Stochastic Skew and Target Volatility Options

Target volatility options (TVO) are a new class of derivatives whose payoff depends on some measure of volatility. These options allow investors to take a joint exposure to the evolution of the underlying asset, as well as to its realized volatility. For instance, a target volatility call can be viewed as a European call whose notional amount depends on the ratio of the target volatility (a fixed quantity representing the investor's expectation of the future realized volatility) and the realized volatility of the underlying asset over the life of the option. In equity options markets the slope of the skew is largely independent of the volatility level. A single-factor Heston based volatility model can generate steep skew or flat skew at a given volatility level but cannot generate both for a given parameterization. Since the payoff corresponding to TVO is a function of the joint evolution of the underlying asset and its realized variance, the consideration of stochastic skew is a relevant question for the valuation of TVO. In this sense, this article studies the effect of considering a multifactor stochastic volatility specification in the valuation of the TVO. To this end, we consider the two-factor Heston-based model of Christoffersen et al. (2009) in order to investigate TVO, as well as forward-start TVO, that is, TVO where the strike is determined at a later date