Pricing of Asian options using Monte carlo method

Abstract

Monte Carlo methods provide approximate solutions to a variety of mathematical problems by performing statistical sampling experiments. They can be loosely defined as statistical simulation methods, where statistical simulation is defined in quite general terms to be any method that utilizes sequences of random numbers to perform the simulation. Among various Asian options, we will focus on the discretely geometric average Asian option, and survey how to evaluate the analytic solution of price of discretely geometric average Asian option and numerical solutions using two Monte Carlo methods. Moreover, we compare variances of numerical solutions, which are crude Monte Carlo and Stratified sampling and proof that Stratified sampling method is more accurate than crude Monte Carlo method by computing experiments.