摘要
在资产收益率及其波动率均满足随机跳跃且具有跳跃相关性的仿射扩散模型下,用广义双指数分布和伽玛分布分别刻画非对称性收益率及其波动率的跳跃波动变化,研究了具有几何平均特征的水平重置期权定价问题.通过Girsanov测度变换和多维Fourier逆变换方法,给出了此类重置期权定价的解析公式.最后,通过数值实例着重分析了联合跳跃参数及杠杆效应对水平重置看涨期权价格的影响,并对风险对冲特征作了分析.结果表明,上跳概率,跳跃频率,杠杆效应,收益率波动的两个跳跃参数和双跳跃相关系数对期权价格有正向影响,上跳和下跳幅度对期权价格有反向影响,而期权的风险对冲参数没有出现明显的跳跃现象.这说明文章建立的期权定价模型比经典Black-Scholes模型具有更好的实际拟合能力.
The pricing problem for the geometric average trigger reset option with predetermined levels has been considered under an affine jump-diffusion model in which both the asset return and its volatility satisfy random jumps with jump correlation.These jumps are described by generalized double exponential distribution and gamma distribution respectively.Applying the Girsanov method and multidimensional fourier inverse transform technique,analytical formulas for the reset options are obtained.Furthermore,both the influence of combined jump parameters and leverage effect on the call option price are analyzed by numerical examples.In addition,the risk hedging characteristics are also analyzed.The results show that the up jump probability,jump frequency,leverage effect,the two jump parameters of yield fluctuation and the double-jump correlation coefficient all have a positive effect on the option price,while the up jump and down jump amplitude both have a negative effect on the option price.Besides the risk hedging parameters of the option do not show an obvious jump phenomenon.These results show that the proposed model established in this paper has a better ability in fitting practice than the classical Black-Scholes model.
作者
奚欢
邓国和
XI Huan;DENG Guohe(Department of Statistics,Shanghai University of Finance and Economics Zhejiang College,Jinhua 321013;College of Mathematics and Statistics,Guangri Normal University,Guilin 541004)
出处
《系统科学与数学》
CSCD
北大核心
2021年第1期59-74,共16页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11461008)
浙江省教育厅科研项目(Y201738176)
广西自然科学基金项目(2018GXNSFAA281016)资助课题。
关键词
仿射跳扩散模型
几何平均
水平重置期权
Fourier逆变换法
Affine jump-diffusion model
geometric average
reset options with predetermined levels
Fourier inverse transform
