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.
['Geraldine Tour', 'Désiré Yannick Tangman']
Option pricing under a Markov modulated model using a cubic B-spline collocation method