The Term Structure of Variance Swaps and Risk Premia

Institute of Finance

Variance swaps are basic contracts to trade volatility. Over the last two decades, such contracts have become increasingly popular to hedge volatility risk in portfolio management. Surprisingly, risk premia embedded in such contracts have remained unexplored until recently. Professor Loriano Mancini at the Institute of Finance and Junior Chair at the Swiss Finance Institute develops a novel econometric technique to analyze risk premia in variance swaps in his article “The Term Structure of Variance Swaps and Risk Premia” that will appear in the renowned Journal of Econometrics.

A variance swap is effectively an insurance contract against volatility risk over a predetermined time horizon. The buyer of a variance swap agrees at inception that it will pay a fixed amount at the maturity of the contract, the variance swap rate, in exchange for receiving a floating amount based on the realized variance of the underlying asset, usually measured as the sum of the squared daily log-returns, from inception to maturity. Thus, buyers of variance swaps receive positive payoffs in high volatility periods and suffer financial losses during low volatility periods.

The above figure shows the term structure of variance swaps namely the variance swap rates over various maturities, ranging from 2 months to 2 years, quoted on any day between 1996 to 2010. The figure indicates that buying volatility protection during the 2007-2009 financial crisis was substantially more expensive than during quiet times such as 2005-2006.

Prof. Mancini and his co-authors, Yacine Ait-Sahalia (Princeton University) and Mustafa Karaman (University of Zurich), find that different parts of the variance swap term structure respond to different factors. For example, after a market drop, the risk premia investors are willing to pay (to insure against future volatility risk) generally increase across all maturities. The impact of a market drop on risk premia is more pronounced over short maturities but more persistent over long maturities.

The research article of Prof. Mancini and his co-authors generated a post written by the editor of “Systemic Risk and Systemic Value ― a non-profit project from and for senior managers and researchers”; see

The full research article is available at