Barrier option pricing under the 2-hypergeometric stochastic volatility model

The purpose of this thesis is to investigate the pricing of financial options under the 2-hypergeometricstochastic volatility model. This is an analytically tractable model which has recently been introducedas an attempt to tackle one of the most serious shortcomings of the famous Black and Scholes optionpricing model: the fact that it does not reproduce the volatility smile and skew effects which are commonlyseen in observed price data from option markets.After a review of the basic theory of option pricing under stochastic volatility, we employ the regularperturbation method from asymptotic analysis of partial differential equations to derive an explicit andeasily computable approximate formula for the pricing of barrier options — one of the most popular typesof exotic options — under the 2-hypergeometric stochastic volatility model. The asymptotic convergenceof the method is proved under appropriate regularity conditions, and a multi-stage method for improvingthe quality of the approximation is also discussed.