Variance Trading and Market Price of Variance Risk

Abstract:     
This paper develops a new approach for the variance trading. The approach departs from the existing literature by focusing on the empirically relevant realized variance, as opposed to the unobservable integrated variance. We show that the discretely-sampled realized variance can be robustly replicated under very general conditions, including when the price can jump. The replication strategy specifies the optimal timing for rebalancing in the underlying. The deviations from the optimal schedule can lead to surprisingly large hedging errors. The results have important implications for hedging actual instruments, such as OTC variance swaps and CBOE variance futures.

In the empirical application, we synthesize the prices of the variance contract on S&P 500 index over the 20-year period from 01/1990 to 12/2009. We find that the market variance risk is priced, its risk premium is negative and economically very large. The variance risk premium cannot be explained by the known risk factors and option returns. The variance contract appears to be even more “expensive” than the already puzzling index puts.

Number of Pages in PDF File: 49

Keywords: Variance Risk, Option Valuation, Risk-Neutral Density, Stochastic Volatility

JEL Classification: G12, G13, G23

working papers series