In this paper we present a class of regime switching diffusion models described by a pair (X(t),Y(t)) ∈ Rn × S, S = {1, 2, . . . , 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 theMargrabe Option formula and the Heston stochastic volatility formula for a plain vanilla.
Ramponi, A. (2011). Mixture dynamics and regime switching diffusions with application to option pricing. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 13(2), 349-368 [10.1007/s11009-009-9155-1].
Mixture dynamics and regime switching diffusions with application to option pricing
RAMPONI, ALESSANDRO
2011-01-01
Abstract
In this paper we present a class of regime switching diffusion models described by a pair (X(t),Y(t)) ∈ Rn × S, S = {1, 2, . . . , 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 theMargrabe Option formula and the Heston stochastic volatility formula for a plain vanilla.File | Dimensione | Formato | |
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