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利用支持向量回归机(SVR),通过求解线性算子方程,提出了一种全新的非参数类恢复隐含风险中性概率密度函数的方法.首先,介绍了支持向量回归机应用于函数逼近的基本原理,当仅知算子方程右边函数的一些函数值而不知其函数形式时,描述了基于支持向量回归机的线性算子方程求解方法.然后,给出了基于支持向量回归机的隐含风险中性概率密度函数求解原理及交叉核函数的构建方法.最后,通过实证研究,验证了该方法的有效性.研究结果表明,所提方法克服了传统参数类方法对期权执行价格有严格限制的缺陷,同时对数据量的要求也比其他非参数类方法少,是一种很有前景的还原隐含风险中性概率方法与手段.
By using support vector regression (SVR), a new nonparametric method for recovering implicit risk neutral probability density function is proposed by solving linear operator equations.Firstly, the application of support vector regression (SVR) to function approximation The basic principle is that when we only know some function values of the function on the right side of the operator but do not know the function form, we describe the solution of the linear operator equation based on support vector regression.And then, we give the implication based on support vector regression The risk neutral probability density function and the construction method of cross-kernel function.Finally, the effectiveness of this method is verified by empirical research.The results show that the proposed method overcomes the strict restriction on the price of the option , But also requires less data than other non-parametric methods. It is a very promising method and means to restore the implicit risk neutral probability.