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A numerical scheme based on semi-static hedging strategy

Author

Listed:
  • Imamura Yuri

    (Department of Mathematical Sciences, Ritsumeikan University, 1-1-1, Nojihigashi, Kusatsu, Shiga, 525-8577, Japan)

  • Ishigaki Yuta

    (COSMEDIA. CO., LTD, Iwamotocho Toyo Building, 3-1-2, Iwamotocho, Chiyodaku, Tokyo, 101-0032, Japan)

  • Okumura Toshiki

    (Mizuho-DL Financial Technology Co., Ltd, Kojimachi-odori Building 12F, 2-4-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083, Japan)

Abstract

In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. To get the static hedging formula, the underlying process needs to have a symmetry. We introduce a way to “symmetrize” a given diffusion process. Then the pricing of a barrier option is reduced to that of plain options under the symmetrized process. To show how our symmetrization scheme works, we will present some numerical results of path-independent Euler–Maruyama approximation applied to our scheme, comparing them with the path-dependent Euler–Maruyama scheme when the model is of the type Black–Scholes, CEV, Heston, and (λ)-SABR, respectively. The results show the effectiveness of our scheme.

Suggested Citation

  • Imamura Yuri & Ishigaki Yuta & Okumura Toshiki, 2014. "A numerical scheme based on semi-static hedging strategy," Monte Carlo Methods and Applications, De Gruyter, vol. 20(4), pages 223-235, December.
    • Handle: RePEc:bpj:mcmeap:v:20:y:2014:i:4:p:223-235:n:1
    DOI: 10.1515/mcma-2014-0002
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    References listed on IDEAS

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    1. Yuri Imamura, 2011. "A remark on static hedging of options written on the last exit time," Review of Derivatives Research, Springer, vol. 14(3), pages 333-347, October.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    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. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Hideharu Funahashi & Masaaki Kijima, 2016. "Analytical pricing of single barrier options under local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 867-886, June.

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