The Correlation-neutral Measure for Portfolio Credit

We derive a formula for a Fourier transform of a counting process that describes the arrival of unpredictable events, and we show how this transform facilitates an analytical treatment of a range of valuation, hedging and risk management problems that arise in single name and portfolio credit risk. Example applications include reduced form pricing of credit sensitive securities referenced on single or multiple issuers, hedging of constituent risks, model estimation, and credit portfolio risk measures. Our results cover situations with feedback, in which events have an impact on arrival rates (as with contagion) and risk-free interest rates (as with flights to quality). A complex-valued measure change neutralizes this feedback.