Extends multi-curve framework for fully collateralized markets.
problem Lack of a complete multi-currency setup with cross-currency basis.
method Develops a new formulation of currency funding spread and a discretization of the HJM framework.
result Better formulation of currency funding spread for general dependence.
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.
Study multi-curve extension of short rate models with Gaussian factor processes.
problem Derivative pricing in multi-curve financial models.
method Gaussian factor model with short rate and spreads as second order polynomials of Gaussian processes.
result Adjustment factor for pricing linear and optional derivatives in multi-curve setup.
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.
Develops EM algorithm for analyzing multi-curve data with switching nonparametric regression models.
problem Analyzing multi-curve data with switching latent state processes.
method Switching nonparametric regression models and an EM algorithm for parameter estimation.
result Frequentist properties of parameter estimates validated through simulation studies and real data application.
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.
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…
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework w…
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…
Critical graphs of quadratic differentials equidistribute in moduli space.
problem Distribution of critical graphs in moduli space.
method Study of Jenkins-Strebel differentials and their critical graphs.
result Critical graphs equidistribute to the Kontsevich measure.
The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.
problem Dynamics of group actions on SU(2)-representation varieties of surfaces and non-orientable surfaces.
method Description and analysis of group actions generated by Dehn twists on SU(2)-representation varieties.
result Explicit invariant rational functions on SU(2)-representation varieties for specific cases of surfaces and non-orientable surfaces.
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.
The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.
problem Characterizing isotopy classes of links in 3-manifolds, especially in contact structures.
method Developed theory of links transverse to a nowhere-zero vector field, constructing examples in both Legendrian and pseudo-Legendrian settings.
result Non-simple isotopy classes of links exist, including Legendrian and pseudo-Legendrian examples.
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.
Counting hyperbolic multi-geodesics with individual component lengths.
problem Counting hyperbolic multi-geodesics with specific component lengths.
method Unified geometric and topological techniques, combining Mirzakhani's results and Margulis's ideas.
result Asymptotic polynomial counts of multi-geodesics in mapping class group orbits, generalizing Wolpert's conjecture.
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…
We show that any grafting ray in Teichmüller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichmüller geodesic ray. As a consequence the projection of a generic grafting ray to moduli space is dense. We also show that the set of points in Teichmüller space obtained by integ…
Formula connects linking number to spectral theory on 3-torus.
problem Computing linking number of multi-geodesics on 3-torus.
method Spectral theory of Laplace operator on differential forms.
result Formula for linking number of multi-geodesics on 3-torus.
Paper examines pricing and hedging for cross-currency swaps referencing backward-looking rates.
problem Pricing and hedging cross-currency swaps with backward-looking rates.
method Uses interest rate and currency futures for hedging, analyzes arbitrage-free multi-curve setting.
result Explicit pricing and hedging results for CCBS with backward-looking rates.
Study minima of geodesic lengths for specific curves on surfaces.
problem Finding the shortest geodesic paths on surfaces.
method Using curves related to dessins d'enfants and Grothendieck-Belyi surfaces.
result Minima of geodesic lengths are achieved on Riemann surfaces defined over number fields.
Geometric interpretation of 3-manifold invariants using immersed curves.
problem Obstructing smooth equivalences between 4-manifolds and surfaces with boundary.
method Relating morphisms between bordered Floer invariants to cobordism maps via immersed curves in the punctured torus.
result Morphisms between immersed curve invariants compute certain cobordism maps.
This study tackles XVA model risk and computational effort in derivatives pricing.
problem XVA model risk and computational effort in derivatives pricing, especially for counterparty and funding risk.
method Realistic and complete XVA modelling framework based on multi-curve time-dependent volatility G2++ stochastic dynamics, calibrated on real market data, and multi-step Monte Carlo simulation.
result Identification and quantification of model risk sources and computational effort in XVA figures.
In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one…
Extends classification of invariant measures on geodesic currents.
problem Classifying invariant measures on geodesic currents.
method Decomposition of currents into measured laminations, multi-curves, and bound currents.
result Extension of classification to geodesic currents.
Paper studies metric ribbon graphs and provides a recursion for their volumes.
problem Calculating volumes of combinatorial moduli spaces of directed metric ribbon graphs.
method Decomposes directed ribbon graphs into simpler graphs with one vertex, proving a canonical recursion scheme for volumes.
result Explicit recursion for volumes of four-valent metric ribbon graphs provided.
The study bounds distances in simplicial complexes and defines new invariants for 3-manifolds and handlebody-knots.
problem Estimating distances in simplicial complexes associated with low-dimensional manifolds.
method Obtained bounds on distances in simplicial complexes using topological conditions on vertices and curve complexes. Defined new invariants for 3-manifolds and handlebody-knots using splitting distances.
result Splitting distances in simplicial complexes are bounded from below under stabilizations, leading to converging invariants.
This paper studies a subgroup of the Goeritz group related to Heegaard splittings induced by openbook decompositions.
problem Understanding the subgroup of the Goeritz group associated with Heegaard splittings from openbook decompositions.
method Analyzes the mapping class group of a 3-manifold, focusing on elements that preserve the binding and commute with the monodromy.
result Characterizes the Goeritz group subgroup as a quotient of specific mapping class groups and provides a criterion for certain elements.
