Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

TL;DR

This paper introduces a rational multi-curve model framework for interest rate derivatives, calibrated to market data, and extends it to compute counterparty-risk adjustments like CVA, ensuring consistency between risk-neutral and real-world measures.

Contribution

It develops a rational function-based multi-curve model calibrated to market data and applies it to counterparty-risk valuation adjustments, bridging risk-neutral and real-world measures.

Findings

A rational two-factor model matches market data accurately.

Derived positive default intensities for CVA calculations.

Applied models to basis swap contracts successfully.

Abstract

We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure Q and their consistent equivalence class under the real-world probability measure P. The consistent P-pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as CVA, we show how positive default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.