Encyclopedia of Financial Models I

Pricing of Variance, Volatility, Covariance, and Correlation Swaps

ANATOLIY SWISHCHUK, PhD, DSc

Professor of Mathematics and Statistics, University of Calgary

Abstract: Swaps are useful for volatility hedging and speculation. Volatility swaps are forward contracts on future realized stock volatility, and variance swaps are similar contracts on variance, the square of future volatility. Covariance and correlation swaps are covariance and correlation forward contracts, respectively, of the underlying two assets. Using change of time method, one can model and price variance, volatility, covariance, and correlation swaps.

Variance, volatility, covariance, and correlation swaps are relatively recent financial products that market participants can use for volatility hedging and speculation. The market for these types of swaps has been growing, with many investment banks and other financial institutions now actively quoting volatility swaps on various assets: stock indexes, currencies, and commodities.

A stock’s volatility is the simplest measure of its riskiness or uncertainty. In this entry we describe, model, and price variance, volatility, covariance, and correlation swaps.

DESCRIPTION OF SWAPS

We begin with a description of the different kinds of swaps that we will be discussing in this entry: variance swaps, volatility swaps, covariance swaps, and correlation swaps. Table 1 provides a summary of studies dealing with these swaps.

Table 1 Summary of Studies Dealing with Variance, ...