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.
New combinatorial structures for Teichmüller spaces with Thurston's metric are explored.
problem Understanding the combinatorial structures of Teichmüller spaces with Thurston's metric.
method Analyzing the unit tangent and cotangent spheres of Teichmüller space, proving formulas for dimensions and codimensions of faces.
result The combinatorial structure of unit spheres in Teichmüller spaces is independent of the underlying point and is isomorphic to the extended mapping class group.
Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous, they depend on input distributions that are data-cleaning- and Data-Model-depende…
Introduces AMLB, an open benchmark for AutoML frameworks.
problem Challenges in comparing AutoML frameworks.
method Open benchmark with 9 AutoML frameworks, 71 classification, 33 regression tasks, multi-faceted analysis, Bradley-Terry trees.
result Differences in AutoML frameworks' performance and trade-offs.
EagerPy simplifies writing code for multiple deep learning frameworks.
problem Code duplication and framework lock-in when using different deep learning libraries.
method Integrates multiple frameworks into a single Python framework.
result Automatic compatibility across PyTorch, TensorFlow, JAX, and NumPy.
OBSER framework infers sub-environments from objects, outperforming scene-based methods.
problem Zero-shot recognition of environments from object distributions.
method Bayesian framework using metric and self-supervised learning models to estimate object distributions in latent space.
result OBSER framework reliably performs inference in open-world and photorealistic environments, outperforming scene-based methods.
Unified framework speeds up SMF algorithms via variance reduction.
problem Improving convergence speed and accuracy in stochastic matrix factorization.
method Unified framework using variance reduction for SMF.
result Consistently faster convergence and more accurate output.
Paper introduces a flexible HJM framework for consistent electricity prices.
problem Consistent modeling of intraday, spot, futures, and option prices.
method Flexible HJM-type framework with economic interpretations.
result Allows existing spot price models to be used in HJM setting.
Unified probabilistic framework for nonlinearities in neural networks.
problem Lack of a unified approach to incorporating nonlinearities in neural networks.
method Doubly truncated Gaussian distributions for generating various nonlinearities.
result Performance improvements in RBM, temporal RBM, and TGGM when nonlinearities are learned alongside weights.
A new forecasting framework uses suboptimal embeddings to improve multivariate time series prediction.
problem Randomly selecting embeddings or brute force methods often lead to suboptimal forecasts.
method Develops a framework that uses various suboptimal embeddings obtained via combinatorial optimization.
result Achieves the best results among existing frameworks for various datasets.
Extends DeTEcT framework for token economies with dynamic and probabilistic parameters.
problem Modeling wealth distribution in token economies with dynamic and probabilistic parameters.
method Introduces four parametrization techniques: dynamic vs static, probabilistic vs non-probabilistic.
result Derives existing wealth distribution models from DeTEcT framework with added restrictions.
Geometric framework simplifies CNNs using inner product spaces.
problem Complexity and inefficiency in training CNNs.
method Introduces a geometric approach to CNNs using inner product spaces.
result Gradient calculations simplified for CNN layers, higher-order losses.
Proposes a new theoretical framework for deep locally connected ReLU networks.
problem Understanding theoretical properties of deep locally connected networks.
method Teacher-student setting, explicit formulation of data distribution, disentangled representations, compatibility with regularization techniques.
result Theoretical framework facilitates analysis of practical issues like overfitting and generalization.
New framework assesses and benchmarks ML methods for multivariate time series.
problem Benchmarking and explaining performance of machine learning methods.
method Proposes a new framework with systematized performance-explainability characteristics.
result Illustrates application to multivariate time series classifiers.
RYU framework constructs safe regions for optimization problems.
problem Optimization problems with specific component functions.
method RYU framework for constructing safe regions.
result RYU framework improves upon state-of-the-art methods.
A modular framework for knowledge distillation simplifies experiments and reproducibility.
problem Difficulty in reproducing knowledge distillation studies due to lack of generalized frameworks.
method A configuration-driven PyTorch framework for knowledge distillation studies.
result Demonstrates efficient training strategies and various knowledge distillation methods.
New framework models insurance liabilities with complex dependencies.
problem Complex dependence structures in non-life insurance.
method Generalized reduced-form framework for continuous-time modeling.
result Explicit pricing and hedging formula for non-life insurance.
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only collapsed realizations. In terms of infinitesimal rigidity, realizations of the former…
A new clustering framework using fixed points for data analysis.
problem Lack of unified understanding and application of clustering algorithms in data analysis.
method Restated model-based clustering using fixed point theory, iteratively constructing contraction maps to find cluster centers.
result Unified clustering framework reveals convergence mechanisms and interconnections among clustering algorithms.
The paper analyzes frameworks for integrating sustainability into investment decisions.
problem Understanding how ESG factors influence investment choices.
method Examined and analyzed various theoretical frameworks including Behavioral Finance, Modern Portfolio, and Risk Management.
result Investors increasingly integrate ESG factors to optimize financial outcomes and societal goals.
We explore a framework called boosted Markov networks to combine the learning capacity of boosting and the rich modeling semantics of Markov networks and applying the framework for video-based activity recognition. Importantly, we extend the framework to incorporate hidden variables. We show how the framework can be ap…