Valuation of Continuous Asian Options: Comparison of Laplace Transform Inversion method with Monte Carlo Simulation
Abstract
Finance provides mathematics with challenging problems to be solved. Among them Asian options, i.e. options whose payoff depends on the average price of the underlying asset, that have characteristics such as their valuation requires the use of approximation techniques as, to this date, there is no known closed form analytical solution for arithmetic average options. Hence, different attempts to price average value options have been completed through various approaches (analytical approximation, binomial trees, Monte Carlo simulation...etc).
In this thesis, published on the Vernimmen website, we focus on one of the analytical methods, Laplace transform, developed initially in 1993 by Geman and Yor and extended later in different new modelling approaches. We realize an analysis of the results given by such method using the software Mathematica 7.0.1, using Monte Carlo simulation as a control variable and comparing the set of our results with the outputs from several numerical approximation techniques extracted from the existing literature on average options.
Keywords: Option pricing; Asian option; Laplace transform; Mathematica; Monte Carlo Simulation.
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