A new model prices Bermudan swaptions without calibration.
problem Calibration of Bermudan swaptions models.
method Semi-analytical pricing model using swap rates and correlations.
result No product-specific calibration required.
Proposes efficient calibration method for LIBOR Market Model with stochastic volatility.
problem Calibrating LIBOR Market Model with stochastic volatility.
method Derives analytical gradient of swaptions prices for DDSVLMM and uses it for gradient-based optimization.
result Analytical gradient-based calibration is highly competitive and efficient for DDSVLMM.
Paper improves Gaussian mechanism for differential privacy with analytical calibration and denoising.
problem Limitations in the original Gaussian mechanism's variance formula for high and low privacy regimes.
method Developed an optimal Gaussian mechanism with analytical calibration using the Gaussian cumulative density function and post-processing denoising.
result Analytical calibration reduces noise variance by at least a third compared to the classical Gaussian mechanism, and denoising improves accuracy in high-dimensional data.
Tree-based models biased when trained on imbalanced data, requiring new calibration methods.
problem Bias in tree-based models trained on imbalanced datasets.
method Analytical calibration of random forest models, demonstrating bias in decision trees.
result Calibrating tree-based models on imbalanced data negatively impacts predictions, especially for the minority class.
We enhance short-rate models to control implied volatility analytically.
problem Controlling implied volatility in short-rate models.
method Randomized Affine Diffusion (RAnD) method applied to Heath-Jarrow-Morton framework.
result Randomized short-rate models improve calibration and control implied volatility shapes.
Paper calibrates GARCH diffusion model for option pricing using PDE methods.
problem Lack of fast, semi-analytic solution for GARCH diffusion model option pricing.
method PDE-based finite difference solver for accurate calibrations.
result PDE calibration of GARCH diffusion model to SPX options.
Sharp analysis of isotonic regression for binary data, improving calibration bounds.
problem Improving the calibration of probabilistic predictors using isotonic regression.
method Sharp finite-sample characterization of isotonic regression's degrees of freedom using analytic number theory.
result First nontrivial distribution-free guarantee on Expected Calibration Error (ECE) of isotonic regression.
Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivi…
Paper speeds up energy option pricing calibration.
problem Efficiently calibrate two-factor models for energy option pricing.
method Analytical and numerical methods to derive the variance of multi-factor models.
result The Lyapunov approach speeds up calibration by 14 times.
New methods for volatility modeling using rough paths and signatures.
problem Calibrating implied volatility surfaces in various stochastic models.
method Analytical approximations and signature-based models based on rough path theory.
result Signature-based models achieve comparable accuracy to analytical expansions and can capture more complex dynamics.
Certified calibration methods protect model confidence from adversarial attacks.
problem Adversarial attacks degrade model calibration, reducing confidence in predictions.
method Developed certified calibration methods to provide worst-case bounds on calibration under adversarial perturbations.
result Certified calibration methods produce analytic and approximate bounds for the Brier score and expected calibration error.
Efficiently calibrates Heston model with time-varying parameters for financial derivatives.
problem Calibrating Heston model with time-dependent parameters.
method Simple and numerically efficient approach using semi-analytical formulas and Gauss-Kronrod quadrature.
result Improves Heston model's performance in selected cases.
In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that …
Study adiabatic limits of calibrated submanifolds in Riemannian geometry.
problem Understanding the behavior of calibrated submanifolds under adiabatic limits.
method Define a 1-parameter family of forms and study their adiabatic limit, showing it is a generalized calibration.
result Adiabatic calibrated submanifolds are anisotropic minimal in the classical sense.
The paper studies deformations of submanifolds using a new algebraic structure.
problem Deformations of submanifolds in geometric contexts.
method Introduces strongly homotopy Lie algebras to govern deformations of submanifolds.
result Deformations of submanifolds form an analytic variety under certain assumptions.
This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and their non-hybrid counterparts. The methodology is applied to Heston's model. A …
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
This paper enhances uplift modeling for multi-treatment marketing campaigns.
problem Optimizing marketing strategies by selecting individuals likely to respond to different treatments.
method Leveraging score ranking and calibration techniques.
result Improves overall performance of marketing campaigns.
Study of interactions between functions on manifolds via submersions.
problem Understanding interactions between convex, subharmonic, and pluri-subharmonic functions on manifolds.
method Application of pluri-potential theory and analysis of Kähler and G2 manifolds.
result Previous results on Lagrangian fibrations can be viewed as applications of this framework.
In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tra…
Derives formulae linking SABR model parameters to ATM and option prices.
problem Characterizing SABR model parameters from option prices.
method Analytic formulae linking α, ν, and ρ to ATM price and option prices at strikes. result Characterization of SABR parameters from swap rate probability density function derivatives.
