Risk Models after the Credit Crisis
31 Pages Posted: 15 Dec 2009 Last revised: 13 Jun 2011
Date Written: June 10, 2011
The 2008 credit crisis came as a complete surprise to most financial practitioners and academics. As risk models had largely been unable to predict the crisis and its impact on volatilities and correlations, the usefulness of such models has been widely called into question. This paper proposes a new model to remedy a number of important flaws. First, the possible start of a crisis is modeled by including a low-probability jump process. These jumps are associated with a significant drop in the stock market, lower risk-free interest rates, and a strong increase in credit spreads. 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.
Keywords: essentially affine macro-finance term structure model, time-varying volatilities and correlations, jumps, options, swaptions, asset liability management
JEL Classification: E34, G13
Suggested Citation: Suggested Citation