Post by Hua Chen on Sept 3, 2011 4:27:25 GMT 4
A Family of Mortality Jump Models with Parameter Uncertainty: Application to Hedging Longevity Risk in Life Settlements
Hua Chen
Temple University - Department of Risk, Insurance and Healthcare Management
Samuel H. Cox
University of Manitoba - Asper School of Business
Zhiqiang Yan
Western Illinois University - Department of Marketing and Finance
August 17, 2011
Abstract:
Mortality models are fundamental to quantify mortality/longevity risks and provide the basis of pricing and reserving. The prices of mortality-linked securities based on these stochastic mortality models are subject to model uncertainty and parameter uncertainty. In this paper, we consider a family of mortality jump models and propose a new generalized Lee-Carter model with asymmetric double exponential jumps. It is asymmetric in terms of both time periods of impact and frequency/severity profiles between adverse mortality jumps and longevity jumps. It is mathematically tractable and economically intuitive. It degenerates to a transitory exponential jump model when fitting the U.S. mortality data and is the best fit compared with other jump models. We then take into account parameter uncertainty and investigate its effect on pricing mortality-linked securities. We analyze longevity risk in life settlement portfolios and propose to use longevity options to hedge the risk. We calculate hedging costs for three scenarios: (1) no parameter uncertainty, (2) parameter uncertainty with Bayesian analysis, and (3) parameter uncertainty with actuarial prudence. We find that introducing parameter uncertainty on the mean rate of mortality changes does not have a significant impact on option premiums.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1911688_code1102415.pdf?abstractid=1911688&mirid=2
Hua Chen
Temple University - Department of Risk, Insurance and Healthcare Management
Samuel H. Cox
University of Manitoba - Asper School of Business
Zhiqiang Yan
Western Illinois University - Department of Marketing and Finance
August 17, 2011
Abstract:
Mortality models are fundamental to quantify mortality/longevity risks and provide the basis of pricing and reserving. The prices of mortality-linked securities based on these stochastic mortality models are subject to model uncertainty and parameter uncertainty. In this paper, we consider a family of mortality jump models and propose a new generalized Lee-Carter model with asymmetric double exponential jumps. It is asymmetric in terms of both time periods of impact and frequency/severity profiles between adverse mortality jumps and longevity jumps. It is mathematically tractable and economically intuitive. It degenerates to a transitory exponential jump model when fitting the U.S. mortality data and is the best fit compared with other jump models. We then take into account parameter uncertainty and investigate its effect on pricing mortality-linked securities. We analyze longevity risk in life settlement portfolios and propose to use longevity options to hedge the risk. We calculate hedging costs for three scenarios: (1) no parameter uncertainty, (2) parameter uncertainty with Bayesian analysis, and (3) parameter uncertainty with actuarial prudence. We find that introducing parameter uncertainty on the mean rate of mortality changes does not have a significant impact on option premiums.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1911688_code1102415.pdf?abstractid=1911688&mirid=2