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Calculation of Probability of the Exit of a Stochastic Process from a Band by Monte-Carlo Method: A Wiener-Hopf Factorization

Author

Listed:
  • Grigory Beliavsky

    (Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 8A Milchakov St., Rostov-on-Don 344090, Russia)

  • Natalya Danilova

    (Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 8A Milchakov St., Rostov-on-Don 344090, Russia)

  • Guennady Ougolnitsky

    (Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 8A Milchakov St., Rostov-on-Don 344090, Russia)

Abstract

This paper considers a method of the calculation of probability of the exit from a band of the solution of a stochastic differential equation. The method is based on the approximation of the solution of the considered equation by a process which is received as a concatenation of Gauss processes, random partition of the interval, Girsanov transform and Wiener-Hopf factorization, and the Monte-Carlo method. The errors of approximation are estimated. The proposed method is illustrated by numerical examples.

Suggested Citation

  • Grigory Beliavsky & Natalya Danilova & Guennady Ougolnitsky, 2019. "Calculation of Probability of the Exit of a Stochastic Process from a Band by Monte-Carlo Method: A Wiener-Hopf Factorization," Mathematics, MDPI, vol. 7(7), pages 1-8, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:581-:d:244228
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    References listed on IDEAS

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    1. Ferreiro-Castilla, A. & Kyprianou, A.E. & Scheichl, R. & Suryanarayana, G., 2014. "Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 985-1010.
    2. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
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