Anchoring Options on Variance and Volatility to Terminal Risk Neutral Distribution

Abstract

In this paper the ratio of realized variance to the terminal squared return is modeled as independently distributed. Variance and volatility options are then first priced conditional on the terminal stock price. The variance and volatility options and their risk exposures are associated with option portfolios hedging the conditional price function. In particular the volatility swap vega is observed to be near a point above the variance swap vega. The residual uncertainty given the terminal stock price is modeled both using a log normal model and the empirical distribution.