2015/02/25 by Stéphane Crépey, Stephane Crepey, Crepey, Stephane +6 · 1 citation
Economics, Econometrics and Finance · #Credit Risk and Financial Regulations #FOS: Economics and business #Insurance and Financial Risk Management #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1502.07397
34 pages, 9 figures
arxiv created 2015/02/25 · openalex publication_date 2015/02/25 · arxiv updated 2015/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.