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Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

Author

Listed:
  • Bruno Casella

    (University of Warwick)

  • Gareth O. Roberts

    (University of Warwick)

Abstract

We introduce a novel algorithm (JEA) to simulate exactly from a class of one-dimensional jump-diffusion processes with state-dependent intensity. The simulation of the continuous component builds on the recent Exact Algorithm (Beskos et al., Bernoulli 12(6):1077–1098, 2006a). The simulation of the jump component instead employs a thinning algorithm with stochastic acceptance probabilities in the spirit of Glasserman and Merener (Proc R Soc Lond Ser A Math Phys Eng Sci 460(2041):111–127, 2004). In turn JEA allows unbiased Monte Carlo simulation of a wide class of functionals of the process’ trajectory, including discrete averages, max/min, crossing events, hitting times. Our numerical experiments show that the method outperforms Monte Carlo methods based on the Euler discretization.

Suggested Citation

  • Bruno Casella & Gareth O. Roberts, 2011. "Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 449-473, September.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:3:d:10.1007_s11009-009-9163-1
    DOI: 10.1007/s11009-009-9163-1
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    References listed on IDEAS

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    5. Platen, Eckhard & Rebolledo, Rolando, 1985. "Weak convergence of semimartingales and discretisation methods," Stochastic Processes and their Applications, Elsevier, vol. 20(1), pages 41-58, July.
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    Cited by:

    1. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    2. Wanmo Kang & Jong Mun Lee, 2019. "Unbiased Sensitivity Estimation of One-Dimensional Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 334-353, February.
    3. Yehuda Arav & Eyal Fattal & Ziv Klausner, 2022. "Is the Increased Transmissibility of SARS-CoV-2 Variants Driven by within or Outside-Host Processes?," Mathematics, MDPI, vol. 10(19), pages 1-17, September.
    4. K. Giesecke & H. Kakavand & M. Mousavi, 2011. "Exact Simulation of Point Processes with Stochastic Intensities," Operations Research, INFORMS, vol. 59(5), pages 1233-1245, October.
    5. Herrmann, Samuel & Massin, Nicolas, 2023. "Exact simulation of the first passage time through a given level of jump diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 553-576.
    6. Kay Giesecke & Dmitry Smelov, 2013. "Exact Sampling of Jump Diffusions," Operations Research, INFORMS, vol. 61(4), pages 894-907, August.
    7. Flávio B. Gonçalves & Gareth O. Roberts, 2014. "Exact Simulation Problems for Jump-Diffusions," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 907-930, December.
    8. Hermann, Simone & Ickstadt, Katja & Müller, Christine H., 2018. "Bayesian prediction for a jump diffusion process – With application to crack growth in fatigue experiments," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 83-96.
    9. Rudiger Frey & Verena Kock, 2021. "Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics," Papers 2109.11403, arXiv.org, revised Sep 2021.

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