An Economic Motivation for Variance Contracts

Abstract

Variance contracts permit the trading of 'variance risk', i.e. the risk that the (squared) volatility of stock returns changes randomly over time. We discuss why investors might want to trade this type of risk, and why they might prefer a variance contract to standard calls and puts for this purpose.

Our main argument is that the variance contract is superior to a dynamic replication strategy due to discrete trading, parameter risk, and model risk. To show this we analyze the local hedging errors for the variance contract under different scenarios, namely under pure estimation risk (or parameter risk) in a stochastic volatility and in a jump-diffusion model, under model risk when the wrong type of risk factor is assumed to be present (stochastic volatility instead of jumps or vice versa), and under model risk when risk factors are omitted (e.g. when the true model contains jumps which are not present in the model assumed by the investor). The results confirm that the variance contract is exposed to model risk to an economically significant degree, and that it is much harder to hedge than, e.g., deep OTM puts. We thus conclude that the improvement provided by the introduction of a variance contract is greater than the one offered by the introduction of additional standard options.

Keywords: Variance Risk, Stochastic Volatility, Jump-Diffusion, Model Risk, Parameter Risk, Hedging Error

JEL Classification: G12, G13