Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.
