DOUBLE BARRIER OPTIONS IN REGIME-SWITCHING HYPER-EXPONENTIAL JUMP-DIFFUSION MODELS

Mitya Boyarchenko () and Svetlana Boyarchenko
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Mitya Boyarchenko: Department of Mathematics, University of Michigan, 530 Church Street, 2074 East Hall, Ann Arbor, MI 48109-1043, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 07, 1005-1043

Abstract: We present a very fast and accurate algorithm for calculating prices of finite lived double barrier options with arbitrary terminal payoff functions under regime-switching hyper-exponential jump-diffusion (HEJD) models, which generalize the double-exponential jump-diffusion model pioneered by Kou and Lipton. Numerical tests demonstrate an excellent agreement of our results with those obtained using other methods, as well as a significant increase in computation speed (sometimes by a factor of 5). The first step of our approach is Carr's randomization, whose convergence we prove for barrier and double barrier options under strong Markov processes of a wide class. The resulting sequence of perpetual option pricing problems is solved using an efficient iteration algorithm and the Wiener-Hopf factorization.

Keywords: Option pricing; double barrier options; double-no-touch options; foreign exchange; double-exponential jump-diffusion; Kou's model; hyper-exponential jump-diffusion; Lévy process; regime switching; stochastic volatility; stochastic interest rate; Carr's randomization; Canadization; analytic method of lines; Wiener-Hopf factorization (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (15)

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DOI: 10.1142/S0219024911006620

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