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1
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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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.
3
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.
4
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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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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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.
7
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 UniversityENGLISH 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
8
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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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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O???Brien, Peter Banking & 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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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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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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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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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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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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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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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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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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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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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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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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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 zéroThis 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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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’OMTThis 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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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 tenorsThis 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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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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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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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
31
NIU, LINLIN. "Interest rate term structure modeling and forecasting with macro-finance models." Doctoral thesis, Università Bocconi, 2008. https://hdl.handle.net/11565/4051223.
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Senturk, Huseyin. "An Empirical Comparison Of Interest Rate Models For Pricing Zero Coupon Bond Options." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609786/index.pdf.
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The aim of this study is to compare the performance of the four interest rate
models (Vasicek Model, Cox Ingersoll Ross Model, Ho Lee Model and Black Der-
man Toy Model) that are commonly used in pricing zero coupon bond options.
In this study, 1{5 years US Treasury Bond daily data between the dates June 1,
1976 and December 31, 2007 are used. By using the four interest rate models,
estimated option prices are compared with the real observed prices for the begin-
ing work days of each months of the years 2004 and 2005. The models are then
evaluated according to the sum of squared errors. Option prices are found by
constructing interest rate trees for the binomial models based on Ho Lee Model
and Black Derman Toy Model and by estimating the parameters for the Vasicek
and the Cox Ingersoll Ross Models.
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Hernandez, Urena Luis Gustavo. "Pricing of Game Options in a market with stochastic interest rates." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7005.
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An in depth study of the pricing of Game contingent claims under a general diffusion market model, in which interest rate is non constant, is presented.
With the idea of providing a few numerical examples of the valuation of such claims, we present a detailed description of a Bootstrapping procedure to obtain interest rate information from Swaps rates. We also present a Stripping procedure that can be used to obtain initial spot (caplet) volatility from Market quotes on Caps/FLoors. These methods are of general application and could be used in the calibration of diffusion models of interest rate.
Then we show several examples of calibration of the Hull--White model of interest rates. Our calibration examples are later used in the numerical approximation of the value of a particular form of Game option.
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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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Altay, Suhan. "On Forward Interest Rate Models: Via Random Fields And Markov Jump Processes." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608342/index.pdf.
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The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate models, term structure of defaultable bond prices and forward measures. Also a general framework for bond prices via nuclear space valued semi-martingales is introduced.
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Kazziha, Soraya. "Interest rate models, inflation-based derivatives, trigger notes and cross-currency swaptions." Thesis, Imperial College London, 2000. http://hdl.handle.net/10044/1/7281.
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GAMBARO, ANNA MARIA. "Interest rate and credit risk models applied to finance and actuarial science." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2017. http://hdl.handle.net/10281/158366.
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La prima parte della lavoro di tesi propone dei nuovi limiti per il prezzo di swaptions europee per modelli affini e quadratici di tasso di interesse. Questi limiti sono calcolabili per tutti i modelli la cui funzione caratteristica congiunta è nota. In particolare, il nostro limite inferiore richiede il calcolo di una transformata di Fourier unidimensionale indipendentemente dalla numero di date di pagamento del contratto swap sottostante. Inoltre, possiamo controllare l'erroe del nostro metodo fornendo un limite superiore al prezzo della swaption che è applicabile a tutti i modelli considerati. Abbiamo verificato i nostri prezzi approssimati, ovvero i limiti inferiori e superiori dei prezzi, per diversi modelli affini e per il modello quadratico Gaussiano.
Nella seconda parte della tesi, estendiamo i metodi aprossimati appena descritti al prezzo di swaptions con un modello multi-curva.
Nella terza parte, proponiamo un nuovo modello multi-curva, nell'ambito dei modelli di Heath-Jarrow-Morton e che utilizza i processi di Lévy con tempo stocastico. Il nostro obiettivo è ottenere un modello parsimonioso, ma che sia anche abbastanza flessibile da riprodurre le superfici di volatilità delle opzioni su tasso di interesse quotate.
Il modello è multi-curva e permette di avere tassi negativi.
Per prima cosa, sviluppiamo delle strutture a termine prive di arbitraggio per gli zero coupon bonds e i forward rate agreements. In seguito, valutiamo i derivati su tasso di interesse, come ad esempio caps e swaptions, usando il metodo della trasformata di Fourier. Due differenti costruzioni del processo di Lévy con tempo stocastico son state calibrate su dati reali di mercato e i risultati sono stato esaminati e comparati.
