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Speeding up the Euler scheme for killed diffusions

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  • Cetin, Umut
  • Hok, Julien

Abstract

Let X be a linear diffusion taking values in (ℓ,r) and consider the standard Euler scheme to compute an approximation to E[g(X T)1 {T

Suggested Citation

  • Cetin, Umut & Hok, Julien, 2024. "Speeding up the Euler scheme for killed diffusions," LSE Research Online Documents on Economics 120789, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:120789
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    File URL: http://eprints.lse.ac.uk/120789/
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    References listed on IDEAS

    as
    1. Remigijus Mikulevicius & Eckhard Platen, 1991. "Rate of Convergence of the Euler Approximation for Diffusion Processes," Published Paper Series 1991-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    2. Julien Hok & Sergei Kucherenko, 2021. "Pricing and Risk Analysis in Hyperbolic Local Volatility Model with Quasi Monte Carlo," Papers 2106.08421, arXiv.org.
    3. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    4. Julien Hok & Shih-Hau Tan, 2019. "Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 609-637, December.
    5. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    6. Evans, Steven N. & Hening, Alexandru, 2019. "Markov processes conditioned on their location at large exponential times," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1622-1658.
    7. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion Formulas For European Quanto Options In A Local Volatility Fx-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-43, March.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    9. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion formulas for European quanto options in a local volatility FX-LIBOR model," Papers 1801.01205, arXiv.org, revised Apr 2018.
    10. Alfonsi, Aurélien, 2013. "Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 602-607.
    11. Jacinto Marabel Romo, 2012. "The Quanto Adjustment and the Smile," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(9), pages 877-908, September.
    12. Emanuel Derman & Iraj Kani, 1998. "Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 61-110.
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    More about this item

    Keywords

    diffusions with killing; Euler-Maruyama scheme; drift-implicit scheme; weak convergence; recurrent transformations; strict local martingales; Kato classes; barrier options;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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