Jump and Variance Risk Premia in the S&P 500

Abstract

We analyze the risk premia embedded in the S&P 500 spot index and option markets. We use a long time-series of spot prices and a large panel of option prices to jointly estimate the diffusive stock risk premium, the price jump risk premium, the diffusive variance risk premium and the variance jump risk premium. The risk premia are statistically and economically significant and move over time. Investigating the economic drivers of the risk premia, we are able to explain up to 63 % of these variations.

Inferring information from the S&P 500, CBOE VIX, and CBOE SKEW indices

“…(a) We first consider the stochastic volatility model with contemporaneous jumps in returns and volatility (SVCJ) in Broadie et al (2007) and Eraker et al (2003), that is, λ t ≡ λ 1 which is a constant. This is the most popular affine model in the literature, for example, Bakshi et al (1997), Duan and Yeh (2010), Lin and Chang (2010), Neuberger (2012), Neumann et al (2016), Zhu and Lian (2011, 2012) and others. (b) Aït‐Sahalia et al (2015) and Bates (2006) find that more jumps occur during more volatile periods, suggesting that λ t ≡ λ 1 + λ 2 v t , where λ 1 and λ 2 are two positive constants.…”

“…The first model is the stochastic volatility model with contemporaneous jumps in returns and volatility (SVCJ), which is the most popular affine model in the literature, for example, Bakshi, Cao, and Chen (1997); Broadie, Chernov, and Johannes (2007); Da Fonseca and Ignatieva (2019); Duan and Yeh (2010); Eraker (2004); Eraker, Johannes, and Polson (2003); Kaeck, Rodrigues, and Seeger (2017); Lin and Chang (2010); Neuberger (2012); Neumann, Prokopczuk, and Simen (2016); Ruan and Zhang (2018); Zhu and Lian (2011, 2012); and others. Bakshi et al (1997), Broadie et al (2007), Eraker (2004), and Neumann et al (2016) document that the SVCJ model is good enough to fit options and returns data simultaneously. According to the empirical observation in Bates (2006), that is, more jumps occur during more volatile periods, we adopt the second model from Aït‐Sahalia, Karaman, and Mancini (2015) and Bates (2006).…”

Moment Risk Premiums in Option Markets: On Measurement, Structure, and Investment Implications

“…Empirical evidence, for example fromBollerslev and Todorov (2011) andNeumann et al (2016), supports this notion. These papers find that risk compensation for extreme events determines a large part of the variance risk premium.…”