The risk premium that never was: A fair value explanation of the volatility spread

We present a new framework to investigate the profitability of trading the volatility spread, the upward bias on implied volatility as an estimator of future realized volatility. The scheme incorporates the first four option-implied moments in a growth-optimal payoff that is statically replicated using a portfolio of options. Removing the upward bias on implied volatility worsens the likelihood score of risk-neutral densities obtained from S&P 500 index options when they are used as forecasts of the underlying index return distribution. It also results in negative expected capital growth when they are used in a volatility arbitrage scheme. Our empirical finding is that the upward bias on implied volatility does not represent a long-term return premium, rather it is required to mitigate the large losses associated with tail events when trading volatility in options markets.