A numerical scheme based on semi-static hedging strategy

Imamura Yuri (), Ishigaki Yuta () and Okumura Toshiki ()
Additional contact information
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

Monte Carlo Methods and Applications, 2014, vol. 20, issue 4, 223-235

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.

Keywords: Barrier options; put-call symmetry; static hedging; stochastic volatility models (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/mcma-2014-0002

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