Taiwanese Journal of Mathematics

A Method-of-lines Approach for Solving American Option Problems

Min-Sun Horng, Tzyy-Leng Horng, and Chih-Yuan Tien

Full-text: Open access

Abstract

The early exercise property of American option changes the original Black-Scholes equation to an inequality that cannot be solved via traditional finite difference method. Therefore, finding the early exercise boundary prior to spatial discretization is a must in each time step. This overhead slows down the computation and the accuracy of solution relies on if the early exercise boundary can be accurately located. A simple numerical method based on finite difference and method of lines is proposed here to overcome this difficulty in American option valuation. Our method averts the otherwise necessary procedure of locating the optimal exercise boundary before applying finite difference discretization. The method is efficient and flexible to all kinds of pay-off. Computations of American put, American call with dividend, American strangle, two-factor American basket put option, and two-factor convertible bond with embedded call and put options are demonstrated to show the efficiency of the current method.

Article information

Source
Taiwanese J. Math., Volume 23, Number 5 (2019), 1253-1270.

Dates
Received: 2 April 2018
Revised: 2 October 2018
Accepted: 23 October 2018
First available in Project Euclid: 8 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1541667765

Digital Object Identifier
doi:10.11650/tjm/181010

Mathematical Reviews number (MathSciNet)
MR4012378

Subjects
Primary: 65M06: Finite difference methods 65M20: Method of lines 91G60: Numerical methods (including Monte Carlo methods) 62P05: Applications to actuarial sciences and financial mathematics 97M30: Financial and insurance mathematics

Keywords
American option method of lines finite difference method American strangle option two-factor American basket put option callable and putable convertible bond

Citation

Horng, Min-Sun; Horng, Tzyy-Leng; Tien, Chih-Yuan. A Method-of-lines Approach for Solving American Option Problems. Taiwanese J. Math. 23 (2019), no. 5, 1253--1270. doi:10.11650/tjm/181010. https://projecteuclid.org/euclid.twjm/1541667765


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