Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

Stephane Crepey, Andrea Macrina, Tuyet Mai Nguyen and David Skovmand

Papers from arXiv.org

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.

Date: 2015-02
New Economics Papers: this item is included in nep-mfd and nep-rmg
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