Comparison of Price Simulation of European Lookback Option and Discrete Asian Option

Abstract

As a matter of fact, this study focuses on the comparison of European Lookback Option and Discrete Asian option based on Monte Carlo Method and Binary Tree model. In the first step, options and methods are introduced, together with their mathematical principles and expressions. Next, parameters used are provided, including ideal condition and historic data of Unilever. Simulations are made and price gap and price distribution are discussed. Then, sensitive researches are done through changing volatility and strike price. The relationship among price gaps method and the principles of the method has also been taken into consideration. It is found that price trend based on Monte Carlo Method is linear-like while price based on Binary Tree Model is exponential-like. Price gap keeps gradually increasing, which is due to characteristics of the method. Moreover, for a given and fixed volatility, the higher the strike price, the lower the price simulated and vice versa, this is explained mathematically. Finally, limitations, future outlooks and conclusions are made.