What Does the Volatility Risk Premium Say About Liquidity Provision and Demand for Hedging Tail Risk?

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

“…Previous studies measure VRP by employing synthetic VS rates (e.g., Bollerslev et al, 2009, 2012, Carr and Wu, 2009, Fan et al, 2013, Neumann and Skiadopoulos, 2013. 4 In line with the theoretical results of 2 We distinguish between stock market conditions and economic conditions in line with anecdotal evidence which suggests that the state of the stock market and that of the economy may be disconnected (e.g., a booming stock market may coincide with a poor economic state).…”

“…Interestingly, the negative and statistically significant sign of CS can also be interpreted within a financial intermediaries setting (for a similar explanation, see also Fan et al, 2013). An increase in CS signifies that the financial intermediaries are not willing to take on excessive risk and as a result VRP has to increase in magnitude (i.e.…”

“…Related Literature: Carr and Wu (2009), Fan et al (2013), Nieto et al (2013), and Neumann et al (2014) examine the determinants of VRP within a contemporaneous rather than a predictive setting. Amengual (2009) and Ait-Sahalia et al (2013) examine the dynamics of a (parametrically measured) term structure of VRP.…”

Tail risk premia and return predictability

“…The returns on momentum portfolios have also been shown to exhibit option-like characteristics and be predictable by the "state" of the economy and the volatility of the aggregate market (e.g., Daniel, Jagannathan, and Kim, 2012;Daniel and Moskowitz, 2014), as well as the magnitude of the volatility risk premium (e.g., Nagel, 2012;Fan, Imerman, and Dai, 2013). Consistent with these earlier findings, the much stronger predictability for the "loser" and WML portfolios based on the decomposition of VRP t reported here again support the interpretation of VRP t À LJV t and LJV t as LJV 11.20 separate proxies for market uncertainty and fears, respectively, both of which help predict the momentum returns.…”

Modeling Conditional Factor Risk Premia Implied by Index Option Returns

“… See Jones (2006),Israelov and Kelly (2017),and Horenstein, Vasquez, and Xiao (2018) for notable exceptions.2 For seminal contributions to this literature, see, among others, Pan (2002),Eraker, Johannes, and Polson (2003),Carr and Wu (2009),Bates (2008),Broadie, Chernov, and Johannes (2009),Todorov (2010),Bollerslev, Todorov, and Xu (2015), andAndersen, Fusari, and Todorov (2015a, b).3Barras and Malkhozov (2016),Fan, Imerman, and Dai (2016), and Gârleanu, Pedersen, and Poteshman (2009) study the impact of demand shocks on options Christoffersen et al (2018). show that illiquidity impacts the expected returns on delta-hedged equity options.4 See, for instance,Jones (2003), who develops a nonaffine stochastic volatility model to study index option prices, andEraker and Wang (2015), who develop a nonlinear model of the variance premium.5 This issue also poses a problem when studying the cross-section of stock returns, but it is more critical in the case of option returns because of leverage and heavy tails.…”