TY - JOUR
T1 - A Lévy HJM Multiple-Curve Model with Application to CVA Computation
AU - Crépey, Stéphane
AU - Grbac, Zorana
AU - Ngor, Nathalie
AU - Skovmand, David
PY - 2015
Y1 - 2015
N2 - We consider the problem of valuation of interest rate derivatives in the post-crisis set-up. We develop a multiple-curve model, set in the HJM framework and driven by a Lévy process. We proceed with joint calibration to OTM swaptions and co-terminal ATM swaptions of different tenors, the calibration to OTM swaptions guaranteeing that the model correctly captures volatility smile effects and the calibration to co-terminal ATM swaptions ensuring an appropriate term structure of the volatility in the model. To account for counterparty risk and funding issues, we use the calibrated multiple-curve model as an underlying model for CVA computation. We follow a reduced-form methodology through which the problem of pricing the counterparty risk and funding costs can be reduced to a pre-default Markovian BSDE, or an equivalent semi-linear PDE. As an illustration, we study the case of a basis swap and a related swaption, for which we compute the counterparty risk and funding adjustments
AB - We consider the problem of valuation of interest rate derivatives in the post-crisis set-up. We develop a multiple-curve model, set in the HJM framework and driven by a Lévy process. We proceed with joint calibration to OTM swaptions and co-terminal ATM swaptions of different tenors, the calibration to OTM swaptions guaranteeing that the model correctly captures volatility smile effects and the calibration to co-terminal ATM swaptions ensuring an appropriate term structure of the volatility in the model. To account for counterparty risk and funding issues, we use the calibrated multiple-curve model as an underlying model for CVA computation. We follow a reduced-form methodology through which the problem of pricing the counterparty risk and funding costs can be reduced to a pre-default Markovian BSDE, or an equivalent semi-linear PDE. As an illustration, we study the case of a basis swap and a related swaption, for which we compute the counterparty risk and funding adjustments
KW - Credit valuation adjustment (CVA)
KW - Funding
KW - Interest rate derivative
KW - Lévy process
KW - Multiple-curve term structure model
U2 - 10.1080/14697688.2014.942232
DO - 10.1080/14697688.2014.942232
M3 - Journal article
SN - 1469-7688
VL - 15
SP - 401
EP - 419
JO - Quantitative Finance
JF - Quantitative Finance
IS - 3
ER -