Impact of Multiple Curve Dynamics in Credit Valuation Adjustments under Collateralization

TL;DR

This paper analyzes interest rate derivatives valuation considering credit risk and collateral, emphasizing the importance of stochastic basis models for accurate valuation and risk assessment of sensitive products.

Contribution

It introduces a realistic dynamics framework for multiple interest rate curves, highlighting the need for stochastic basis models in valuation and risk analysis.

Findings

Spot Libor rates should be treated as market primitives.

Including margin period of risk affects valuation outcomes.

Deterministic basis models are insufficient for sensitive products.

Abstract

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact.