英文文献：The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model-随机平均波动模型中的风险-收益权衡和杠杆效应
英文文献作者：Bent Jesper Christensen,Petra Posedel
英文文献摘要：
We study the risk premium and leverage effect in the S&P500 market using the stochastic volatility-in-mean model of Barndor¤-Nielsen & Shephard (2001). The Merton (1973, 1980) equilibrium asset pricing condition linking the conditional mean and conditional variance of discrete time returns is reinterpreted in terms of the continuous time model. Tests are performed on the risk-return relation, the leverage effect, and the overidentifying zero intercept restriction in the Merton condition. Results are compared across alternative volatility proxies, in particular, realized volatility from high-frequency (5-minute) returns, implied Black-Scholes volatility backed out from observed option prices, model-free implied volatility (VIX), and staggered bipower variation. Our results are consistent with a positive risk-return relation and a significant leverage effect, whereas an additional overidentifying zero intercept condition is rejected. We also show that these inferences are sensitive to the exact timing of the chosen olatility proxy. Robustness of the conclusions is verified in bootstrap experiments.

利用Barndor¤-Nielsen & Shephard(2001)的均值随机波动模型研究了标普500市场的风险溢价和杠杆效应。将离散时间收益的条件均值和条件方差联系起来的默顿(1973,1980)均衡资产定价条件用连续时间模型重新解释。对默顿条件下的风险-收益关系、杠杆效应和过度识别的零截距限制进行了检验。通过替代波动率代理，特别是从高频(5分钟)回报中实现的波动率、从观察期权价格中退出的隐含布莱克-斯科尔斯波动率、无模型隐含波动率(VIX)和交错双幂变异，对结果进行比较。我们的结果与一个正的风险回报关系和一个显著的杠杆效应相一致，而一个额外的过度识别的零截距条件被拒绝。我们还表明，这些推论对所选择的颜色代理的准确时间是敏感的。自举实验验证了结论的鲁棒性。