杠杆效应对期权定价的影响研究

Leverage effect on option pricing

本文基于时间序列视角从随机模拟和实证研究两方面探讨随机波动率模型中杠杆效应对期权定价的影响.在随机模拟中,通过与基本的随机波动率模型比较,发现当收益率时间序列存在高杠杆时,带杠杆的随机波动率模型给出的期权价格更接近真实的价格,在MAE和RMSE距离统计量上都存在显著差异,但较低的杠杆对期权定价不会有显著影响;并且,在带杠杆的模型中,路径模拟定价法优于BS框架下的定价方法.此外,在标普500指数的欧式期权上的实证研究,表明指数存在较高的杠杆水平;相较于期权市场价格,带杠杆的模型在定价上好于基本的模型,在MAE和RMSE统计量上存在显著性的差异.

We investigate the leverage effect of stochastic volatility model on option pricing in both sim- ulation analysis and empirical studies. Compared with basic stochastic volatility model （BSV）, stochastic volatility model with leverage （LSV） has substantial advantage and significant difference in option pricing under both the suggested MAE and RMSE criteria when high leverage effect exists in our Monte Carlo simulations. However, low leverage level doesn＇t contribute a significant difference to option pricing. Mean- while, empirical research is done on S＆P 500 index and its options. The results indicate that its leverage level is significantly high, and LSV outperformances BSV for option pricing significantly on both MAE and RMSE criteria.