Risk Models with Jumps and Time-Varying Second Moments

Abstract

In this paper, we propose a new risk model to better address events like the recent credit crisis. First, the possible start of a crisis is modeled by including a low-probability jump process. Second, the risk characteristics of the crisis are captured by allowing for time-varying volatilities and correlations. Time variation in correlations is due to the changing importance of two sources: monetary shocks leading to a positive stock-bond correlation, and risk aversion (or “flight to safety”) shocks leading to a negative stock-bond correlation. The model stays within the essentially affine class, thereby allowing for closed-form solutions for arbitrage-free nominal and real bond prices of all maturities. Moreover, equity options and swaption prices are included in the estimation procedure to enhance the proper modeling of the volatility on the equity and interest rate markets. The model captures a large part of the time variation in financial risks for pension funds due to both changing volatilities and correlations.