Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure ri...Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.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
This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion ...This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.展开更多
This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a s...This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a stochastic descent method where the deterministic sequence, generated by a limited memory BFGS method, is replaced by a sequence of random variables. To enhance the performance of the proposed algorithm and make sure the perturbations lie within the feasible domain, we have developed a novel perturbation technique based on truncating a multivariate double exponential distribution to deal with bound-constrained problems;the theoretical study and the simulation of the developed truncated distribution are also presented. Theoretical results ensure that the proposed method converges almost surely to the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions as well as on some further engineering problems. The numerical comparisons with stochastic and meta-heuristic methods indicate that the suggested algorithm is promising.展开更多
基金Supported by the NNSF of China(40675023)the PHD Foundation of Guangxi Normal University.
文摘Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.
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.
基金Supported by the National Natural Science Foundation of China (70771018)the Natural Science Foundation of Shandong Province (2009ZRB019AV)Mathematical Subject Construction Funds and the Key Laboratory of Financial Information Engineering of Ludong University (2008)
文摘This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.
文摘This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a stochastic descent method where the deterministic sequence, generated by a limited memory BFGS method, is replaced by a sequence of random variables. To enhance the performance of the proposed algorithm and make sure the perturbations lie within the feasible domain, we have developed a novel perturbation technique based on truncating a multivariate double exponential distribution to deal with bound-constrained problems;the theoretical study and the simulation of the developed truncated distribution are also presented. Theoretical results ensure that the proposed method converges almost surely to the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions as well as on some further engineering problems. The numerical comparisons with stochastic and meta-heuristic methods indicate that the suggested algorithm is promising.
