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Exact Sampling of Jump Diffusions

Author

Listed:
  • Kay Giesecke

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Dmitry Smelov

    (Goldman Sachs & Co., New York, New York 10282)

Abstract

This paper develops a method for the exact simulation of a skeleton, a hitting time, and other functionals of a one-dimensional jump diffusion with state-dependent drift, volatility, jump intensity, and jump size. The method requires the drift function to be C 1 , the volatility function to be C 2 , and the jump intensity function to be locally bounded. No further structure is imposed on these functions. The method leads to unbiased simulation estimators of security prices, transition densities, hitting probabilities, and other quantities. Numerical results illustrate its features.

Suggested Citation

  • Kay Giesecke & Dmitry Smelov, 2013. "Exact Sampling of Jump Diffusions," Operations Research, INFORMS, vol. 61(4), pages 894-907, August.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:4:p:894-907
    DOI: 10.1287/opre.2013.1191
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    References listed on IDEAS

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    6. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    7. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    8. 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.
    9. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    10. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    11. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.
    12. Metzler Adam & Scott Alexandre, 2014. "Rare event simulation for diffusion processes via two-stage importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 20(2), pages 77-100, June.
    13. Angelos Dassios & Hongbiao Zhao, 2017. "Efficient Simulation of Clustering Jumps with CIR Intensity," Operations Research, INFORMS, vol. 65(6), pages 1494-1515, December.
    14. Li, Chenxu & Wu, Linjia, 2019. "Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 275(2), pages 768-779.
    15. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    16. Damiano Brigo & Fr'ed'eric Vrins, 2016. "Disentangling wrong-way risk: pricing CVA via change of measures and drift adjustment," Papers 1611.02877, arXiv.org.
    17. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    18. 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.
    19. 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.

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