Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

4 Issues per year


CiteScore 2017: 0.67

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

Mathematical Citation Quotient (MCQ) 2016: 0.33

Online
ISSN
1569-3961
See all formats and pricing
More options …
Volume 20, Issue 4

Issues

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
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-09-16 | DOI: https://doi.org/10.1515/mcma-2014-0002

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

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.

Export Citation

© 2014 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Yuuki Ida, Tsuyoshi Kinoshita, and Tomohiro Matsumoto
Pacific Journal of Mathematics for Industry, 2018, Volume 10, Number 1
[2]
Hideharu Funahashi and Masaaki Kijima
Quantitative Finance, 2016, Volume 16, Number 6, Page 867

Comments (0)

Please log in or register to comment.
Log in