Dyson type formula for pure jump Lévy processes and applications to Finance

J. Vives Santa-Eulalia

The talk is based on the paper below. We obtain a Dyson type formula for integrable functionals of a pure jump Lévy process. We represent the conditional expectation of a random variable F at a time 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. For example, in pricing options under the Poisson-Black-Scholes model or in pricing discount bonds under a 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.

S. Jin, H. Schellhorn and J. Vives (2020): Dyson type formula for pure jump Lévy processes with some applications to finance. Stochastic Processes and their Applications 130 (2): 824-844.

Keywords: Stochastic Analysis, Malliavin calculus, Stochastic Finance

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