Time to Maturity Volatility : An Application to Index Derivatives

The basic assumption of the Black-Scholes option pricing is that volatility is constant over the time to maturity of the option. We consider how the estimation of volatility is affected by the time to maturity. In particular, we consider the empirical distribution of volatility as a function of the time to maturity and propose a threshold estimator based on the reverting behavior of implied volatility towards the median of the empirical volatility distribution. This estimator is compared with implied and historical volatility estimators in a forecasting study of the Australian SPI 200 index futures contract. The new estimator generates smaller forecast errors of realized volatility and is the basis of a profitable trading strategy