This thesis studies pricing and hedging barrier and other exotic options in continuous stochastic volatility models. Classical put-call symmetry relates the price of puts and calls under a suitable dual market transform. One well-known application is the semi-static hedging of path-dependent barrier options with European options. This, however, in its classical form requires the price process to observe rather stringent and unrealistic symmetry properties. In this thesis, we provide a general self-duality theorem to develop pricing and hedging schemes for barrier options in stochastic volatility models with correlation. A decomposition formula for pricing barrier options is then derived by Ito calculus which provides an alternative approach rather than solving a partial differential equation problem. Simulation on the performance is provided. In the last part of the thesis, via a version of the reflection principle by Desire Andre, originally proved for Brownian motion, we study its application to the pricing of exotic options in a stochastic volatility context.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:594152 |
| Date | January 2013 |
| Creators | Chen, Zhanyu |
| Publisher | London School of Economics and Political Science (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.lse.ac.uk/822/ |
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