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A numerical scheme based on semi-static hedging strategy

Author

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  • 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. 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..
    2. 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.
    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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