The Term Structure of Uncertainty Implied by Option Premia

Information describing future asset price distributions is fundamental to nearly all risk management activities. Futures markets are often relied upon to provide information abut the mean of future price distributions, and option markets are often used to recover measures of volatility. In cases where multiple maturities of an underlying asset trade, techniques for inferring implied forward price levels are well-understood, less information is readily accessible about other moments of a future asset price distribution or about the future time path of uncertainty. There is strong and widely-accepted empirical evidence that asset prices do not follow constant volatility models but instead contain intervals of relatively increased and subdued information events (Heynen, et al.). Techniques for recovering implied forward volatility estimates are conceptually equivalent to recovering implied forward price levels, yet little empirical work doing so currently exists. This paper demonstrates a simple technique for inferring implied forward volatilities of asset prices from options data. Using hog futures options market data, the implied term structure of uncertainty is recovered and used to examine the constancy of forecasted volatility, and the expected significance of USDA Hogs and Pigs Report releases. The results indicate a non-constant term structure of uncertainty, yet demonstrate little impact on forecasted volatilities in periods that contain USDA Hogs and Pigs Reports.