The Term Structure of Variance Swaps, Risk Premia and the Expectation Hypothesis

How does the market variance risk premium vary over time? Evidence from S&P 500 variance swap investment returns

“…We can see that the null hypothesis that the slope coefficient equals one (H 0 : b = 1) is rejected in all cases. This suggests that the P &L T t→t+h varies over time and it confirms the similar evidence provided by Carr and Wu (2009) and Ait-Sahalia et al (2013).…”

“…4 Alternatively, previous studies compute VRP by means of option trading strategies (e.g., Kapadia, 2003, Arisoy, 2010) or by taking a parametric approach where an assumed model is fitted either Britten-Jones and Neuberger (2000), Jiang and Tian (2005) and Carr and Wu (2009), these rates are synthesized using a particular portfolio of European options. However, the replication process of the VS rate yields a bias in the VRP calculation because it fails to account for jumps in the underlying asset (Demeterfi et al, 1999, Ait-Sahalia et al, 2013, Bondarenko, 2013, Du and Kapadia, 2013, the finite number of traded options Tian, 2005, 2007) and the artificially induced jumps by the replication algorithm (Andersen et al, 2011). Our VS data allow us to verify that this bias is significant and they enable us to circumvent it, thus providing reliable VRP estimates.…”

“…First, the synthesized VS rate is a biased estimator of E Q (RV ) in the presence of jumps in the underlying S&P 500 index (Demeterfi et al, 1999, Ait-Sahalia et al, 2013, Bondarenko, 2013, Du and Kapadia, 2013. More specifically, synthesized VS rates underestimate actual VS rates when downward jumps dominate with the bias being proportional to the jump intensity (Du and Kapadia, 2013).…”

“…Exploring whether the market VRP is predictable is also of importance to market participants who trade variance. 1 Typically, variance trading strategies yield a negative market VRP indicating that short volatility positions are profitable (e.g., Coval and Shumway, 2001, Driessen and Maenhout, 2007, Ait-Sahalia et al, 2013. However, these positions are vulnerable to sharp increases in market volatility; this was highlighted over the recent 2008 crisis where the single names variance swap market dried up Lee, 2009, Martin, 2013).…”

“…Third, we complement Egloff et al (2010) and Ait-Sahalia et al (2013) by providing evidence on the properties of investment strategies in the index variance swap markets.…”