On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options

Authors:
Robert Frontczak;Rainer Schöbel
Affiliations:
Faculty of Economics and Business Administration, University of Tübingen, Mohlstrasse 36, 72074 Tübingen, Germany;Faculty of Economics and Business Administration, University of Tübingen, Mohlstrasse 36, 72074 Tübingen, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 6
Cited 1

50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications

Management Science
Compact finite difference method for American option pricing

Journal of Computational and Applied Mathematics
Adaptive θ-methods for pricing American options

Journal of Computational and Applied Mathematics
A fast high-order finite difference algorithm for pricing American options

Journal of Computational and Applied Mathematics
Optimal convergence rate of the explicit finite difference scheme for American option valuation

Journal of Computational and Applied Mathematics
Option pricing with Mellin transnforms

Mathematical and Computer Modelling: An International Journal

Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We extend a framework based on Mellin transforms and show how to modify the approach to value American call options on dividend-paying stocks. We present a new integral equation to determine the price of an American call option and its free boundary using modified Mellin transforms. We also show how to derive the pricing formula for perpetual American call options using the new framework. A result due to Kim (1990) [24] regarding the optimal exercise price at expiry is also recovered. Finally, we apply Gauss-Laguerre quadrature for the purpose of an efficient and accurate numerical valuation.