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ON SOME FUNCTIONALS OF THE FIRST PASSAGE TIMES IN MODELS WITH SWITCHING STOCHASTIC VOLATILITY

Pavel V. Gapeev (), Oliver Brockhaus and Mathieu Dubois
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Pavel V. Gapeev: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK
Oliver Brockhaus: Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK
Mathieu Dubois: Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 01, 1-21

Abstract: We compute some functionals related to the joint generalized Laplace transforms of the first times at which two-dimensional diffusion-type Markov processes exit half strips. It is assumed that the state space components are driven by constantly correlated Brownian motions and the dynamics of the coefficients are described by a continuous-time Markov chain. The method of proof is based on the solutions of the equivalent boundary-value problems for systems of elliptic-type partial differential equations for the associated value functions. The results are illustrated on several two-dimensional continuous mean-reverting or diverting models of switching stochastic volatility.

Keywords: Two-dimensional diffusion-type processes; continuous-time Markov chains; first exit times; generalized Laplace transforms; stochastic volatility; boundary-value problems; elliptic-type partial differential equations; mean-reverting and diverting property (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219024918500012

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