Abstract
In this talk we address new issues related to the valuation of interest rate derivatives due to the recent credit crisis. Firstly, we present a multiple-curve interest rate model based on the HJM methodology and driven by time-inhomogeneous Levy processes. This model is capable of capturing various spreads between quantities that had been essentially the same before the crisis and which emerged due to interbank risk, such as the LIBOR-OIS spreads and the basis swap spreads. Using the model, a “clean value” of a portfolio of interest rate derivatives is calculated, which is a value in a hypothetical situation where the two parties would be risk-free and funded at a risk-free rate. Next, to account for counterparty risk and funding issues, various valuation adjustments have to be computed, jointly referred to as Total Valuation Adjustment (TVA). We streamline the reduced-form methodology through which the TVA pricing problem can be reduced to Markovian pre-default TVA BSDEs. Numerical results are presented for two different short rate interest rate models, thus also illustrating the related model risk issue.
This is joint work with Stéphane Crépey.
[PDF] Slides of the presentation.