This paper improves SABR/LMM for better practical use in global banks.
problem Inflexibility of existing SABR/LMM models.
method Develops a comprehensive SABR/LMM model with time-dependent skew and smile.
result Provides a flexible and practical SABR/LMM model for global banks.
Extends LIBOR market model to reduce exploding scenarios.
problem Exploding scenarios in market-consistent guarantees valuation.
method Mean-field extension of the LIBOR market model.
result Existence and uniqueness of MF-LMM proved.
Efficient Bayesian LMM framework for high-dimensional longitudinal data.
problem Scalability and dependence in high-dimensional longitudinal data.
method Partitioned empirical Bayes ECM algorithm for scalable MAP estimation.
result Identification of genes and clinical factors associated with a lupus biomarker.
In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the Lévy Libor model developed by Eberlein and Özkan (2005). This model is an extension to Lévy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is signif…
The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.
problem Arbitrage in implied volatility calculations.
method Analytical proofs for BBF, SABR, and rough SABR formulas under specific models.
result These formulas offer asymptotically arbitrage-free approximations of implied volatility.
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effect…
Linear Mixed Models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure…
New method selects sparse predictors in large LMMs.
problem Sparse learning for LMMs is computationally infeasible for large datasets.
method Developed an ℓ0 regularized method with coordinate descent and local search algorithms. result Method selects thousands of predictors in seconds to minutes.
Derives a rough SABR formula for short maturities.
problem Modeling volatility smiles under rough volatility.
method Derives an ODE and solves it numerically.
result Develops a very accurate approximation called the rough SABR formula.
A new method calculates accurate SABR model option prices and deltas.
problem Inaccurate and arbitrageable SABR model option prices and deltas.
method Gaussian quadrature integration scheme for the normal SABR model.
result Accurate and arbitrage-free SABR model option prices and deltas calculated with 49 points.
LMM predicts healthcare costs and risks with improved accuracy.
problem Wasteful healthcare spending and inefficiencies in risk prediction.
method Generative pre-trained transformer trained on patient event sequences.
result Improves cost prediction by 14.1% and chronic conditions prediction by 1.9%.
Quantum computing speeds up interest rate derivative pricing using LMM.
problem Challenges in pricing interest rate derivatives, especially caps.
method Hybrid classical-quantum approach using quantum amplitude estimation.
result Quantum computing improves convergence in pricing interest rate derivatives.
Extends SABR model for pricing RFR caplets.
problem Pricing backward RFR caplets in a post-Libor market.
method Closed-form effective SABR parameters for backward RFR caplets.
result Closed-form solution for backward RFR caplets.
Develops a novel SABR DNN for accurate volatility surface calibration.
problem Inaccurate SABR model approximation for high volatility, long maturities, and out-of-the-money options.
method A specialized Artificial Deep Neural Network (DNN) architecture trained on a large dataset of interest rate volatility surfaces.
result Arbitrage-free calibration of real market volatility surfaces and Cap/Floor prices for any maturity and strike.
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.
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends …
Bayesian method selects subsets for LMMs with structured dependence.
problem Subset selection challenge in LMMs with structured dependence.
method Bayesian decision analysis with Mahalanobis loss function.
result Optimal linear coefficients for subsets and cardinality constraints.
The SABR model is a benchmark stochastic volatility model in interest rate markets, which has received much attention in the past decade. Its popularity arose from a tractable asymptotic expansion for implied volatility, derived by heat kernel methods. As markets moved to historically low rates, this expansion appeared…
Enhanced SABR model captures complex volatility smiles in Chinese financial options.
problem Limited accuracy of classical SABR model in fitting implied volatility curves.
method Proposes skew-SABR model with an extended stochastic dynamics and a new Black implied volatility expression.
result Skew-SABR model achieves high and stable fitting accuracy across various market conditions.
Lower bound found for volatility swap in SABR model.
problem Finding a lower bound for volatility swap in SABR model.
method Short time to maturity limit analysis of conditionally lognormal SABR model.
result Zero vanna implied volatility is a lower bound for volatility swap strike.
Study uses SABR model to create implied volatilities from sparse quotes.
problem Creating accurate implied volatility surfaces from limited market data.
method Multitask Gaussian process with SABR model embeddings and hierarchical regularization.
result Model produces more accurate volatilities than single-task methods.
We refine the analysis of hedging strategies for options under the SABR model carried out in [2]. In particular, we provide a theoretical justification of the empirical observation made in [2] that the modified delta ("Bartlett's delta") introduced there provides a more accurate and robust hedging strategy than the con…
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…
We derive variance-optimal hedging strategies for SABR and rough Bergomi models.
problem Finding efficient hedging strategies in lognormal SABR and rough Bergomi models.
method Analytic expressions for variance-optimal hedging strategies and mean-square hedging errors.
result The variance-optimal hedging strategy in SABR coincides with Delta adjustment.
