Asymptotic extrapolation of model-free implied variance: exploring structural underestimation in the VIX Index

Abstract We show that the VIX Index structurally underestimates model-free implied volatility because its implementation omits extrapolation of smile in tails. use asymptotic behavior surface to construct a correction term is model-independent and only requires option prices at two outermost strikes. how apply this ex-post as well modify accordingly. Furthermore, we degree underestimation varies over time. For S&P 500 DJIA error larger periods sustained low volatility. This cannot be observed for Volatility-of-VIX Index.