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Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

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  • Alessandro Ramponi

    (University of Rome—Tor Vergata)

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.

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  • Alessandro Ramponi, 2011. "Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 349-368, June.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9155-1
    DOI: 10.1007/s11009-009-9155-1
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    Cited by:

    1. Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.
    2. Zhang, Xiaoyuan & Zhang, Tianqi, 2023. "On pricing double-barrier options with Markov regime switching," Finance Research Letters, Elsevier, vol. 51(C).
    3. Lux, Thomas, 2013. "Exact solutions for the transient densities of continuous-time Markov switching models: With an application to the poisson multifractal model," Kiel Working Papers 1871, Kiel Institute for the World Economy (IfW Kiel).
    4. Samuel Drapeau & Yunbo Zhang, 2019. "Pricing and Hedging Performance on Pegged FX Markets Based on a Regime Switching Model," Papers 1910.08344, arXiv.org, revised May 2020.

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