Nell'ultima parte, analizziamo le pratiche comunemente utilizzate per valutare i beni e le passività di fondi assicurativi e proponiamo un modello stocastico privo di arbitraggio per tasso di interesse, rischio di credito e rischio di liquidità, che tenga in conto la dipendenza tra differenti emittenti. Infine, testiamo l'impatto delle pratiche comuni rispetto al modello da noi proposto nella valutazione di opzioni finanziarie scritte su polizze emesse da compagnie assicurative europee.The first part of the thesis proposes new bounds on the prices of European-style swaptions for affine and quadratic interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known. In particular, our lower bound involves the computation of a one-dimensional Fourier transform independently of the swap length. In addition, we control the error of our method by providing a new upper bound on swaption price that is applicable to all considered models. We test our bounds on different affine models and on a quadratic Gaussian model. In the second part of the work, we extended the lower and upper bounds to pricing swaption in a multiple-curve framework. In the third part, we propose a novel multiple-curve model, set in the Heath-Jarrow-Morton framework, with time-changed Lévy processes, in order to obtain a parsimonious but also flexible model, which is able to reproduce quoted volatility surface of interest rate options. The model is developed in a multiple-curve post crisis set-up and it allows for negative rates. First, we build arbitrage free term structures for zero coupon bonds and Libor Forward Rate Agreement (FRA) rates. Then, we price interest rate derivatives, as caps and swaptions, using the Fourier transform method. Two choices for the construction of the driving processes are calibrated to market data and results are examined and compared. In the last part, we analyse common practice for determining the fair value of asset and liabilities of insurance funds and we propose an arbitrage free stochastic model for interest rate, credit and liquidity risks, that takes into account the dependences between different issuers. The impact of the common practice against our proposed model is tested for the evaluation of financial options written on with-profit policies issued by European insurance companies.
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Dalmagro, Lucas Bassani. "Avaliação de derivativos de taxas de juros : uma aplicação do Modelo CIR sobre opções de IDI." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/127250.
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Este trabalho tem por objetivo principal aplicar o modelo de precificação de opções de taxas de juros proposto por Barbachan e Ornelas (2003), com base nos modelos de taxa de juro e avaliação de opções de Cox, Ingerssol e Ross (1985), para avaliação de opções de compra sobre o Índice de Taxa Média de Depósitos Interfinanceiros de Um Dia (IDI), negociadas na BM&FBovespa. Para estimação dos parâmetros deste modelo, foi empregado o método de Máxima Verossimilhança. Neste contexto, também fez-se uso da fórmula de precificação de opções proposta por Black (1976), adaptada para o mercado de derivativos brasileiros, conforme implementação verificada no trabalho de Gluckstern et al. (2002). Tal aplicação torna-se interessante, pois este modelo é amplamente utilizado pelo mercado brasileiro para avaliação de opções sobre o IDI. De forma a verificar a aderência dos preços teóricos gerados pelos modelos, em comparação aos preços de mercado, métricas de erro foram empregadas. De forma geral, nossos resultados mostraram que ambos os modelos apresentam erros sistemáticos de precificação, onde o modelo CIR subavalia os prêmios das opções e o modelo de Black superprecifica. No entanto, bons resultados foram encontrados ao avaliarmos opções in-the-money e out-of-money com o modelo de Black.This work aims to apply the interest rate option pricing model proposed by Barbachan and Ornelas (2003), based on the interest rate model and option pricing model developed by Cox, Ingersoll and Ross (1985), to evaluate call options on the 1 day Brazilian Interfinancial Deposits Index - IDI, traded at BM&FBovespa. The Maximum Likelihood method was applied to estimate the model parameters. In this context, the option pricing formula proposed by Black (1976), adapted for the Brazilian derivative Market, was also used, according implementation verified in Gluckstern et al. (2002). This application becomes interesting because this model is widely used by the Brazilian Market to evaluate options on IDI. In order to verify the adherence of theoretical prices generated by the models, in comparison to the Market prices, error metrics were applied. In general, our results pointed out that both models presented systematic pricing errors, in which the CIR model underestimates the option prices and Black’s model overestimates. However, good results were found on the evaluation of options in-the-money and out-of-money with the Black’s Model.
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Hyll, Magnus. "Essays on the term structure of interest rates." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögsk.] (EFI), 2000. http://www.hhs.se/efi/summary/548.htm/.
