Title: Option pricing under a Markov modulated model using a cubic B-spline collocation method

Authors: Geraldine Tour; Désiré Yannick Tangman

Addresses: Department of Mathematics, University of Mauritius, Réduit, Mauritius ' Department of Mathematics, University of Mauritius, Réduit, Mauritius

Abstract: In this paper, we consider the extension of the cubic B-spline collocation method to price path-dependent and exotic options when the price dynamics of the underlying asset are governed by a Markovian process. In this setting, the classical Black-Scholes model is generalised to incorporate Markov-switching (regime-switching) properties which account for the influence of economic factors on asset price dynamics. Our numerical results presented using the Black-Scholes two regime-switching model demonstrate that the cubic B-spline collocation method not only yields second order convergent prices and hedging parameters, but it is also more accurate when the problem is convectively dominated.

Keywords: collocation method; option pricing; Markov switching; cubic B-splines; asset price dynamics; second order convergent prices; hedging parameters.

DOI: 10.1504/IJBIDM.2014.068459

International Journal of Business Intelligence and Data Mining, 2014 Vol.9 No.4, pp.356 - 370

Published online: 10 Apr 2015 *

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