Poisson Q Term Risk Model of Yields : Measuring Systematic Dynamic Risk Over the EU Debt Crisis

A new model, the Poisson Q, is presented which determines the term risk premium in markets from the Ornstein Uhlenbeck version of the Poisson intensity process. The risk neutral properties are obtained by Fourier frequency analysis and a logarithmic Cauchy change in measure. The Poisson Q martingale is then precisely orthogonal to the Wiener martingale. It is demonstrated how Poisson Q Yield Curve and Credit Spread Models can endogenously characterize the term risk premiums in the EU economic cycle. The model is evidenced by comparisons with existing models in determining the macro-typography of market extremes in the EU debt crisis