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dc.contributor.advisorDamjanovic, Vladislav
dc.contributor.authorTsujimoto, Tsunehiro
dc.description.abstractIn 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.en_US
dc.publisherUniversity of St Andrews
dc.subjectQuantitative financeen_US
dc.subjectMathematical financeen_US
dc.subjectInterest rate modellingen_US
dc.subjectPotential approachen_US
dc.subjectStochastic volatilityen_US
dc.subject.lcshInterest rates--Mathematical modelsen_US
dc.subject.lcshBusiness mathematicsen_US
dc.subject.lcshStochastic processesen_US
dc.titleCalibration of the chaotic interest rate modelen_US
dc.contributor.sponsorScottish Institute for Research in Economics (SIRE)en_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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