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Pricing longevity derivatives via Fourier transforms. (English) Zbl 1460.91212

The paper provides a Fourier transform approach for European-style longevity option pricing. The guidelines related to the valuation of longevity derivatives with different payoff structures, by means of a Fourier transform approach, are described; these guidelines, that cover option-type contracts, S-forwards and longevity swaps, provide the basis for the pricing model. Then, the analytical pricing model for longevity derivatives under a risk-adjusted probability pricing measure is developed within a stochastic framework, where both the mortality intensity and interest rates are described by means of a continuous-time affine jump-diffusion stochastic process. Moreover the model calibration is in-depth; numerical examples about the valuation of longevity derivatives complete the study and show the contribution of the results presented in the paper to applied cases. Some technical issues can be obtained by a supplementary file available through the link in Appendix.

MSC:

91G05 Actuarial mathematics
91G20 Derivative securities (option pricing, hedging, etc.)

Software:

Human Mortality
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