Variance Contracts: Fixed Income Security Design

This chapter provides a general framework for designing and pricing variance swaps referencing fixed income securities. In a variance swap contract, the seller pays the amount by which the realized variance of some market variable of interest over a fixed time horizon exceeds a threshold—the variance swap rate—agreed upon at the trade’s inception. As such, the variance swap rate represents the market’s expectation of future variance, and in turn serves as the basis of a volatility gauge. Certain conditions are required of the contract design in order for the variance swap rate to be priced with as few modeling assumptions as possible, and ideally lead to a model-independent volatility gauge. Some theoretical and empirical properties of these volatility gauges are presented.