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Dyson type formula for pure jump Lévy processes with some applications to finance

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In this paper we obtain a Dyson type formula for integrable functionals of a pure jump Lévy process. We represent the conditional expectation of a $\mathscr{F}_T$-measurable random variable $F$ at a time $t \leq T$ as an exponential formula involving Malliavin derivatives evaluated along a frozen path. The series representation of this exponential formula turns out to be useful for different applications, and in particular in quantitative finance, as we show in the following examples: the first one is the pricing of options in the Poisson-Black-Scholes model; the second one is the pricing of discount bonds in the Lévy quadratic model. We also obtain, for the conditional expectation of a function of a finite number of the process values, a backward Taylor expansion, that turns out to be useful for numerical calculations.

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Stochastic Processes and their Applications, 2020, vol. 130, num. 2, p. 824-844

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Dyson type formula for pure jump Lévy processes with some applications to finance