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

Arithmetic variance swaps

“…Using market quotes instead of the synthesised rates employed in previous research, Konstantinidi and Skiadopoulos [2016] show that a dealer's funding liquidity has a substantial effect on the variance risk premium. Their trading-activity model predicts the market variance risk premium much better than a variety of alternative predictive models and the premium becomes significantly more negative when funding illiquidity increases, i.e.…”

Variance and skew risk premiums for the volatility market: The VIX evidence

“…Extracting distribution information from option prices, like higher moments, has a long history, let us quote without pretending to be exhaustive the work of Carr and Madan (1998), and has found many applications; see among many others the works of Bakshi et al (2003) for individual options; Bakshi and Madan (2006) and Carr and Wu (2009)) for a variance risk premium analysis of equity index options (options on S&P500, S&P100 and other major indexes as well as equity); Byun and Kim (2013), Fleming (1998), Konstantinidi and Skiadopoulos (2016), and Neumann and Skiadopoulos (2013) for forecasting aspects (using S&P500 options); Ammann and Buesser (2013) for variance risk premium properties for the foreign exchange market; investors' risk aversion analysis as in Duan and Zhang (2014); Kostakis, Panigirtzoglou, and Skiadopoulos (2011) (using S&P500 options); and variance risk premiums in commodity markets in Prokopczuk, Symeonidis and Wese-Simen (2017).…”

Tail Risk Premia for Long-Term Equity Investors

“…The S&P500 studies of Carr and Wu [2009], Egloff et al [2010], Ait-Sahalia et al [2014] and Konstantinidi and Skiadopoulos [2014] all employ a sample starting in 1996, the shortest (Carr and Wu) ending in 2003 and the longest (Ait-Sahalia et al) ending in 2010. In every case the investment horizon corresponds to the maturity of the swap: 9 1 month in Carr and Wu [2009] and Trolle and Schwartz [2010]; 1 and 3 months in Amman and Buesser [2013]; and the same term structure of horizons from 2 to 24 months in Egloff et al [2010], Ait-Sahalia et al [2014] and Konstantinidi and Skiadopoulos [2014].…”

“…This is one of the major challenges to measuring variance risk premia, andAit-Sahalia et al [2014] show that market rates for S&P500 variance swaps were very often more than 5% different from their theoretical fair value during the turbulent year surrounding the Lehman Brothers collapse in September 2008. Some recent work on the variance risk premia such asEgloff et al [2010] andKonstantinidi and Skiadopoulos [2014] employs market quotes rather than theoretical values, but long time series of market quotes are not available for most alternative swap rates other than, of course, the futures price.7 There is a large literature on the use of ultra-high frequency data for realised variance when it is used as an estimator of the quadratic variation, but this is more relevant to very short-term speculators and will not be discussed in this paper.…”

“…Fixed-strike European options are a case in point here: call prices always increase with term (up to about one or two years, when the discount rate effect might dominate) and put prices increase with term when the trend is negative and also -up to about 6 months -when the trend is positive. The exact point when put prices start to decrease with term depends on the strike and the trend in the underlying futures.9 OnlyKonstantinidi and Skiadopoulos [2014] also allow it to be shorter.…”