November 2000
Menachem Brenner, Ernest Y. Ou, and Jin E. Zhang
ABSTRACT
Volatility risk has played a major role in several financial debacles (for example, Barings Bank, Long Term
Capital Management). This risk could have been managed using options on volatility which were proposed in the past
but were never offered for trading mainly due to the lack of a tradable underlying asset.
The objective of this paper is to introduce a new volatility instrument, an option on a straddle, which can be
used to hedge volatility risk. The design and valuation of such an instrument are the basic ingredients of a successful
financial product. Unlike the proposed volatility index option, the underlying of this proposed contract is a traded
at-the-money-forward straddle, which should be more appealing to potential participants. In order to value these
options, we combine the approaches of compound options and stochastic volatility. We use the lognormal process
for the underlying asset, the Orenstein-Uhlenbeck process for volatility, and assume that the two Brownian motions
are independent. Our numerical results show that the straddle option price is very sensitive to the changes in
volatility which means that the proposed contract is indeed a very powerful instrument to hedge volatility risk.
Menachem Brenner
Institution: Stern School of Business, New York University
Email: mbrenner@stern.nyu.edu
Telephone: (212) 998-0323
Ernest Y. Ou
Institution: ABN AMRO, Inc.
Email: Yi.Ou@abnamro.com
Jin E. Zhang
Institution: Department of Economics and Finance, City University of Hong Kong
Email: efjzhang@cityu.edu.hk
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