Pricing and hedging defaultable participating contracts with regime switching and jump risk

This paper develops a transform-based approach for the pricing of participating life insurance contracts with a constant or floating guaranteed rate. Our analysis incorporates credit, market (jump), and economic (regime switching) risks, where the evolution of the reference portfolio is described by a regime switching double exponential jump-diffusion model. We provide semi-analytical formulas for the contract value by using a Laplace or Laplace–Fourier transform that involves matrix Wiener–Hopf factors. Then, the price is obtained by implementing the matrix Wiener–Hopf factorization and by performing a numerical Laplace and Fourier inversion. By comparing the results with Monte Carlo simulations, we show that our pricing method is easy to implement and accurate. We also show that the contract with a floating guaranteed rate is riskier but more profitable than the contract with a constant guaranteed rate. Two hedging strategies are introduced to hedge jump and regime switching risks in the participating contracts.