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On Some Functionals Of The First Passage Times In Models With Switching Stochastic Volatility

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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)

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.

Suggested Citation

  • Pavel V. Gapeev & Oliver Brockhaus & Mathieu Dubois, 2018. "On Some Functionals Of The First Passage Times In Models With Switching Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-21, February.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:01:n:s0219024918500012
    DOI: 10.1142/S0219024918500012
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    References listed on IDEAS

    as
    1. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.
    2. Artur Sepp, 2004. "Analytical Pricing Of Double-Barrier Options Under A Double-Exponential Jump Diffusion Process: Applications Of Laplace Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 151-175.
    3. Zhengjun Jiang & Martijn Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Finance and Stochastics, Springer, vol. 12(3), pages 331-355, July.
    4. Giuseppe Di Graziano & L. C. G. Rogers, 2009. "Equity with Markov-modulated dividends," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 19-26.
    5. Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.
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