Asian Options And Programming

In this master dissertation, first we introduce different ways to evaluate the asian options by the means of statistics, martingale and PDEs. Then we develop a model of Asian options with the drift rate and the volatility which follow some stochastic differential equations. Then with a non-random stopping time, I have calculated a lower bound for the geometric average Asian options with fixed strike price. Thanks to the dual martingale, we can get explicit solutions to the geometric average Asian options with fixed strike price. Then, I incorporate the stochastic volatility into the Asian option model, and by the means of Monte Carlo Method,I give a numerical solution to it. At last, based on the Black-Scholes model, using the work of modeling the effects of transaction costs which was done by Hoggard, Whalley and wilmott, we have developed a model for Asian options where we have the costs both proportional to the value traded and constant and give a numerical solution.