22 research outputs found
Affine LIBOR models with multiple curves: theory, examples and calibration
We introduce a multiple curve framework that combines tractable dynamics and
semi-analytic pricing formulas with positive interest rates and basis spreads.
Negatives rates and positive spreads can also be accommodated in this
framework. The dynamics of OIS and LIBOR rates are specified following the
methodology of the affine LIBOR models and are driven by the wide and flexible
class of affine processes. The affine property is preserved under forward
measures, which allows us to derive Fourier pricing formulas for caps,
swaptions and basis swaptions. A model specification with dependent LIBOR rates
is developed, that allows for an efficient and accurate calibration to a system
of caplet prices.Comment: 42 pages, 11 figures. Updated version, added section on negative
rates and positive spread
Information, no-arbitrage and completeness for asset price models with a change point
We consider a general class of continuous asset price models where the drift
and the volatility functions, as well as the driving Brownian motions, change
at a random time . Under minimal assumptions on the random time and on
the driving Brownian motions, we study the behavior of the model in all the
filtrations which naturally arise in this setting, establishing martingale
representation results and characterizing the validity of the NA1 and NFLVR
no-arbitrage conditions.Comment: 21 page
Affine LIBOR models with multiple curves: Theory, examples and calibration
We introduce a multiple curve LIBOR framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine property is preserved under forward measures, which allows to derive Fourier pricing formulas for caps, swaptions and basis swaptions. A model specification with dependent LIBOR rates is developed, that allows for an efficient and accurate calibration to a system of caplet prices
A tractable LIBOR model with default risk
We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are analytically tractable under defaultable forward measures. This leads to explicit formulas for CDS spreads, while semi-analytical formulas are derived for other credit derivatives. Finally, we give an application to counterparty risk.
Discrete tenor models for credit risky portfolios driven by time-inhomogeneous L\'evy processes
The goal of this paper is to specify dynamic term structure models with discrete tenor structure for credit portfolios in a top-down setting driven by time-inhomogeneous L\'evy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion and pricing formulas for STCDOs and options on STCDOs. A calibration to iTraxx data with an extended Kalman filter shows an excellent fit over the full observation period. The calibration is done on a set of CDO tranche spreads ranging across six tranches and three maturities.