44 research outputs found
Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models
The LIBOR market model is very popular for pricing interest rate derivatives,
but is known to have several pitfalls. In addition, if the model is driven by a
jump process, then the complexity of the drift term is growing exponentially
fast (as a function of the tenor length). In this work, we consider a
L\'evy-driven LIBOR model and aim at developing accurate and efficient
log-L\'evy approximations for the dynamics of the rates. The approximations are
based on truncation of the drift term and Picard approximation of suitable
processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet
caps show that the approximations perform very well. In addition, we also
consider the log-L\'evy approximation of annuities, which offers good
approximations for high volatility regimes.Comment: 32 pages, 21 figures. Added an example of a path-dependent option
(sticky ratchet caplet). Forthcoming in the Journal of Computational Financ
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
Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments
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.Comment: 34 pages, 9 figure
Term Rates, Multicurve Term Structures and Overnight Rate Benchmarks: a Roll-Over Risk Approach
Modelling the risk that a financial institution may not be able to roll over its debt at the market reference rate, the so–called “roll–over risk”, we construct a model framework for the dynamics of reference term rates (e.g., LIBOR) and their spread vis–à –vis benchmarks based on overnight reference rates, e.g., rates implied by overnight index swaps (OIS). In this framework, different interest rate term structures are endogenously generated for each tenor, that is, a different term structure for each choice of the length of the interest rate accrual period, be it overnight (e.g., OIS), three–month LIBOR, six–month LIBOR, etc. A concrete model instance in this framework can be calibrated simultaneously to available market instruments at a particular point in time, but more importantly, we explicitly obtain dynamics of term rates such as LIBOR. Thus models in our framework are amenable to econometric estimation. For a model class based on affine dynamics, we conduct an empirical analysis on EUR data for OIS, interest–rate swaps, basis swaps and credit default swaps. Our model achieves a better fit to time series data than other models proposed in prior literature. We find that credit risk typically contributes only about 30% of the IBOR/OIS spread, with the balance of the spread due to the funding liquidity component of roll–over risk. Looking ahead, we show that, even if credit risk is entirely mitigated by repo transactions, the presence of roll–over risk confounds attempts to obtain term rates from overnight rate benchmarks. As various jurisdictions transition away from panel–based term rate benchmarks towards transaction–based overnight ones (such as SOFR in the United States), the framework presented in this paper thus provides important insights into some of the consequences of this transition
Efficient and accurate log-LĂ©vy approximations to LĂ©vy driven LIBOR models
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a L'evy-driven LIBOR model and aim at developing accurate and efficient log-L'evy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps and swaptions show that the approximations perform very well. In addition, we also consider the log-L'evy approximation of annuities, which offers good approximations for high volatility regimes
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