基于奈特不确定性随机波动率期权定价

Knightian uncertainty based option pricing with stochastic volatility

不同于传统的思路,本文以奈特不确定的视角处理带有随机波动率的期权定价问题.首先,证明随机波动率模型本质上是一个奈特不确定问题;并且用折现相对熵来度量奈特不确定大小.然后,通过一个效用函数来权衡奈特不确定和奈特溢价,求得个体在奈特不确定下最优概率测度,导出了含奈特厌恶度γ的欧式看涨期权定价公式.通过Monto Carlo模拟发现个体奈特厌恶度γ和期权的到期日对期权的价格有重要影响,并使用沪市权证实例给出奈特厌恶度,γ的具体估算方法.

This paper deals with the stochastic volatility option pricing model in the viewpoint of Knightian uncertainty. First, we prove that the stochastic volatility model is in fact a Knightian uncertainty model; and we use the discounted relative entropy to measure the Knighitan uncertainty. Then, having balanced the Knightian uncertainty and Knightian premium through a utility function, we get the optimum probability measure, and we get the price formula of European call option with Knightian aversion degree γ. We find that γ and expiration date have important effect on the price of option by Monte Carlo simulation, and we give an example to show how to estimate the values of γ.