Numerical pricing of several types of Asian options

Abstract

Option valuation is one of the more applied areas of mathematics. Options are financial derivatives whose value depends on the value of an underlying asset. They are frequently used in hedging to minimize the risk when trading in the underlying stock and therefore require accurate pricing. Though quite some research has been conducted on standard option types such as European options and American options, more exotic options such as conditional Asian options or Asian tail options are less known and therefore enjoyed far less attention from the research community. In this bachelor thesis we will focus on computing the correct price for the Asian option and various types of Asian options. A short introduction on these types of options will be given, after which mathematical models for pricing these types of options will be derived. Several numerical methods such as the Monte Carlo method and the finite difference method (applied to the Black-Scholes partial differential equation) will be used to approximate the true value of these types of options.