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On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes

Author

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  • Pavel V. Gapeev

    (Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

  • Neofytos Rodosthenous

    (School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK)

  • V. L. Raju Chinthalapati

    (Southampton Business School, University of Southampton, Southampton SO17 1BJ, UK)

Abstract

We obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an independent exponential random time. It is assumed that the coefficients of the diffusion-type process are regular functions of the current values of its running maximum and minimum. The proof is based on the solution to the equivalent inhomogeneous ordinary differential boundary-value problem and the application of the normal-reflection conditions for the value function at the edges of the state space of the resulting three-dimensional Markov process. The result is related to the computation of probability characteristics of the take-profit and stop-loss values of a market trader during a given time period.

Suggested Citation

  • Pavel V. Gapeev & Neofytos Rodosthenous & V. L. Raju Chinthalapati, 2019. "On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes," Risks, MDPI, vol. 7(3), pages 1-15, August.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:3:p:87-:d:254934
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    References listed on IDEAS

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    7. Gapeev, Pavel V. & Rodosthenous, Neofytos, 2016. "Perpetual American options in diffusion-type models with running maxima and drawdowns," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2038-2061.
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    Cited by:

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