Pricing Guaranteed Annuity Options in a Linear-Rational Wishart Mortality Model - Da Fonseca, José (Elsevier BV, 2024)
This paper proposes a new model, the linear-rational Wishart model, which allows the joint modelling of mortality and interest rate risks. Within this framework, we obtain closed-form solutions for the survival bond and the survival floating rate bond. We also derive a closed-form solution for the guaranteed annuity option, i.e., an option on a sum of survival (floating rate) bonds, which can be computed explicitly up to a one-dimensional numerical integration, independent of the model dimension. Using realistic parameter values, we provide a model implementation for these complex derivatives that illustrates the flexibility and efficiency of the linear-rational Wishart model.
Keywords: 4901 Applied Mathematics; 3502 Banking, Finance and Investment; 49 Mathematical Sciences; 35 Commerce, Management, Tourism and Services; 3 Good Health and Well Being; 01 Mathematical Sciences; 14 Economics; 15 Commerce, Management, Tourism and Services; Statistics & Probability; 35 Commerce, management, tourism and services; 38 Economics; 49 Mathematical sciences