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Calibrating affine stochastic mortality models using term assurance premiums. (English) Zbl 1218.91093

Summary: In this paper, we focus on the calibration of affine stochastic mortality models using term assurance premiums. We view term assurance contracts 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 premiums of three Italian insurance companies.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G30 Interest rates, asset pricing, etc. (stochastic models)
91G40 Credit risk
62P05 Applications of statistics to actuarial sciences and financial mathematics
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