摘要
为了预测欧式期权资产价格,提出了一种跳幅度为常数的跳-扩散模型。利用有限差分方法计算出欧式期权价格;通过搜集市场交易的标准普尔500指数数据得到市场价格,运用非线性最小二乘方法得到符合实际市场的模型参数,绘制跳幅度为常数的跳-扩散模型在不同到期日下的隐含波动率变化曲线图,检验跳参数对隐含波动率图像的影响。实证结果表明,跳幅度为常数的跳-扩散定价模型,能够解释欧式期权市场资产价格收益变化的波动率呈现出的“微笑”特征。校正算法具有稳定性,可应用于欧式期权资产价格预测。
To predict the price of assets in the real market,a jump-diffusion option pricing model with constant jump amplitude calibrated based on real data and optimization method is proposed.Firstly,the finite difference method is used to calculate the European option price.Secondly,the market price is obtained by collecting the market transaction S&P 500 data,and the model parameters in line with the real market is obtained by using the nonlinear least squares method.The plot of the implied volatility of the constant jump-diffusion model under different expiration dates is then drawn.Finally,the effect of the jump parameters on the implied volatility surface is examined.Empirical results show that the jump-diffusion model with constant jump amplitude can explain the“smile”characteristic of the volatility of asset price,has stability and can be used to predict European option pricing.
作者
高雄
张素梅
GAO Xiong;ZHANG Sumei(School of Sciences,Xi'an University of Posts and Telecommunications,Xi'an 710121,China)
出处
《西安邮电大学学报》
2019年第5期81-87,共7页
Journal of Xi’an University of Posts and Telecommunications
基金
陕西省自然科学基金资助项目(2017JM1021)
陕西省教育厅科学计划资助项目(17JK0714)
关键词
有限差分法
非线性最小二乘法
跳-扩散模型
期权定价
finite difference
nonlinear least square method
jump-diffusion model
valuation of options
