Longevity bond pricing under the threshold CIR model

While mean reversion is a well-documented feature in interest rate and commodity prices, empirical studies show that the long-term mean level and the mean reversion rate are not persistent in time. This paper introduces a threshold Cox-Ingersol-Ross (TCIR) model in which a regime shift is determined endogenously by the underlying financial asset. We derive the joint moment-generating function (MGF) of the terminal TCIR value and an average of it. The MGF enables us to value risk-free bonds and Longevity bonds analytically.