跳扩散模型下具有情绪的期权定价

Option pricing with sentiment under the jump-diffusion model

在跳扩散模型下考虑具有股票情绪和期权情绪的期权定价模型。假设标的资产跳跃的到达服从泊松过程,跳跃的幅度服从正态过程,且股票情绪和期权情绪都服从O-U过程。对所构建的模型,求得了欧式期权定价解析式。利用上证50ETF看涨期权数据进行实证研究,通过与几何布朗运动模型,带跳的几何布朗运动模型和Heston模型进行对比,发现在平稳样本时期、波动样本时期和全样本时期,文章所提模型在上证50ETF看涨期权价格的拟合和预测误差均是最小的,以及在隐含波动率的拟合和预测误差也是最小的,表明文章的模型在平稳时期,非平稳时期以及既有平稳时期又非平稳时期,期权价格的拟合和预测能力以及隐含波动率的拟合和预测能力都是优于对比模型的。

The option pricing with stock sentiment and option sentiment under jump diffusion model is considered.Assume that the arrival of the underlying asset jump follows a Poisson process,the jump amplitude follows a normal process,and the stock sentiment and option sentiment follow an OU process.The analytical formula of European option pricing is obtained.Using the 50ETF call option data of Shanghai Stock Exchange for empirical research,by comparing with geometric Brownian motion model,geometric Brownian motion model with jump and Heston model,it is found that in the period of stable sample,the period of fluctuation sample and the period of full sample,the fitting and prediction errors of the model are the smallest in the 50ETF call option price of Shanghai Stock Exchange,and the fitting and prediction errors in the implied volatility are also the smallest.It shows that the proposed model is superior to the comparison model in terms of fitting and forecasting ability of option price and implied volatility in stable period,non-stationary period and both stable and non-stationary periods.