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Speeding up the Euler scheme for killed diffusions

Author

Listed:
  • Umut Çetin

    (London School of Economics and Political Science)

  • Julien Hok

    (Investec Bank)

Abstract

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

Suggested Citation

  • Umut Çetin & Julien Hok, 2024. "Speeding up the Euler scheme for killed diffusions," Finance and Stochastics, Springer, vol. 28(3), pages 663-707, July.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:3:d:10.1007_s00780-024-00534-4
    DOI: 10.1007/s00780-024-00534-4
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    References listed on IDEAS

    as
    1. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    2. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    3. 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.
    4. 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.
    5. 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.
    6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Julien Hok & Sergei Kucherenko, 2021. "Pricing and Risk Analysis in Hyperbolic Local Volatility Model with Quasi Monte Carlo," Papers 2106.08421, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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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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