Option pricing under a Markov modulated model using a cubic B-spline collocation method
by Geraldine Tour; Désiré Yannick Tangman
International Journal of Business Intelligence and Data Mining (IJBIDM), Vol. 9, No. 4, 2014

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.

Online publication date: Fri, 10-Apr-2015

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