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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

CiteScore 2017: 0.67

SCImago Journal Rank (SJR) 2017: 0.417
Source Normalized Impact per Paper (SNIP) 2017: 0.860

Mathematical Citation Quotient (MCQ) 2017: 0.25

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Volume 20, Issue 4


A numerical scheme based on semi-static hedging strategy

Yuri Imamura / Yuta Ishigaki / Toshiki Okumura
  • Mizuho-DL Financial Technology Co., Ltd, Kojimachi-odori Building 12F, 2-4-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083, Japan
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Published Online: 2014-09-16 | DOI: https://doi.org/10.1515/mcma-2014-0002


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

MSC: 91G20; 91G60

About the article

Received: 2014-02-04

Accepted: 2014-08-28

Published Online: 2014-09-16

Published in Print: 2014-12-01

Funding Source: JSPS KAKENHI

Award identifier / Grant number: 24840042

Funding Source: JSPS KAKENHI

Award identifier / Grant number: 25285102

Funding Source: JSPS KAKENHI

Award identifier / Grant number: 26780193

Citation Information: Monte Carlo Methods and Applications, Volume 20, Issue 4, Pages 223–235, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2014-0002.

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