Rational multi-curve models with counterparty-risk valuation adjustments

Stéphane Crépey, Andrea Macrina, Tuyet Mai Nguyen and David Skovmand

Quantitative Finance, 2016, vol. 16, issue 6, 847-866

Abstract: We develop a multi-curve term structure set-up in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to London Interbank Offer Rate swaptions data and show that a rational two-factor log-normal 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 and their consistent equivalence class under the real-world probability measure . The consistent -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 credit valuation adjustment, we show how default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.

Date: 2016
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DOI: 10.1080/14697688.2015.1095348

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