Correlated intensity, counter party risks, and dependent mortalities

In this paper we use an intensity-based framework to analyze and compute the correlated default probabilities, both in finance and actuarial sciences, following the idea of "change of measure" initiated by Collin-Dufresne et al. (2004). Our method is based on a representation theorem for joint survival probability among an arbitrary number of defaults, which works particularly effectively for certain types of correlated default models, including the counter-party risk models of Jarrow and Yu (2001) and related problems such as the phenomenon of "flight to quality". The results are also useful in studying the recently observed dependent mortality for married couples involving spousal bereavement. In particular we study in details a problem of pricing Universal Variable Life (UVL) insurance products. The explicit formulae for the joint-life status and last-survivor status (or equivalently, the probability distribution of first-to-default and last-to-default in a multi-firm setting) enable us to derive the explicit solution to the indifference pricing formula without using any advanced results in partial differential equations.