基于混合规避策略的期权定价及其数值分析

Option Pricing and Its Numerical Analysis Based on Mixed Hedging Strategy

考虑现实市场中红利的存在、波动率等参数随时间变化以及交易时间不连续产生的对冲风险不可忽略,研究离散时间、支付红利条件下基于混合规避策略的期权定价模型.由平均自融资-极小方差规避策略得到相应欧式看涨期权定价方程,并且分别使用偏微分方法和概率论方法得到统一的闭形解.数值分析表明,与经典的期权定价模型相比,新模型中的期权价格更接近对冲成本.

Essentially, considering the existence of dividend, the change of volatility with different time, and the fact the risk of hedging caused by a discrete time case can＇t be neglected in the real world, this paper studies the option pricing model based on the mixed hedging strategy in a discrete time incomplete market and dividend payout. The corresponding Euro- pean call option pricing equation is obtained from an average self-finance minimal variance hedging strategy, and then the partial closed-form solution is obtained from the partial differential method and the probability theory method in detail. From numerical analysis, we found that the option price in the new model is closer to the hedging cost than the B-S model. It illustrates that re- sidual risks, risk preference, the trading frequency and dividend as well as the mixed hedging strategy play an important role in option pricing and portfolio hedging in a discrete time case.