Rational Multi-curve Models with Counterparty-risk Valuation Adjustments

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

Research output: Contribution to journalJournal articleResearchpeer-review


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 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 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.
Original languageEnglish
JournalQuantitative Finance
Issue number6
Pages (from-to)847-866
Number of pages20
Publication statusPublished - 2016


  • Multi-curve interest rate term structure models
  • Rational asset pricing models
  • Calibration
  • Counterparty-risk
  • Risk management
  • Markov functionals
  • Basis swap

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