We develop an HMC algorithm to easily marginalize random effects in LMMs.
problem Bayesian inference in LMMs is challenging, especially marginalizing random effects.
method Developed an HMC algorithm to marginalize random effects in LMMs efficiently.
result Marginalization is always beneficial when applicable and improves various models, especially cognitive science models.
Efficiently calibrates SABR/LIBOR models to real market caplets and swaptions data.
problem Calibration of stochastic volatility models to real market data.
method Proposes a parallelized simulated annealing algorithm for multi-GPUs.
result Numerical results show advantages of using multi-GPUs for SABR/LIBOR model calibration.
Improved option pricing for SABR model using Gauss-Hermite quadrature.
problem Improving accuracy of option pricing in the SABR model.
method Using Gauss-Hermite quadrature for numerical integration of the integrated variance.
result New method provides accurate option prices across all strike prices.
We discuss a semi-analytical method for solving SABR-type equations based on path integrals. In this approach, one set of variables is integrated analytically while the second set is integrated numerically via Monte-Carlo. This method, known in the literature as Conditional Monte-Carlo, leads to compact expressions fun…
VolNP learns IVS from sparse quotes via meta-learning and SABR priors.
problem Reconstructing implied volatility surfaces from sparse option quotes.
method Meta-learning Neural Process with SABR-induced priors.
result VolNP outperforms SABR, SSVI, and Gaussian process on SPX options.
Hybrid method improves SABR implied volatility approximation.
problem Improving SABR implied volatility approximation.
method Combining analytical structure with machine learning, using geometric features and residual correction.
result Hybrid model improves accuracy and robustness compared to analytical and neural-network approaches.
Paper proposes LMM-PQS for cross-domain few-shot learning.
problem Cross-domain few-shot learning problem.
method Generates pseudo query images and fine-tunes feature extraction modules with a large margin mechanism.
result LMM-PQS outperforms baseline models in cross-domain few-shot learning.
Efficiently simulates SABR model with novel sampling methods.
problem Sampling integrated variance and terminal forward price in SABR model.
method Moment-matched shifted lognormal approximation for integrated variance, CEV approximation for terminal forward price.
result Enhanced simulation scheme is highly efficient, accurate, and reliable.
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show i…
We propose a deterministic numerical method for pricing vanilla options under the SABR stochastic volatility model, based on a finite element discretization of the Kolmogorov pricing equations via non-symmetric Dirichlet forms. Our pricing method is valid under mild assumptions on parameter configurations of the proces…
The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The solution is then verified using Rama Cont's functional calculus.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
MarS simulates financial markets using generative models.
problem Simulating realistic financial market effects.
method Order-level generative foundation model (LMM) for realistic, interactive, and controllable order generation.
result Strong scalability and robust realism in MarS.
Safe RL with binary feedback using SABRE algorithm.
problem Safe reinforcement learning with binary safety feedback.
method SABRE algorithm, combining active learning and reinforcement learning.
result Provable safe policy with high probability, no unsafe actions during training.
In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs, instead of solving the 1+2 dimensional SABR PDE, it is sufficient to solve NV u…
Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models
problem Computing option prices and Greeks for stochastic volatility models
method Matrix approximation using elementary linear algebra
result Option prices and Greeks computed for infinitely many strikes with a finite number of expectations
New method for pricing barrier options in time-dependent λ-SABR model.
problem Pricing barrier options in the time-dependent λ-SABR model.
method Modified integral transform method and Fourier-Bessel series solution.
result Semi-analytical solution for barrier options in λ-SABR model.
Extensive neural networks eliminate the need for SABR pricing formulas.
problem Lack of exact pricing formulas for the SABR model.
method Used a GPU-based simulation and an extensive neural network to learn implied volatilities.
result Neural networks achieve high accuracy and efficiency comparable to Monte-Carlo simulations.
Study on VIX options pricing in SABR model, showing infinite prices due to volatility explosion.
problem Infinite VIX futures and call prices due to volatility explosion in SABR model.
method Analyzing SABR model, showing vt as unique solution to diffusion process, proving explosion using Feller test, proposing capped volatility process. result VIX futures and call prices are infinite for any maturity due to volatility explosion, but capped volatility process mitigates this issue.
This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error i…
In this short note, using our geometric method introduced in a previous paper \cite{phl} and initiated by \cite{ave}, we derive an asymptotic swaption implied volatility at the first-order for a general stochastic volatility Libor Market Model. This formula is useful to quickly calibrate a model to a full swaption matr…
We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models for pricing contingent claims on risky assets. In particular, by restricting to domains of bounded volatility, we …
Study shows non-convergence of short-maturity expansion in SABR model.
problem Analyzing convergence of SABR model option prices.
method Analyzing analyticity properties of the payoff function and using the McKean kernel.
result Short-maturity expansion for SABR model is asymptotic and non-convergent.
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper we develop an approach for dimension reduction that exploits the assumpt…