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On a symmetrization of diffusion processes

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  • Jirô Akahori
  • Yuri Imamura

Abstract

The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion processes. The present paper aims to give a basis to the use of the numerical scheme for Heston and SABR-type stochastic volatility models. This will be done by showing a fairly general result on the symmetrization (in multi-dimension/multi-reflections). Further applications (to time-inhomogeneous diffusions/ to time-dependent boundaries/to curved boundaries) are also discussed.

Suggested Citation

  • Jirô Akahori & Yuri Imamura, 2014. "On a symmetrization of diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1211-1216, July.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:7:p:1211-1216
    DOI: 10.1080/14697688.2013.825923
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    References listed on IDEAS

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    1. Yuri Imamura & Katsuya Takagi, 2011. "Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion," Papers 1104.4548, arXiv.org, revised Oct 2012.
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    Cited by:

    1. Yuji Hishida & Yuta Ishigaki & Toshiki Okumura, 2019. "A Numerical Scheme for Expectations with First Hitting Time to Smooth Boundary," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(4), pages 553-565, December.
    2. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2017. "The Value of Timing Risk," Papers 1701.05695, arXiv.org.
    3. Akahori, Jirô & Fan, Jie Yen & Imamura, Yuri, 2023. "On the convergence order of a binary tree approximation of symmetrized diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 263-277.
    4. Yuri Imamura & Yuta Ishigaki & Takuya Kawagoe & Toshiki Okumura, 2012. "A Numerical Scheme Based on Semi-Static Hedging Strategy," Papers 1206.2934, arXiv.org, revised Aug 2012.
    5. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2018. "Asymptotic Static Hedge via Symmetrization," Papers 1801.04045, arXiv.org.
    6. Ngo, Hoang-Long & Taguchi, Dai, 2017. "Strong convergence for the Euler–Maruyama approximation of stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 55-63.
    7. Ngo, Hoang-Long & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 102-112.

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