New Approach to Estimating VIX Truncation Errors Using Corridor Variance Swaps

Abstract

The original VIX index (now called VXO) uses 8 at the money calls and puts to measure implied volatility for the S&P 100 Index at a 30-day maturity. The new VIX formula uses all out of the money calls and puts to implement a formula that, in principle, requires options with strike prices that span the full range of possible stock prices at expiration. No actual market lists strike prices over such a wide range. Even for options on a highly active and liquid index like the S&P 500, the most remote tails of the risk neutral density will be missing. Coverage of the tails can be very asymmetrical and it can vary quite a lot from period to period. The coverage in less active emerging markets is distinctly worse. Liu and Wu propose a way to estimate the resulting truncation error using corridor variance swaps. In the course of deriving it, they develop a new approach to pricing corridor variance swaps. Comparing estimates of the truncation error for the S&P 500 versus the Chinese ETF50, they find it is about 0.1 vol points for the S&P but 2.61 vol points in the Chinese market. Results are also reported for Mexico, Korea, India and Russia and show that in some cases significant truncation is present on one or both tails.