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arXiv · 1206.2934

A Numerical Scheme Based on Semi-Static Hedging Strategy

Yuri Imamura·Yuta Ishigaki·Takuya Kawagoe·Toshiki Okumura
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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. For getting 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 applying (path-independent) Euler-Maruyama approximation to our scheme, comparing them with the path-dependent Euler-Maruyama scheme when the model is of the Black-Scholes, CEV, Heston, and $ (λ) $-SABR, respectively. The results show the effectiveness of our scheme.

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Yuri Imamura, Yuta Ishigaki, Takuya Kawagoe, Toshiki Okumura. 2012-08-18. A Numerical Scheme Based on Semi-Static Hedging Strategy. https://arxiv.org/abs/1206.2934

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