基于前景理论框架和Heston模型的行为期权定价

Behavioral Option Pricing under Prospect Theory Framework and Heston Model

行为期权定价是当前国际金融领域的热门研究主题之一。虽然随机波动率模型已成为国际衍生品定价领域的标准模型,但该模型对短到期期权(尤其是虚值期权)的定价仍不准确,其原因之一是传统的期权定价方法忽略了现实市场中的非理性心理和行为因素。针对上述问题,本文运用前景理论期权定价框架,引入价值函数来刻画投资者面对收益与损失的前景价值判断,引入决策权重函数来修正Heston随机波动率模型刻画的资产价格路径的概率密度函数,将期权合约签订与交割的现金流视为分散的心理账户情形,在市场均衡条件下推导出Heston模型下欧氏行为期权的定价公式。上证50ETF期权的实证结果表明:考虑了前景理论的Heston随机波动率模型,能显著地提升短到期虚值期权的定价准确度;参数校正结果发现,定价性能的提升要归因于Heston模型中纳入的表征非理性心理与情绪的行为参数;相对而言,投资者对实值期权的风险态度偏中性,因此行为参数对其定价精度的提升有限。

Behavioral option pricing has been one of the hottest frontiers in the area of international finance.Stochastic volatility model has become the de facto standard model of international derivatives pricing,but it is not accurate enough in the pricing of short-term options,especially for OTM.One of the reasons is that the traditional option pricing methods ignore the irrational psychological and behavioral factors in the real market.To solve this problem,prospect theory is brought into the traditional option pricing framework,the different value judgments of investors facing gains and losses are described by introducing the subjective value function,the subjective decision weight function is used to modify the probability density function of the asset price path described by Heston model,and then the cash flow in the two periods of signing and executing European option contracts is regarded as two separate mental accounts.Prices of European options under Heston model are derived under the condition of market equilibrium.The empirical results of SSE 50ETF option show that the Heston stochastic volatility model considering the prospect theory can significantly improve the pricing accuracy of short maturity OTM option.The model parameter correction results show that the improvement of pricing performance is due to the behavioral parameters representing irrational psychology and emotion included in Heston model.Relatively speaking,investors'risk attitude towards ITM options is nearly neutral,so the improvement of behavior parameters on its pricing accuracy is limited.