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 p...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.展开更多
Extreme mortality bonds(EMBs),which can transfer the extreme mortality risks confronted by life insurance companies into the capital market,refer to the bonds whose nominal values or coupons are associated with mortal...Extreme mortality bonds(EMBs),which can transfer the extreme mortality risks confronted by life insurance companies into the capital market,refer to the bonds whose nominal values or coupons are associated with mortality index.This paper first provides the expected value of mortality index based on the double exponential jump diffusion(DEJD)model under the risk-neutral measure;then derives the pricing models of the EMBs with principal reimbursement non-cumulative and cumulative threshold respectively;finally simulates the bond prices and conducts a parameter sensitivity analysis.This paper finds that the jump and direction characteristics of mortality index have significant impacts on the accuracy of the EMB pricing.展开更多
基金The National Natural Science Foundation of China (No.70671025)
文摘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.
文摘Extreme mortality bonds(EMBs),which can transfer the extreme mortality risks confronted by life insurance companies into the capital market,refer to the bonds whose nominal values or coupons are associated with mortality index.This paper first provides the expected value of mortality index based on the double exponential jump diffusion(DEJD)model under the risk-neutral measure;then derives the pricing models of the EMBs with principal reimbursement non-cumulative and cumulative threshold respectively;finally simulates the bond prices and conducts a parameter sensitivity analysis.This paper finds that the jump and direction characteristics of mortality index have significant impacts on the accuracy of the EMB pricing.
