Pricing Asian options via compound gamma and orthogonal polynomials Academic Article

abstract

• 2015 Elsevier Inc. All rights reserved. Abstract We develop two approximations (CG3 and CGn) for pricing arithmetic Asian options. Approximation CG3 utilizes a compound gamma distribution of the price average. It is calibrated by analytically matching the first three moments. Approximation CG3 outperforms many other existing approximations. Approximation CGn expands CG3 by utilizing the concept of orthogonal polynomials and matches n > 3 moments. It produces "near-exact" results, within 1 s, when volatility and maturity are not too high. Two useful insights of our work are (i) demonstrating that orthogonal polynomials can be used effectively to improve accuracy and (ii) showing that matching higher moments is beneficial.

authors

• Aprahamian, Hrayer

published proceedings

• APPLIED MATHEMATICS AND COMPUTATION

author list (cited authors)

• Aprahamian, H., & Maddah, B.

citation count

• 9

complete list of authors

• Aprahamian, Hrayer||Maddah, Bacel

publication date

• January 2015

publisher

• Elsevier  Publisher

published in

• Applied Mathematics and Computation  Journal

keywords

• Analytical Approximation
• Asian Options
• Compound Gamma Distribution
• Exotic Options
• Orthogonal Polynomials

Digital Object Identifier (DOI)

• 10.1016/j.amc.2015.04.041

start page

• 21

end page

• 43

volume

• 264

issue

• C

URL

• http://dx.doi.org/10.1016/j.amc.2015.04.041