Weak Euler Scheme for Stochastic Differential Equations with Applications in Finance

Abstract

In this thesis, a new type of path-dependent options, referred to as the average-Asian options, are introduced to further reduce the volatility of the underlying price risk and minimize the option manipulation threat. Euler method is adopted to discretize the associated stochastic differential equation, based on which the options are priced by using Monte Carlo simulations for both the cases when volatility is constant and when it is stochastic during the life of the option.