Application of the Trefftz method for option pricing

Abstract

Purpose: Option pricing is hardly a new topic, however, in many cases they lack an analytical 11 solution. The article proposes a new approach to option pricing based on the semi-analytical 12 Trefftz method. 13 Design/methodology/approach: An appropriate transformation makes it possible to reduce the 14 Black-Scholes equation to the heat equation. This admits the Trefftz method (which has shown 15 its effectiveness in heat conduction problems) to be employed. The advantage of such 16 an approach lies in its computational simplicity and in the fact that it delivers a solution 17 satisfying the governing equation. 18 Findings: The theoretical option pricing problem being considered in the paper has been solved 19 by means of the Trefftz method, and the results achieved appear to comply with those taken 20 from the Black-Scholes formula. Numerical simulations have been carried out and compared, 21 which has confirmed the accuracy of the proposed approach. 22 Originality/value: Although a number of solutions to the Black-Scholes model have appeared, 23 the paper presents a thoroughly novel idea of implementation of the Trefftz method for solving 24 this model. So far, the method has been applied to problems having nothing in common with 25 finance. Therefore the present approach might be a starting point for software development, 26 competitive to the existing methods of pricing options.