Pricing Lookback Option under Stochastic Volatility

Abstract

Derivative securities, when used correctly, can help investors to increase theirs expected returns and minimize theirs exposure to risk. Options o er in uence and insurance for risk-averse investors. The pricing problems of the exotic options in nance do not have analytic solutions under stochastic volatility model and so it is di cult to calculate option prices or at least it requires a lot of time to compute them. Also the e ect of stochastic volatility model resolving shortcoming of the Black-Scholes model its ability to generate volatility satisfying the market observations and also providing a closed-form solution for the European options. This study provides the required theoretical framework to practitioners for the option price estimation. This thesis focuses on pricing for oating strike lookback put option and testing option pricing formulas for the Heston stochastic volatility model, which de nes the asset volatility as the stochastic process. Euler Maruyama method is the numerical simulation of a stochastic di erential equation and generate the stochastic process way approximation. To simulate stock price and volatility stochastic processes in Heston's model the Euler discretization can be used to approximate the paths of the stock price and variance processes on a discretize grid. The pricing method depends on the partial differential equation approach on Heston stochastic volatility model and homotopy analysis method. Heston model has received the most attention then it can give a acceptable explanation of the underlying asset dynamics. The resulting formula is well connected to a Black-Scholes price that is the rst term of the series expansion, which makes computing the option prices fairly e cient.