Pricing and Hedging Defaultable Participating Contracts with Regime Switching and Jump Risk

Abstract

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.