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Hedging European Derivatives with the Polynomial Variance Swap Under Uncertain Volatility Environments

23 Pages Posted: 22 Oct 2009 Last revised: 20 Jul 2011

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Yukihiro Tsuzuki

University of Tokyo - Graduate School of Economics

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: August 1, 2009

Abstract

This paper proposes a new hedging scheme of European derivatives under uncertain volatility environments, in which a weighted variance swap called the polynomial variance swap is added to the Black-Scholes delta hedging for managing exposure to volatility risk. In general, under these environments one cannot hedge the derivatives completely by using dynamic trading of only an underlying asset owing to volatility risk. Then, for hedging uncertain volatility risk, we design the polynomial variance, which can be dependent on the level of the underlying asset price. It is shown that the polynomial variance swap is not perfect, but more efficient as a hedging tool for the volatility exposure than the standard variance swap. In addition, our hedging scheme has a preferable property that any information on the volatility process of the underlying asset price is unnecessary. To demonstrate robustness of our scheme, we implement Monte Carlo simulation tests with three different settings, and compare the hedging performance of our scheme with that of standard dynamic hedging schemes such as the minimum-variance hedging. As a result, it is found that our scheme outperforms the others in all test cases. Moreover, it is noteworthy that the scheme proposed in this paper continues to be robust against model risks.

Keywords: European Derivatives, Black-Scholes Delta Hedging, Uncertain Volatility Risk, Polynomial Variance Swap

Suggested Citation

Takahashi, Akihiko and Tsuzuki, Yukihiro and Yamazaki, Akira, Hedging European Derivatives with the Polynomial Variance Swap Under Uncertain Volatility Environments (August 1, 2009). International Journal of Theoretical and Applied Finance, Vol. 14, No. 4, 2011. Available at SSRN: https://ssrn.com/abstract=1492276

Akihiko Takahashi (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Yukihiro Tsuzuki

University of Tokyo - Graduate School of Economics ( email )

Tokyo
Japan

Akira Yamazaki

Hosei University - Graduate School of Business Administration ( email )

Japan

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