Switching Levy Models in Continuous Time: Finite Distributions and Option Pricing
University of Essex, Centre for Computational Finance and Economic Agents (CCFEA) Working Paper
39 Pages Posted: 4 Nov 2005 Last revised: 23 May 2008
Date Written: 2005
Abstract
This paper introduces a general regime switching Levy process, and constructs the characteristic function in closed form. Correlations between the underlying Markov chain and the asset returns are also allowed, by imposing asset price jumps whenever a regime change takes place. Based on the characteristic function the conditional densities and vanilla option prices can be rapidly computed using FFT. It is shown that the regime switching model has the potential to capture a wide variety of implied volatility skews. The paper also discusses the pricing of exotic contracts, like barrier, Bermudan and American options, by implementation of a quadrature method. A detailed numerical experiment illustrates the application of the regime switching framework.
Keywords: volatility smile, volatility skew, derivative pricing, exotic derivatives, calibration
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