The paper connects hyperbolicity in calibrated geometry to properties of Smith immersions.
problem Hyperbolicity in calibrated manifolds and its relation to Smith immersions.
method Establishes a theorem relating hyperbolicity to the equicontinuity of Smith immersions, proving a new Schwarz lemma.
result Calibrated hyperbolicity of compact φ-replete manifolds is equivalent to the equicontinuity of Smith immersions. We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration t…
New methods correct bias in LLM-as-a-Judge evaluations, but reliability depends on judge quality and model calibration.
problem Systematic bias in LLM-as-a-Judge evaluations using naive estimators.
method Analytical results, simulations, and real-data case study to diagnose reliability of corrected estimates.
result Corrected estimates, especially shared-calibration comparisons, can be unreliable under certain conditions.
A fast calibration method for rough volatility models with jumps.
problem Calibrating stochastic volatility models to market data efficiently.
method Structure-preserving approach: split pricing formula, precompute data-independent integrals, and approximate market-dependent remainder with neural networks.
result Calibration achieves high accuracy and speed, and a pure-jump rough volatility model adequately captures VIX dynamics.
The paper proposes a new method to calibrate multiple computer models simultaneously.
problem Calibrating multiple computer models one at a time is inefficient.
method Developed a probabilistic framework using customized neural networks.
result Simultaneous calibration improves predictive accuracy but can be non-identifiable in high dimensions.
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston characteristic function and modify it to avoid discontinuities caused by branch switchi…
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to …
A new method for effective VAE training using calibrated decoders.
problem Training VAEs requires hyperparameter tuning, leading to inefficiency.
method Calibrated decoders that learn uncertainty and automatically determine information retention.
result Calibrated decoders can simplify VAE training without heuristic modifications.
We establish a twistor correspondence between a cuspidal cubic curve in a complex projective plane, and a co-calibrated homogeneous G2 structure on the seven--dimensional parameter space of such cubics. Imposing the Riemannian reality conditions leads to an explicit co-calibrated G2 structure on SU(2,1)/U(1). …
Unified Bayesian-AI framework improves epidemiological risk prediction and uncertainty quantification.
problem Lack of calibrated uncertainty in machine learning models for epidemiology.
method Combines Bayesian prediction with Bayesian hyperparameter optimization using logistic regression and Gaussian-process Bayesian optimization.
result Unified Bayesian-AI framework provides reliable coverage and improved calibration, enhancing epidemiological decision making.
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
problem Calibration of mean-reverting SABR models to equity volatilities.
method Derive closed-form approximations using a CIR process for volatility, lognormal process for volatility, and CIR process for squared volatility. Calibrate to empirical volatilities using a computer algebra system.
result Calibrated mean-reverting SABR models provide excellent fits to equity volatilities with only five parameters per surface.
New PDEs for k-harmonic maps link to calibrated fibrations.
problem Understanding k-harmonic maps and their relation to calibrated fibrations. method Analyzing two special classes of k-harmonic maps between Riemannian manifolds. result Explicit noncompact examples of the second class of maps.
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the approach proposed in LiptonSepp2011 is developed by i) replacing a piecewise constant…
This paper explores the vol-of-vol parameter in the Heston model and its relation to VVIX.
problem Calibrating the Heston model to market data for stable exotic option pricing.
method Four approaches to estimate VVIX in the Heston model: transition density, analytical approximation, and PDE-based.
result Improved calibration stability of the Heston model using the estimated VVIX.
Proposes a flexible framework for implied volatility surfaces with random parameters.
problem Inconsistent calibration of parametric implied volatility models when market volatility deviates from the model's regime.
method Introduces random coefficients for parametric implied volatility formulas, preserving analytic flexibility and efficiency.
result Demonstrates improved modeling of implied volatility curves, especially for short-term options and earnings announcements.
Develops a diagnostic framework for interest rate model calibration, showing equivalence to Weighted Least Squares and revealing boundary-dominated leverage and local parameter instability.
problem Calibration of stochastic interest rate models
method Diagnostic framework using non-linear regression and analytical tractability of At-The-Money caps
result Reveals boundary-dominated leverage and local parameter instability
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 …
In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatility ideally associated with a scenario based underlying firm debt. We show how to calibrate this model using a chosen number of reference Credit Default Swap (CDS) …
We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for nu…
We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an α-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the Lévy propagator. Using distributional and Cn tools, we derive an analytic …
This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (200…
GNIs induce a regulariser that penalizes high-frequency components in neural network activations.
problem Understanding the regularizing effect of Gaussian noise injections on neural network activations.
method Deriving the explicit regularizer by marginalizing out injected noise and analyzing its effect in the Fourier domain.
result GNIs induce a regularizer that produces calibrated classifiers with large margins.
In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distri…
Analytical model prices options with moving barriers under non-Gaussian distributions.
problem Pricing options with moving barriers under non-Gaussian distributions.
method Path-integral formalism adapted from galaxy formation models, incorporating higher-order cumulants.
result Analytical pricing model for vanilla and barrier options without volatility smile.
This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.
problem Insufficient interpretability and probability calibration of complex-valued neural networks.
method Newton-Puiseux framework to examine local decision geometry, fitting a polynomial surrogate and factorizing it using Newton-Puiseux expansions.
result Enhanced Expected Calibration Error in ECG and wireless modulation datasets compared to uncalibrated softmax and standard post-hoc baselines.
The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is non-negative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options.…