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A Numerical Scheme for Expectations with First Hitting Time to Smooth Boundary

Author

Listed:
  • Yuji Hishida

    (Mizuho Securities Asia Limited)

  • Yuta Ishigaki

    (COSMEDIA. CO., LTD)

  • Toshiki Okumura

    (The Dai-ichi Life Insurance Company, Limited)

Abstract

In the present paper, we propose a numerical scheme to calculate expectations with first hitting time to a given smooth boundary, in view of the application to the pricing of options with non-linear barriers. To attack the problem, we rely on the symmetrization technique in Akahori and Imamura (Quant Finance 14(7):1211–1216, 2014) and Imamura et al. (Monte Carlo Methods Appl 20(4):223–235, 2014), with some modifications. To see the effectiveness, we perform some numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:apfinm:v:26:y:2019:i:4:d:10.1007_s10690-019-09278-0
    DOI: 10.1007/s10690-019-09278-0
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    References listed on IDEAS

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    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. Yuuki Ida & Tsuyoshi Kinoshita, 2019. "Hyperbolic Symmetrization of Heston Type Diffusion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 355-364, September.
    3. Jirô Akahori & Yuri Imamura, 2014. "On a symmetrization of diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1211-1216, July.
    Full references (including those not matched with items on IDEAS)

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