摘要
首先,从误差和时间复杂度两方面入手,分析如今主流期权定价方法的优劣,进而引出主体研究对象傅里叶余弦方法;其次,在Black-Scholes模型假设下进行傅里叶COS方法的欧式期权定价,对该方法的理论可行性进行详细的推导和证明;最终,通过运用风险中性定价原理,得到改进的COS方法定价公式,相对于原方法在运算速度上有一定提高。得到数值结果后,继续对影响COS方法定价效果的因素进行对比分析,先固定原参数不变,通过数值验证发现截断系数L对整体方法影响是非常大的,也把L的固定值修改为适应区间;其次转而分析参数影响,表明到期时间T和傅里叶展开项数N对L有较大影响。最后,尝试将BS模型上的COS方法推广至Heston模型中,并解决一定的理论推导和数值分析问题。
Firstly,this paper briefly introduces several main pricing methods at present,and analyses their advantages and disadvantages from two aspects of error and time complexity,then draws out the main research object of this paper-Fourier Cosine method.Secondly,under the assumption of Black-Scholes model,European option pricing based on Fourier COS method is carried out,and the theoretical feasibility of this method is deduced and proved in detail.By applying the risk-neutral pricing principle,the improved pricing formula of COS method is finally obtained,which is faster than the original method.After obtaining the numerical results,this paper continues to make a comparative analysis of the factors affecting the pricing effect of COS method.Firstly,we fix the original parameters unchanged.Through numerical verification,we find that the truncation coefficient L has a great impact on the overall method,and also revise the fixed value of L to the adaptive range.Secondly,we turn to analyze the influence of the parameters,showing that the option expiration date T and the number of Fourier expansion terms N have a significant impact on L.Finally,this paper attempts to extend the COS method on BS model to Heston model,and solve some theoretical derivation and numerical analysis problems.
作者
周欣涛
陈萍
ZHOU Xin-tao;CHEN Ping(Nanjing University of Science and Technology,School of Science,Nanjing 210094,China)
出处
《经济研究导刊》
2019年第15期90-95,134,共7页
Economic Research Guide
