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
Full-text PDF Free Access
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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.
References
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References
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Additional Information
Michael Schröder
Affiliation:
Keplerstraße 30, D-69469 Weinheim (Bergstraße), Germany
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