The paper analyzes credit valuation adjustments under collateralized interest rate derivatives, introducing a new dynamics for multiple interest rate curves.
problem The impact of multiple interest rate curves on credit valuation adjustments under collateralized models.
method Formulated a consistent dynamics for multiple interest rate curves, including the margin period of risk and stochastic basis for wrong-way risk analysis.
result Numerical results confirm the importance of stochastic basis for proper wrong-way risk analysis of sensitive products like basis swaps.
Develops a new model for interest rates allowing negative rates and superior calibration.
problem Current market environment with negative interest rates and poor calibration of existing models.
method Forward price process approach using time-inhomogeneous Lévy processes.
result The model allows for negative interest rates and superior calibration properties.
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of c…
The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe the market of interest rate products. On the other hand, using different yield c…
Develops a framework for modeling interest rate markets with jumps.
problem Stochastic discontinuities in interest rate markets.
method Extended HJM framework with stochastic discontinuities, affine semimartingales.
result Fundamental theorem of asset pricing based on NAFLVR.
We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market…
Develops a new model for multiple yield curves using branching processes.
problem Reproduce empirical features of spreads between interbank rates.
method Continuous-state branching processes with immigration (CBI processes).
result Models can generate contagion effects among different spreads.
For a long time interest-rate models were built on a single yield curve used both for discounting and forwarding. However, the crisis that has affected financial markets in the last years led market players to revise this assumption and accommodate basis-swap spreads, whose remarkable widening can no longer be neglecte…
Continuous tenor extension of affine LIBOR models for multiple curves, with applications to XVA calculations.
problem Modeling interest rates with multiple curves and arbitrage-free value adjustments.
method Introducing an interpolating function to extend discrete tenor models to continuous tenor models, deriving expressions for instantaneous forward rates and short rates.
result The continuous tenor model is arbitrage-free and analytically tractable under the spot martingale measure, allowing consistent computation of value adjustments.
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 …
Genetic Algorithm improves Nelson-Siegel-Svensson model calibration for interest rates.
problem Calibrating the Nelson-Siegel-Svensson model is difficult due to nonlinearity and parameter co-dependence.
method Applied Genetic Algorithm to optimize model parameters.
result Constructs stable interest rate curves and model parameters over time.
Study multi-currency markets with multiple interest rates and collateral.
problem Characterize absence of arbitrage in a multi-currency market.
method Generalize results from Bielecki and Rutkowski (2015) to a multi-currency framework, linking with Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). Characterize absence of arbitrage without collateral, then study collateralization schemes under various conventions.
result Complete study of absence of arbitrage and pricing in multi-currency markets with multiple interest rates and collateral.
Abstract framework for cross-currency interest rate contracts.
problem Handling cross-currency markets with collateral and incompleteness.
method Developed a general HJM framework for abstract market indices.
result Enabled simultaneous description of multiple currency interest rate products.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
The paper explores using machine learning for yield curve calibration in multiple markets.
problem Calibration challenges in multiple yield curve markets.
method Gaussian process regression and Adam optimizer.
result Good results for single curve markets, but many challenges for multi curve markets.
New tensor approach models global fixed income risks across maturities and economies.
problem Lack of models capturing multi-dimensional data in global fixed income markets.
method Introduces tensor-valued approach to model shared risks among multiple interest rate curves.
result Estimates risk factors decomposable into maturity and country domains, enabling tailored portfolio management.
Study shows Nelson-Siegel curves fit well with Ho-Lee and Hull-White models.
problem Fitting observed interest rate term structures with interest rate models.
method Examined Nelson-Siegel curves in the context of Ho-Lee and Hull-White models.
result Extended Nelson-Siegel curves emerge from the forward curve process of the models.
Constructs rational models for pricing and managing inflation-linked derivatives.
problem Pricing and risk management of inflation-linked derivatives.
method Rational models constructed in a multiplicative manner, isolating inflation convexity-adjustment.
result Closed-form pricing of various inflation products and exotic swaps.
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modellin…
This paper uses crypto derivatives data to estimate yield curves for cryptocurrencies.
problem Estimating yield curves for cryptocurrencies without bond markets.
method Using mathematical tools and data from cryptocurrency derivatives markets.
result Yield curves can be constructed for cryptocurrencies using derivative data.
This study updates a model for Mexican interest rate swaps post-crisis.
problem Post-crisis divergence of interest rates and new regulatory requirements.
method Used Fujii et al. 2010b model with collateral currencies USD, EUR, MXN.
result Validated model for Mexican interest rate derivatives with collateral currencies.
This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous. We term the process followed by the shocks to the forward curve ``stochastic str…
The paper explains the concave shape of yield curves from trading perspectives.
problem Lack of explanation for the concavity of yield curves from economics theory.
method Explains the concavity of yield curves from trading perspectives.
result Offers an explanation for the concave shape of yield curves.
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of the short rate, the long rate and the fluctuations of the curve around its avera…
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
problem Financial pricing under multiple interest rates and collateralization.
method Derives a change of measure formula for recursive conditional expectations in a jump-diffusion setting.
result Generalizes the change of numéraire technique for multiple interest rates and collateralization.
