A New Term Risk Dynamic for Q Jumps for Measuring Systemic Risk

Abstract

We propose a model which enables the measurement of term risk in markets which are sensitive to systemic risk. With its origins in the spectralisation of the AR(1) process (using the Wiener-Khintchine theorem, and a P ~ Q transform), a Q jump martingale solution is found which is unique and independent of the wiener process. The model is tested, in differential equation form, on the risk premia generated in the yield curve, the credit spread of risky bonds, and the term risk in the implied volatility skew (forward variance). An excellent agreement, in both graphical and regression forms for the scale and patterns of term risk premia, is displayed. Because these measures also typify systemic risk characteristics (with their traded risk versions seen in the CDS and forward VIX markets), the model also defines a useful connection between systemic (bank distress) risk with the Q jump systematic risk.