Abstract
We propose a simple but practical methodology for the quantification of correlation risk in the context of credit derivatives pricing and credit valuation adjustment (CVA), where the correlation between rates and credit is often uncertain or unmodelled. We take the rates model to be Hull–White (normal) and the credit model to be Black–Karasinski (lognormal). We summarise recent work furnishing highly accurate analytic pricing formulae for credit default swaps (CDS) including with defaultable Libor flows, extending this to the situation where they are capped and/or floored. We also consider the pricing of contingent CDS with an interest rate swap underlying. We derive therefrom explicit expressions showing how the dependence of model prices on the uncertain parameter(s) can be captured in analytic formulae that are readily amenable to computation without recourse to Monte Carlo or lattice-based computation. In so doing, we crucially take into account the impact on model calibration of the uncertain (or unmodelled) parameters.
Highlights
We have proposed a framework for the quantification of model risk in credit derivatives pricing in circumstances where the correlation between rates and credit is either uncertain in its value or not included in the calculation
We considered in particular the cases of (a) an interest rate swap extinguisher, (b) a contingent credit default swaps (CDS) on an interest rate swap underlying, and (c) an extinguisher with capped or floored Libor flows
We derived explicit analytic expressions for the model risk as a function of the degree of uncertainty associated with the correlation, under an asymptotic assumption of the interest rate and the credit default intensity being small and taking into account the potential impact of correlation on model calibration
Summary
Much effort is currently being invested into managing the risk faced by financial institutions as a consequence of model uncertainty One strand to this effort is an increased level of regulatory scrutiny of the performance of the model validation function, both in terms of ensuring that adequate testing is performed for all models used for pricing and risk management purposes and of enforcing a governance policy that only models so tested are so used. As is stated in the Supervision and Regulation Letter of US Federal Reserve (2011): An integral part of model development is testing, in which the various components of a model and its overall functioning are evaluated to show the model is performing as intended; to demonstrate that it is accurate, robust, and stable; and to evaluate its limitations and assumptions Another concern is model risk monitoring and management. We consider rates–credit correlation risk in relation to credit derivatives pricing, but it is suggested the methodology may be applicable more widely to other types of model risk and a wider class of financial instruments
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