基于扇形偏好的期权定价方法

An option pricing method based on the fanning preference

"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.引入基于扇形偏好的非预期效用函数后,均衡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显著的"厚尾"与"左偏"特征.

Empirical findings suggest two violations of the Black-Scholes model: the volatility smile and the asymmetrical distribution for underlying asset returns. Although stochastic volatility models based on the no-arbitrage theorem can explain these two phenomena,the alternative pricing method under general equilibrium framework has been seldom studied. The traditional equilibrium model incorporating the expected utility fails to differentiate the investor's different risk preferences towards the diffusive uncertainty and the jump risk. However,with the fanning preference,the model is able to capture an additional risk premium,and generates a pronounced volatility smile. On the other hand,adopting the fanning effect results in a leptokurtic and leftskewed distribution.