Calibrating affine stochastic mortality models using insurance contracts premiums
نویسندگان
چکیده
In this paper, we focus on the calibration of affine stochastic mortality models using insurance contracts premiums. Viewing insurance contracts as “market products,” we propose fitting stochastic models on the quotes of insurance policies. For this purpose, insurance contracts are viewed as a “swap” in which policyholders exchange cash flows (premiums vs. benefits) with an insurer analogous to a generic interest rate swap or credit default swap. Using a simple bootstrapping procedure, we derive the term structure of mortality rates from a stream of contract quotes with different maturities. This term structure is used to calibrate the parameters of affine stochastic mortality models where the survival probability is expressed in closed form. The Vasicek, Cox-Ingersoll-Ross, and jump-extended Vasicek models are considered for fitting the survival probabilities term structure. An evaluation of the performance of these models is provided with respect to representative premiums of Italian insurance contracts for individuals at different ages. keyword: affine stochastic models, bootstrapping, calibration, stochastic force of mortality, mortality risk, insurance contracts, Vasicek model, Cox-Ingersoll-Ross model, jump-extended Vasicek model. Acknowledgement The authors acknowledge the support from the Italian National Grant PRIN 2007 “Financial innovation and demographic changes: new products and pricing instruments with respect to the stochastic factor aging”(local coordinator M. Bertocchi).
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