The Characteristic Function of the Time-Integral of Geometric Brownian Motion and its Application in Asian Option Pricing

Master thesis (2023)

Authors

T. Wever Electrical Engineering, Mathematics and Computer Science

Contributors

F. Fang Numerical Analysis - EEMCS (graduation committee member)
Cornelis Vuik Delft Institute of Applied Mathematics (mentor)
A. Papapantoleon Applied Probability - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Teun Wever
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Published Date

17-03-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this research a new method for pricing continuous Arithmetic averaged Asian options is proposed. The computation is based on Fourier-cosine expansion, namely the COS method. Therefore, we derive the characteristic function of Integrated Geometric Brownian Motion based on Bougerol's identity.

Extensive numerical error analysis on the CDF recovery of IGBM and the option prices is performed. Via numerical tests, the convergence of errors using our new method has been proved. We are able to price continuous Arithmetic averaged Asian options with a minimal error of order 10-2, and a maximum precision of order 10-5 within seconds.