On some functionals of the first passage times in jump models of stochastic volatility. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Gapeev, Pavel V.; Stoev, Yavor I.
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 1(2020)
• Page Start: 149
• Page End: 170
• Publication Date: 2020-01-02
• Subjects: Two-dimensional jump processes -- first exit times -- generalized Laplace transforms -- stochastic volatility -- boundary-value problems -- partial integro-differential equations -- solvable stochastic differential equations -- non-affine processes -- mean-reverting and diverting property; Primary: 60J65 -- 60G40 -- 60E10 -- Secondary: 34B05 -- 60J60 -- 35A09; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1657023
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We compute some functionals related to the generalized joint Laplace transforms of the first times at which two-dimensional jump processes exit half strips. It is assumed that the state space components are driven by Cox processes with both independent and common (positive) exponential jump components. The method of proof is based on the solutions of the equivalent partial integro-differential boundary-value problems for the associated value functions. The results are illustrated on several two-dimensional jump models of stochastic volatility which are based on non-affine analogs of certain mean-reverting or diverting diffusion processes representing closed-form solutions of the appropriate stochastic differential equations.