Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
  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
Published electronically: October 7, 2008
MathSciNet review: 2465139
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 33Cxx, 91B28, 33F05, 41A58, 41A60, 44A10

Retrieve articles in all journals with MSC (2000): 33Cxx, 91B28, 33F05, 41A58, 41A60, 44A10


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0033-569X-08-01107-X
PII: S 0033-569X(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 Schr\"oder



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2015 Brown University
Comments: qam-query@ams.org
AMS Website