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

Akihiko Takahashi, Yukihiro Tsuzuki and Akira Yamazaki
Additional contact information
Akihiko Takahashi: Faculty of Economics, University of Tokyo
Yukihiro Tsuzuki: Mizuho-DL Financial Technology Co., Ltd.
Akira Yamazaki: Graduate School of Economics, University of Tokyo

No CIRJE-F-777, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 22pages
Date: 2010-11
New Economics Papers: this item is included in nep-fmk and nep-rmg
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf777.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2010cf777

Access Statistics for this paper

More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by CIRJE administrative office ().