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A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes

Author

Listed:
  • Maria Teresa Giraudo

    (Torino University)

  • Laura Sacerdote

    (Torino University)

  • Cristina Zucca

    (Torino University)

Abstract

A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.

Suggested Citation

  • Maria Teresa Giraudo & Laura Sacerdote & Cristina Zucca, 2001. "A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 3(2), pages 215-231, June.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:2:d:10.1023_a:1012261328124
    DOI: 10.1023/A:1012261328124
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    Citations

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    Cited by:

    1. L. Sacerdote & C. E. Smith, 2004. "Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 6(3), pages 323-341, September.
    2. Mario Abundo & Sara Furia, 2019. "Joint Distribution of First-Passage Time and First-Passage Area of Certain Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1283-1302, December.
    3. Qinglai Dong & Lirong Cui, 2019. "First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 1-23, March.
    4. Liqun Wang & Klaus Pötzelberger, 2007. "Crossing Probabilities for Diffusion Processes with Piecewise Continuous Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 21-40, March.
    5. Virginia Giorno & Amelia G. Nobile, 2021. "On the First-Passage Time Problem for a Feller-Type Diffusion Process," Mathematics, MDPI, vol. 9(19), pages 1-27, October.
    6. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.
    7. Giraudo, Maria Teresa, 2009. "An approximate formula for the first-crossing-time density of a Wiener process perturbed by random jumps," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1559-1567, July.
    8. Gustavo Manso, 2011. "Feedback Effects of Credit Ratings," 2011 Meeting Papers 1338, Society for Economic Dynamics.
    9. Manso, Gustavo, 2013. "Feedback effects of credit ratings," Journal of Financial Economics, Elsevier, vol. 109(2), pages 535-548.

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