Pricing Asian options via compound gamma and orthogonal polynomials
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Elsevier Inc.
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. © 2015 Elsevier Inc. All rights reserved.
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Analytical approximation, Asian options, Compound gamma distribution, Exotic options, Orthogonal polynomials, Costs, Polynomials, Probability distributions, Exotic option, Gamma distribution, Orthogonal polynomial, Orthogonal functions