We present an explicit formula and a multinomial approach for pricing contingent claims under a regime-switching jump–diffusion model. The explicit formula, obtained as anexpectation of Merton-type formulae for jump–diffusion processes, allows to compute theprice of European options in the case of a two-regime economy with lognormal jumps,while the multinomial approach allows to accommodate an arbitrary number of regimesand a generic jump size distribution, and is suitable for pricing American-style options.The latter algorithm discretizes log-returns in each regime independently, starting fromthe highest volatility regime where a recombining multinomial lattice is established. Inthe remaining regimes, lattice nodes are the same but branching probabilities are adjusted.Derivative prices are computed by a backward induction scheme.

Option pricing under regime-switching jump-diffusion models

COSTABILE, Massimo;LECCADITO, ARTURO;MASSABO', Ivar;RUSSO, EMILIO
2014-01-01

Abstract

We present an explicit formula and a multinomial approach for pricing contingent claims under a regime-switching jump–diffusion model. The explicit formula, obtained as anexpectation of Merton-type formulae for jump–diffusion processes, allows to compute theprice of European options in the case of a two-regime economy with lognormal jumps,while the multinomial approach allows to accommodate an arbitrary number of regimesand a generic jump size distribution, and is suitable for pricing American-style options.The latter algorithm discretizes log-returns in each regime independently, starting fromthe highest volatility regime where a recombining multinomial lattice is established. Inthe remaining regimes, lattice nodes are the same but branching probabilities are adjusted.Derivative prices are computed by a backward induction scheme.
2014
Option pricing, Regime-switching models, Jump–diffusion models, Multinomial tree
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/134617
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