Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

Alessandro Ramponi

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 2, 349-368

Abstract: Abstract In this paper we present a class of regime switching diffusion models described by a pair $(X(t), Y(t)) \in \mathbb{R}^n \times {\cal S}$ , ${\cal S} = \{1,2,\ldots, N \}$ , Y(t) being a Markov chain, for which the marginal probability of the diffusive component X(t) is a given mixture. Our main motivation is to extend to a multivariate setting the class of mixture models proposed by Brigo and Mercurio in a series of papers. Furthermore, a simple algorithm is available for simulating paths through a thinning mechanism. The application to option pricing is considered by proposing a mixture version for the Margrabe Option formula and the Heston stochastic volatility formula for a plain vanilla.

Keywords: Regime switching models; Mixture dynamics; Monte Carlo simulation; Option pricing; 60J60; 60J27; 65C05; 60H30 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11009-009-9155-1

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