In this thesis we study low-dimensional stochastic volatility interest rate models for pricing and hedging exotic derivatives. In particular we develop a stochastic volatility Markov-functional model. In order to implement the model numerically, we further propose a general algorithm by working with basis functions and conditional moments of the driving Markov process. Motivated by a data driven study, we choose a SABR type model as a driving process. With this choice we specify a pre-model and develop an approximation to evaluate conditional moments of the SABR driver which serve as building blocks for the practical algorithm. Having discussed how to set up a stochastic volatility Markov-functional model next we study the calibration of a LIBOR based version of the model with the SABR type driving process. We consider a link between separable SABR LIBOR market models and stochastic volatility LIBOR Markov-functional models. Based on the link we propose a calibration routine to feed in SABR marginals by calibrating to the market vanilla options. Moreover we choose the parameters of the SABR driver by fitting to the market correlation structure. We compare the stochastic volatility Markov-functional model developed in the thesis with one-dimensional (non-stochastic-volatility) swap Markov-functional models in terms of pricing and hedging Bermudan type products. By doing so we investigate effects of correlation structure, implied volatility smiles and the introduction of stochastic volatility on Bermudan type products. Finally we compare Quasi-Gaussian models with Markov-functional models in terms of specification and calibration. In particular we study Quasi-Gaussian models formulated in the Markov-functional model framework to make clear the relationship between the two models.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:723106 |
| Date | January 2016 |
| Creators | Guo, Chuan |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/91418/ |
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