Life insurance pricing in a Heston market with CIR interests

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In finance, the Heston model describes a stochastic process with a constant drift and a stochastic diffusion coefficient modeled by a Cox-Ingersoll-Ross process. This publication extends the model by incorporating stochastic behavior of the drift, utilizing an affine Cox-Ingersoll-Ross model for stochastic interest rates. This modification offers greater flexibility compared to standard models like Black-Scholes, making it suitable for modeling portfolios of stocks and bonds. We demonstrate that this enhanced Heston model is an affine process, with its density and characteristic function derivable analytically through Fourier transformations and specific Riccati equations. Such closed-form solutions are essential for analyzing the impact of parameters on the process and its characteristics, including expectation, variance, and density function. In the finance and insurance sectors, the Heston model is recognized as the standard for deriving risk-return profiles, which reflect the probability distribution of returns for various old age provision products in the German market. In this context, complex old age provision products are evaluated using Monte Carlo simulations based on the modified Heston model. Our work provides an analytical framework for the model, enhancing the clarity of results and enabling rapid assessment of the effects of changes in parameters such as interest rates, risk premiums, or average volatilities.