Exotic Option Pricing In Incomplete Market

In this thesis, we study the exotic option Pricing theory and risk management theory under incomplete market, including, Asian options, Barrier options, Lookback options.Following Dennis Yang, we developed how to price exotic options with stochastic volatility in incomplete market. Under the exponential utility preference, we show that the fair price of exotic options is related to investor’s position holding. As well-known, based on the arbitrage pricing theory the PDE satisfied by the option price is derived with a undetermined parameter-market price of risk. Under different assumption, the market price of risk is also different. Based on the dynamic derivation methodology, we get an explicit expression for market price of risk, and we found that market price of risk is related to the position and the type of option contained in the portfolio. Fol-lowing Dennis Yang, we call it personal price of risk on Asian option(or Lookback option,and so on)We also discussed the portfolio optimization problem under stochastic volatility framework when the market consists all type of options, i.e. vanilla options and exotic options, we found that all options’ price is mutual dependence, i.e. the fair price of vanilla option is dependent on smax and never path-independence when the portfolio contain European option and Lookback options. Furthermore, we give the numerical result of option price, and verified the theoretical properties of options.Finally, we analysised the KODA option(Knock Out Discount Accumulator) which is popular in Hong Kong market recently. Under the risk-neutral martingale frame-work, we give an explicit formula for KODA option, and caculus some Hedging para-meters, like Delta and Gamma.