Efficient Estimation of Pricing Kernels and Market-Implied Densities

Jeroen Dalderop
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Abstract

This paper studies the nonparametric identification and estimation of projected pricing kernels implicit in European option prices and underlying asset returns using conditional moment restrictions. The proposed series estimator avoids computing ratios of estimated risk-neutral and physical densities. Instead, we consider efficient estimation based on the conditional Euclidean empirical likelihood or continuously-updated GMM criterion, which takes into account the informativeness of option prices of varying strike prices beyond observed conditioning variables. In a second step, we convert the implied probabilities into predictive densities by matching the informative part of cross-sections of option prices. Empirically, pricing kernels tend to be U-shaped in the S&P 500 index return given high levels of the VIX, and call and ATM options are more informative about their payoff than put and OTM options.
定价核和市场隐含密度的有效估计
本文利用条件矩约束研究了欧式期权价格和标的资产收益中隐含的预测定价核的非参数识别和估计。所提出的序列估计器避免了计算估计的风险中性密度和物理密度的比率。相反,我们考虑基于条件欧几里得经验似然或连续更新的GMM准则的有效估计,它考虑了超出观察条件变量的不同执行价格的期权价格的信息量。第二步,我们通过匹配期权价格横截面的信息部分,将隐含概率转换为预测密度。从经验上看,在波动率指数处于高位的情况下,标普500指数的定价核心往往呈u型,看涨期权和ATM期权比看跌期权和场外期权更能说明它们的收益。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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