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On a Symmetrization of Diffusion Processes

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  • Jiro 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 process. The present paper aims to give a mathematical credit to the use of the numerical scheme for Heston or 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

  • Jiro Akahori & Yuri Imamura, 2012. "On a Symmetrization of Diffusion Processes," Papers 1206.5983, arXiv.org.
  • Handle: RePEc:arx:papers:1206.5983
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    Cited by:

    1. 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.
    2. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2018. "Asymptotic Static Hedge via Symmetrization," Papers 1801.04045, arXiv.org.
    3. 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.
    4. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2017. "The Value of Timing Risk," Papers 1701.05695, arXiv.org.

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