Bilateral Credit Valuation Adjustment for Large Credit Derivatives Portfolios

TL;DR

This paper derives an explicit formula for bilateral CVA in large credit derivatives portfolios using a doubly stochastic intensity model, highlighting the impact of credit risk volatility and default correlation.

Contribution

It introduces a novel explicit formula for bilateral CVA in large portfolios under a doubly stochastic framework with default correlation.

Findings

Counterparty adjustments are highly sensitive to credit risk volatility.

Default correlation significantly influences CVA calculations.

Theoretical predictions are validated through numerical analysis.

Abstract

We obtain an explicit formula for the bilateral counterparty valuation adjustment of a credit default swaps portfolio referencing an asymptotically large number of entities. We perform the analysis under a doubly stochastic intensity framework, allowing for default correlation through a common jump process. The key insight behind our approach is an explicit characterization of the portfolio exposure as the weak limit of measure-valued processes associated to survival indicators of portfolio names. We validate our theoretical predictions by means of a numerical analysis, showing that counterparty adjustments are highly sensitive to portfolio credit risk volatility as well as to default correlation.