Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On constructive complex analysis in finance: Explicit formulas for Asian options

Author: Michael Schröder
Journal: Quart. Appl. Math. 66 (2008), 633-658
MSC (2000): Primary 33Cxx, 91B28; Secondary 33F05, 41A58, 41A60, 44A10
DOI: https://doi.org/10.1090/S0033-569X-08-01107-X
Published electronically: October 7, 2008
MathSciNet review: 2465139
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Abstract: This paper develops a two-stage approach to the explicit valuation of Asian options which stresses the rôle of complex analytic techniques in general, and special functions in particular. First, integral representations for their Black-Scholes values in terms of Hermite functions are obtained; this is based on a Laplace transform arising in the work of Yor, and proceeds by analytical inversion. Explicit formulas for these integrals are then derived as a second step; this is done by combining series and asymptotic expansions which have as terms at worst special functions such as the error integral. Numerical examples then illustrate how the results enable a benchmark valuation of these options.

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Michael Schröder
Affiliation: Keplerstraße 30, D-69469 Weinheim (Bergstraße), Germany

DOI: https://doi.org/10.1090/S0033-569X-08-01107-X
Keywords: Complex analytic methods and special functions in finance, Asian options, asymptotic expansions and series for Asian option valuation, parabolic cylinder functions, hypergeometric and confluent hypergeometric functions
Received by editor(s): March 1, 2007
Published electronically: October 7, 2008
Article copyright: © Copyright 2008 Michael Schröder

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