股灾期间上证50ETF期权定价研究

从理论上探讨了股灾期间大盘指数对期权定价的影响,改进了用于表征股灾期间上证指数宽幅震荡过程的欠阻尼二阶系统阶跃响应函数,并考虑了上证指数对标的资产价格的耦合影响,在风险中性定价法则下构建出股灾期间的期权定价模型;详细考察了大盘指数模型中的参数(如阻尼系数、衰减速率以及无阻尼震荡频率等)、大盘指数影响作用过程的波动系数以及大盘与标的资产的关联系数等对期权定价的影响.最后,运用Monte Carlo仿真技术,对上证50ETF期权进行实证与预测.数值结果表明:所提出的股灾期间的期权定价模型,能有效地为上证50ETF期权定价,并具有良好的鲁棒性.

Pricing the SSE 50ETF options during stock market crash

This paper theoretically explores the impact of the market index on the option pricing during the stock market crash. The step response function of underdamped second-order system that used to characterize the Shanghai Stock Exchange (SSE) Composite Index under big shocks during the stock market crash, is improved. A novel option pricing model, considering the coupling effect of the SSE Composite Index on underlying asset prices, is built up. The effects of parameters such as damping coefficient, decay rate and undamped oscillation frequency in the market index model, the volatility coefficient of the impact of the market index and the correlation coefficient between the market and the underlying asset, etc., are studied in detail. Finally, the empirical research on the SSE 50ETF option pricing is carried out, applying the Monte Carlo simulation technology. Numerical results show that the proposed option pricing model during the stock market crash can effectively evaluate the SSE 50ETF option and has good robustness.