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Ji, Inyeob Economics Australian School of Business UNSW. "Essays on testing some predictions of RBC models and the stationarity of real interest rates." Publisher:University of New South Wales. Economics, 2008. http://handle.unsw.edu.au/1959.4/41441.
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This dissertation contains a series of essays that provide empirical evidence for Australia on some fundamental predictions of real business cycle models and on the convergence and persistence of real interest rates. Chapter 1 provides a brief introduction to the issues examined in each chapter and provides an overview of the methodologies that are used. Tests of various basic predictions of standard real business cycle models for Australia are presented in Chapters 2, 3 and 4. Chapter 2 considers the question of great ratios for Australia. These are ratios of macroeconomic variables that are predicted by standard models to be stationary in the steady state. Using time series econometric techniques (unit root tests and cointegration tests) Australia great ratios are examined. In Chapter 3 a more restrictive implication of real business cycle models than the existence of great ratios is considered. Following the methodology proposed by Canova, Finn and Pagan (1994) the equilibrium decision rules for some standard real business cycle are tested on Australian data. The final essay on this topic is presented in Chapter 4. In this chapter a large-country, small-country is used to try and understand the reason for the sharp rise in Australia??s share of world output that began around 1990. Chapter 5 discusses real interest rate linkages in the Pacific Basin region. Vector autoregressive models and bootstrap methods are adopted to study financial linkages between East Asian markets, Japan and US. Given the apparent non-stationarity of real interest rates a related issue is examined in Chapter 6, viz. the persistence of international real interest rates and estimation of their half-life. Half-life is selected as a means of measuring persistence of real rates. Bootstrap methods are employed to overcome small sample issues in the estimation and a non-standard statistical inference methodology (Highest Density Regions) is adopted. Chapter 7 reapplies the High Density Regions methodology and bootstrap half-life estimation to the data used in Chapters 2 and 5. This provides a robustness check on the results of standard unit root tests that were applied to the data in those chapters. Main findings of the thesis are as follows. The long run implications of real business cycle models are largely rejected by the Australia data. This finding holds for both the existence of great ratios and when the explicit decision rules are employed. When the small open economy features of the Australian economy are incorporated in a two country RBC model, a country-specific productivity boom seems to provide a possible explanation for the rise in Australia??s share of world output. The essays that examine real interest rates suggest the following results. Following the East Asian financial crisis in 1997-98 there appears to have been a decline in the importance of Japan in influencing developments in the Pacific Basin region. In addition there is evidence that following the crisis Korea??s financial market became less insular and more integrated with the US. Finally results obtained from the half-life estimators suggest that despite the usual findings from unit root tests, real interest rates may in fact exhibit mean-reversion.
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Yu, Wing Tong Bosco. "Interest rate swaps : why do they exist and how should they be priced?" Thesis, University of Southampton, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326617.
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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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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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Hambouri, Zaphiro. "Risk and asset/liability management of fixed income portfolios." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312022.
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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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Jamdee, Sutthisit. "MULTIFRACTAL MODELS AND SIMULATIONS OF THE U.S. TERM STRUCTURE." Kent State University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=kent1115064950.
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Ogunc, Fethi. "Estimating The Neutral Real Interest Rate For Turkey By Using An Unobserved Components Model." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607426/index.pdf.
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In this study, neutral real interest rate gap and output gap are estimated jointly under two
different multivariate unobserved components models with the motivation to provide
empirical measures that can be used to analyze the amount of stimulus that monetary
policy is passing on to the economy, and to understand historical macroeconomic
developments. In the analyses, Kalman filter technique is applied to a small-scale
macroeconomic model of the Turkish economy to estimate the unobserved variables for
the period 1989-2005. In addition, two alternative specifications for neutral real interest
rate are used in the analyses. The first model uses a random walk model for the neutral
real interest rate, whereas the second one employs more structural specification, which
specifically links the neutral real rate with the trend growth rate and the long-term course
of the risk premium. Comparison of the models developed by using various performance
criteria clearly indicates the use of more structural specification against random walk
specification. Results suggest that though there is relatively high uncertainty surrounding
the neutral real interest rate estimates to use them directly in the policy-making process,
estimates appear to be very useful for ex-post monetary policy evaluations.
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Tsai, Angela C. F. "Valuation of Eurodollar futures contracts under alternative term structure models : theory and evidence." Thesis, University of Strathclyde, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366802.
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Hatgioannides, John. "Essays on asset pricing in continuous time." Thesis, Birkbeck (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244543.
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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.