Hedging Volatility Risk

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 ofsuch an instrument are the basic ingredients of a successful financial product. Unlike theproposed volatility index option, the underlying of this proposed contract is a traded atthe-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.

Keywords: Straddle, Compound Options, Stochastic Volatility