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Essentially exact asymptotic solutions for Asian derivatives

Published online by Cambridge University Press:  10 January 2012

S. SIYANKO
S. SIYANKO*
Affiliation:
University College London, Gower Street, London WC1E 6BT, UK email: sergei.siyanko.10@ucl.ac.uk
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Abstract

In this paper, we will show how to obtain asymptotic solutions for the problem of pricing Asian options. Under the assumption that the underlying follows geometric Brownian motion, we will derive Taylor expansion series for the fixed and floating strike Asian options. While there will be no analytical formulae for calculating expansion coefficients, we will provide relatively simple algorithms for calculating them. The methodology is particularly effective for the case of continuously sampled fixed-strike Asian calls where it takes only seconds to obtain constants for the Taylor expansion series that can converge beyond 10 significant digits. It is needless to say that we need to calculate Taylor expansion constants only once and the option price would be an analytical expression constructed from a cumulative normal distribution function, an exponential function and finite sums.

Keywords

Asian optionsoption pricingmatched asymptotic expansionsfinancial derivatives
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 3 , June 2012 , pp. 395 - 415
Copyright
Copyright © Cambridge University Press 2012

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