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Title: Calibration of the chaotic interest rate model
Author: Tsujimoto, Tsunehiro
ISNI:       0000 0004 2720 1240
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 2010
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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.
Supervisor: Damjanovic, Vladislav Sponsor: The Scottish Institute for Research in Economics
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Quantitative finance ; Mathematical finance ; Interest rate modelling ; Potential approach ; Stochastic volatility ; HG1621.T8 ; Interest rates--Mathematical models ; Business mathematics ; Stochastic processes