Unspanned Stochastic Volatility from an Empirical and Practical Perspective

Abstract

I study the relationship between interest rates and interest-rate volatility, particularly the idea of unspanned stochastic volatility (USV): volatility risk that cannot be hedged with bonds or swaps. Simulated data is used to assess the ability of regression-based techniques, popular but controversial in the literature, to identify and measure USV. With this backing, I consider data from several modern interest-rate markets, and find volatility to be largely, and often fully, unspanned. By comparing hedged and unhedged returns of interest-rate options, I assess volatility risk relative to interest-rate risk, providing a conceptual framework with quantitative guidelines.

Keywords: Interest-rate volatility, Unspanned stochastic volatility, Volatility risk, Hedging, Market completeness, Term structure models

JEL Classification: C63, E43, G12, G13