Model Risk in Variance Swap Rates

Different theoretical and numerical methods for calculating the fair-value of a variance swap give rise to systematic biases that are most pronounced during volatile periods. For instance, differences of 10-20 percentage points would have been observed on fair-value index variance swap rates during the banking crisis in 2008, depending on the formula used and its implementation. Our empirical study utilizes more than 16 years of FTSE 100 daily options prices to compare three fair-value variance swap rates. The exchange's variance swap rate formula, used to quote volatility indices such as VIX, has an upward bias induced by Riemann sum numerical integration that empirically outweighs the negative jump and discrete-monitorization biases that are inherent in this fair-value formula. On average, the exchange's methodology provides less accurate predictors of discretely-monitored realised volatility than the approximate swap rate formula introduced in this paper, which we implement using an almost exact analytical integration technique