Pricing and hedging exotic options in stochastic volatility models

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.