Metaheuristics improve yield curve estimation for Costa Rica.
problem Estimating the yield curve for Costa Rica using historical data.
method Used Nelson-Siegel and Svensson models with four metaheuristics (Ant colony, Genetic, Particle Swarm, Simulated Annealing) for optimization.
result Metaheuristics achieved better results than classical methods, especially Particle Swarm and Simulated Annealing.
Unified framework for multiple yield curve models using affine processes.
problem Consolidation of various multiple yield curve modeling approaches.
method Modeling Libor rates and OIS rates as functions of an underlying affine process.
result Tractable valuation formulas and new model developments.
By adopting the polynomial interpolation method, we propose an approach to hedge against the interest-rate risk of the default-free bonds by measuring the nonparallel movement of the yield-curve, such as the translation, the rotation and the twist. The empirical analysis shows that our hedging strategies are comparable…
Develops a model for cryptocurrency interest rates.
problem Modeling interest rates for cryptocurrencies.
method Term structure model with zero short rate, price processes of crypto bonds, and expressions for forward rates.
result Model can be calibrated to market data and uses strict local martingales for pricing kernels.
A robust machine learning approach forecasts U.S. Treasury yields, reducing risk for investors.
problem Noisy and uncertain U.S. Treasury yields pose risk to forecast users.
method Formulates yield curve forecasting as a distributionally robust problem, combining factor models and machine learning.
result Robust forecast combinations improve out-of-sample performance across different maturity periods.
The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Geostatistical models and machine le…
Consistent valuation across different interest rate curves using pricing kernels.
problem Asset pricing with varying discount and cash flow rates.
method Pricing kernel framework linking distinct markets with consistent curve-conversion factors.
result Derivation of an across-curve pricing formula enabling consistent valuation and hedging.
We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinit…
Study reveals strong co-jumping behavior in U.S. yield curves compared to Europe.
problem Understanding co-jumps in interest rate futures markets.
method Localized co-jumps through wavelet coefficients, identified statistically significant ones, and analyzed using high frequency data.
result Stronger co-jumping behavior in U.S. yield curves compared to European ones.
Model interest rates and energy futures with regime-switching dynamics.
problem Modeling interest rates and energy futures with regime-switching dynamics.
method HJM model with Markov-chain modulated forward rates, proving affine structure for term structure.
result Explicit solutions for forward curves in many cases.
We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJ…
Italian banks use swaps to hedge against rising interest rates, offsetting losses on debt securities.
problem Interest rate risk on Italian banks' debt securities.
method Analysis of granular regulatory data on euro interest rate swap trades.
result Swaps can offset losses on debt securities, reducing interest rate exposure.
Study optimizes dividend payout strategies under fluctuating interest rates.
problem Maximizing dividends under stochastic interest rates with negative values.
method Analytical HJB approach and backward SDEs for analysis.
result Explicit optimal strategies found for both time-dependent and strategy-independent stopping times.
Study analyzes correlation structure in two-factor Hull-White model for XVA calculations.
problem Capturing the correlation structure in two-factor Hull-White model for accurate XVA calculations.
method Combination of approximation formula and Monte-Carlo simulation to investigate correlation structure.
result Hull-White model effectively captures de-correlation of the yield curve under specific parameter conditions.
This paper tests yield curve generators for property-casualty insurers.
problem Quantifying interest-rate risk for property-casualty insurers with high bond holdings.
method Develops and tests yield curve generators to quantify bond-value changes.
result Tests yield curve generators against known distributional properties of yield curves.
Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non-trivial observational e…
Derives equations for life insurance reserves with interest rate uncertainty.
problem Life insurance reserves with stochastic interest rates.
method Partial differential equations for reserves under stochastic interest rates.
result Explicit solutions for reserves under specific models.
We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportun…
Clarifies when solutions to stochastic PDEs stay near given subsets.
problem Understanding the proximity of solutions to stochastic PDEs to given subsets.
method Analyzes distance between closed sets and solutions to stochastic PDEs.
result Clarifies conditions for solutions to stay near given subsets.
We present an arbitrage-free non-parametric yield curve prediction model which takes the full (discretized) yield curve as state variable. We believe that absence of arbitrage is an important model feature in case of highly correlated data, as it is the case for interest rates. Furthermore, the model structure allows t…
Modeling interest rates for multiple tenors considering rollover risk.
problem Tackling the risk of borrowing at a shorter tenor and lending at a longer tenor.
method Constructing a stochastic model framework with endogenous frequency basis, incorporating credit and liquidity risks.
result The model can be calibrated to market data and used for pricing interest rate derivatives.
New method models yield curve probability distribution for better forecasting.
problem Difficult to model and forecast changes in interest rate structure.
method Reconstructs joint probability distribution of yield curve parameters in functional space via high degree polynomial.
result Proposes a new approach to complement standard models like ARIMA.
Empirical study on long-term discount rates using historical bond prices.
problem Estimating long-term real interest rates and discount rates from historical bond data.
method Using Fourier transforms to derive the discount function and fitting it to historical data.
result Estimated long-term discount rates of 1.7% for UK and 2.2% for US.