基于扇形偏好的一般均衡期权定价方法及其对股价跳跃风险的应用

Since the Black-Scholes model has made a great success in option pricing, a number of empirical studies found that it is difficult to explain the volatility smile or smirk pattern for the plot of implied volatility across moneyness. Therefore, to improve its cross-sectional performance, a type of general equilibrium model based on the pure exchange economy is developed. Under this equilibrium framework, our project incorporates a fanning preference to reflect the investor's risk aversion to future risks implicit in option prices, and propose a new option pricing model compared with the traditional one based on the expected utility function. A major constribution of this model is that the risk aversion adjusted by the fanning preference is able to disentangle the different attitudes of investors to the diffusive risk and jump risk. As a result, it can predict the deep OTM (out-of-the-money) put options with a larger risk premium, espcially the jump risk premium, than that implicit in the ATM (at-the-money) options. This virtually implies a pronounced volatility smirk. ..Moreover, most existing literatures in the area of option pricing employ normally distributed jump sizes which is first pioneered by Merton (1976). But, up to now, littlet papers have studied whether this assumption is accordant with the real distribution for jump sizes. According to the option pricing model established in our project, the real distribution for jump sizes can be estimated, as the model imposes a general assumption on jump sizes. More specifically, resorting to the Wavelet technique, this project estimates the option prcing model with the real trading option data, and thus, the jump size distribution implicit in the real data can be derived.

自Black-Scholes期权定价模型取得巨大成功后，大量的实证研究发现该模型很难解释"波动率微笑"（volatility smile or smirk）的现象。因此，为了改进其截面数据的拟合效果，一种基于交换经济的一般均衡期权定价方法孕育而生。本课题既是在此框架下，引入扇形偏好以调整风险厌恶系数，从而区分投资者对股价波动与跳跃风险的不同厌恶程度。并且，根据在此基础上产生的期权定价模型，拟合出显著的"波动率微笑"曲线，以区别于现有的预期效用模型。.此外，目前大量的期权定价方法沿用了Merton（1976）的跳跃幅度服从正态分布的假设，但是探讨其是否符合实际情况的研究还比较少。借助本项目中建立的模型所采用的一般化分布形式，跳跃幅度的真实分布可以从实际交易数据中估计出来。所采用的方法是，反向运用期权定价模型，利用Wavelet技术，从实际交易价格中估计出跳跃幅度分布的整体函数。

“波动率微笑”与资产收益的非正态分布一直是Black-Scholes期权定价模型无法解释的两种现象。为了改进该模型，一种基于交换经济的均衡模型孕育而生。但是传统均衡模型中所假设的预期效用函数无法区分投资人对于波动风险与跳跃风险的不同厌恶程度，从而低估了市场风险溢酬。本项目的研究中建立了基于扇形偏好的资产定价模型与期权定价模型。该模型产生了由扇形效应所导致的部分风险溢酬，并且可以拟合出显著的波动率微笑曲线。同时，考虑扇形效应后，风险中性的资产收益分布出现了“厚尾”与“左偏”的特征。本项目中建立的理论模型说明了波动率曲线的斜率取决于资产收益分布的偏度和峰度，而这两者都受到资产价格跳跃幅度分布假设的影响。通过对比Laplace跳跃幅度分布与传统的正态分布假设，本项目发现前者可以产生更加显著的波动率“微笑”曲线和风险中性资产收益的非对称特征。特别是在考虑非预期效用函数下，二者的差别更加明显。. 基于已有的理论模型，本项目进一步研究了中国股票市场的波动率风险溢酬。国外一些研究发现股票市场的波动率风险溢酬（Variance Risk Premium，VRP）对未来股票市场收益率具有预测作用，并且这种预测能力在预测期限的中期内最强。然而，目前针对中国股票市场的相关研究还比较少。本项目基于一般均衡资产定价模型，利用中国股票市场的实际数据，得出时变波动率风险溢酬, 并以此为预测因子对未来股票市场收益率进行样本内和样本外的预测检验。研究发现，与国外相关研究一致，中国股票市场的波动率风险溢酬同样对未来股票收益率具有预测作用，且这种预测能力在3-6个月的预测期限内最强。