gary. "An application of stochastic interest rate models in life assurance." Thesis, Heriot-Watt University, 1992. http://hdl.handle.net/10399/1440.

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Although assurance companies are pooling many risks, the law of large numbers does not fully apply. This leaves the companies with a possibility of insolvency and a corresponding need for contingency reserves which are matters of serious concern. In this thesis we derive some fundamental results that are useful when the time comes to set contingency reserves or to assess solvency. We use a model where both the mortality and the interest rates are random variables. We choose to model the force of interest by the Ornstein-Uhlenbeck process. For temporary assurances and endowment assurances we derive an efficient recursive method to find the first three moments of the present value of a portfolio of identical policies. We then use these moments to approximate accurately the distribution of the present value of such a portfolio, firstly when the number of policies in the portfolio tends to infinity, and secondly, for a portfolio of finite size.

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42

Zhang, Jiangxingyun. "International Portfolio Theory-based Interest Rate Models and EMU Crisis." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1G011/document.

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L'objectif de cette thèse est d’étudier à côté du risque défaut, le rôle spécifique des risques de volatilité et de co-volatilité dans la formation des taux longs dans la zone euro. On propose en particulier un modèle théorique de choix de portefeuille à deux pays permettant d’évaluer la contribution des primes de risque de volatilité aux processus de contagion et de fuite vers la qualité dans différents épisodes de la crise de la dette souveraine. Ce modèle permet également d’analyser le rôle des achats d’actifs (QE) de la BCE sur l’équilibre des marchés obligataires. Nos tests empiriques suggèrent que les programmes QE de la BCE à partir de mars 2015 n’ont fait qu’accélérer « une défragmentation » des marchés obligataires de la zone euro, apparue plus tôt dans la crise, dès la mise en place de l’OMT
This thesis examines the specific role of volatility risks and co-volatility in the formation of long-term interest rates in the euro area. In particular, a two-country theoretical portfolio choice model is proposed to evaluate the volatility risk premia and their contribution to the contagion and flight to quality processes. This model also provides an opportunity to analyze the ECB's role of asset purchases (QE) on the equilibrium of bond markets. Our empirical tests suggest that the ECB's QE programs from March 2015 have accelerated the "defragmentation" of the euro zone bond markets

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43

Roussellet, Guillaume. "Non-Negativity, Zero Lower Bound and Affine Interest Rate Models." Thesis, Paris 9, 2015. http://www.theses.fr/2015PA090012/document.

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Cette thèse présente plusieurs extensions relatives aux modèles affines positifs de taux d'intérêt. Un premier chapitre introduit les concepts reliés aux modélisations employées dans les chapitres suivants. Il détaille la définition de processus dits affines, et la construction de modèles de prix d'actifs obtenus par non-arbitrage. Le chapitre 2 propose une nouvelle méthode d’estimation et de filtrage pour les modèles espace-état linéaire-quadratiques. Le chapitre suivant applique cette méthode d’estimation à la modélisation d’écarts de taux interbancaires de la zone Euro, afin d’en décomposer les fluctuations liées au risque de défaut et de liquidité. Le chapitre 4 développe une nouvelle technique de création de processus affines multivariés à partir leurs contreparties univariées, sans imposer l’indépendance conditionnelle entre leurs composantes. Le dernier chapitre applique cette méthode et dérive un processus affine multivarié dont certaines composantes peuvent rester à zéro pendant des périodes prolongées. Incorporé dans un modèle de taux d’intérêt, ce processus permet de rendre compte efficacement des taux plancher à zéro
This thesis presents new developments in the literature of non-negative affine interest rate models. The first chapter is devoted to the introduction of the main mathematical tools used in the following chapters. In particular, it presents the so-called affine processes which are extensively employed in no-arbitrage interest rate models. Chapter 2 provides a new filtering and estimation method for linear-quadratic state-space models. This technique is exploited in the 3rd chapter to estimate a positive asset pricing model on the term structure of Euro area interbank spreads. This allows us to decompose the interbank risk into a default risk and a liquidity risk components. Chapter 4 proposes a new recursive method for building general multivariate affine processes from their univariate counterparts. In particular, our method does not impose the conditional independence between the different vector elements. We apply this technique in Chapter 5 to produce multivariate non-negative affine processes where some components can stay at zero for several periods. This process is exploited to build a term structure model consistent with the zero lower bound features

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44

Mamon, Rogemar S. "Market models of interest rate dynamics with a joint short rate/HJM approach." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0011/NQ59628.pdf.

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45

Yueh, Meng-Lan. "Numerical lattice methods for implementing interest rate and credit risk models." Thesis, University of Warwick, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252479.

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46

Rinaz, Sofiane. "Positive interest rate models with sticky barrier for the Japanese market." Kyoto University, 2006. http://hdl.handle.net/2433/143926.

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Kyoto University (京都大学)
0048
新制・課程博士
博士(経済学)
甲第12043号
経博第244号
新制||経||209(附属図書館)
23879
UT51-2006-J38
京都大学大学院経済学研究科経済動態分析専攻
(主査)教授木島正明, 教授森棟公夫, 助教授島本哲朗
学位規則第4条第1項該当

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47

Hadjipetri, Stala. "Coherent chaos interest rate models and the Wick calculus in finance." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/25098.

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This thesis develops new tools in stochastic analysis with applications to finance. The first part presents novel developments in the Wiener chaos approach to the modelling, calibration, and pricing of interest rate derivatives. To price financial instruments it suffices to specify the pricing kernel, which in Brownian models can be represented as the conditional variance of a square-integrable random variable which serves as the 'generator' of the pricing kernel. The coefficients of the chaos expansion of the generator act as the parameters of a generic interest-rate model. A special class of generators, arising from 'coherent' chaos expansions, is considered, and the resulting interest rate models are investigated. Coherent representations are important since a kernel generator can be expressed as a linear superposition of coherent generators. This property is exploited to derive general expressions for the pricing kernel, along with the associated discount bond and short rate processes. Pricing formulae for bond options and swaptions are obtained in closed form. The pricing kernel of a generic incoherent model is then obtained by use of the underlying coherent elements. Finite-dimensional representations of coherent chaos models are investigated, and used to construct a class of tractable models having the feature that discount bond prices are piecewise-flat processes. In the second part of the thesis, a general theory of the Wick calculus is developed. Novel results concerning the Wick orders of random variables are derived. In the case where the underlying process is a Brownian motion the Wick calculus reduces to the Ito calculus, but the former is not restricted to the Gaussian class, and is applicable to other cases, such as Lévy processes. With financial applications in mind, the Wick calculus is extended to a wider class of stochastic processes. The thesis concludes with a change of measure analysis for Wick exponentials of Lévy processes, indicating that the Wick calculus can be used as a tool for modelling the dynamics of asset prices.

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48

Corr, Anthony School of Mathematics UNSW. "Finite dimensional representability of forward rate and LIBOR models." Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17606.

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This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

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Elhouar, Mikael. "Essays on interest rate theory." Doctoral thesis, Handelshögskolan i Stockholm, Finansiell Ekonomi (FI), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-451.

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Liu, Kit-ying Ida, and 廖潔瑩. "Empirical exchange rate models: out-of-sampleforecasts for the HK$/Yen exchange rate." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B3195456X.

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Dissertations / Theses on the topic 'Interest rate models – Mathematical models'

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