Statistical Inference on a Black-Scholes Model with Jumps. Application in Hydrology

Jasmine Cesars (1, 2) , Sylvère Paul Nuiro (1, 2) , Jean Vaillant (2, 1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications [UR1_1]
2 UA - Université des Antilles

We consider a Stochastic Differential Equation (SDE) driven by a Wiener process and a Poisson measure. This latter measure is associated with a sequence of identically distributed jump amplitudes. Properties of the SDE solution are presented with respect to the associated Wiener and Poisson processes. An algorithm is provided allowing exact numerical simulations of such SDE and implementable within R environment. Statistical inference tools are presented and applied to hydrology data.

Mots clés: Stochastic Differential Equation; Wiener Process; Poisson Process; Likelihood Technique

Domaines: Théorie [stat.TH]; Mathématiques [math]; Statistiques [math.ST]; Applications [stat.AP]

Jasmine Cesars, Sylvère Paul Nuiro, Jean Vaillant. Statistical Inference on a Black-Scholes Model with Jumps. Application in Hydrology. Journal of Mathematics and Statistics, 2019, ⟨10.3844/jmssp.2019.196.200⟩. ⟨hal-02306481⟩