On pricing barrier options with regime switching

• Autores: Robert J. Elliott, Tak Kuen Siu, Chan Leunglung
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 256, Nº 1, 2014, págs. 196-210
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.07.034
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• Resumen

  • We consider the valuation of both European-style and American-style barrier options in a Markovian, regime-switching, Black�Scholes�Merton economy, where the price process of an underlying risky asset is governed by a Markovian, regime-switching, geometric Brownian motion. Both the probabilistic and partial differential equation (PDE), approaches are used to price the barrier options. For the probabilistic approach to value a Europeanstyle barrier option, we employ the fundamental matrix solution and the Fourier transform space to derive a (semi)-analytical solution. The PDE approach is employed to value an American barrier option, where we obtain a system of free-boundary, coupled PDEs and an analytical quadratic approximation to the price by solving the free-boundary problem.