Paper: arXiv 2601.11209

Authors: Hans Buehler, Blanka Horvath, Anastasis Kratsios, Yannick Limmer, Raeid Saqur

Abstract

We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as a smooth generalization of the widely-known linear interpolation scheme, and retains the simplicity and transparency of that baseline. Calibration of the model to observed market quotes is formulated as a linear program, allowing bid-ask spreads to be incorporated directly via linear penalties or inequalities, and delivering materially lower computational cost than most of the currently available implied-volatility surface fitting routines. As a further contribution, we derive an equivalent parameterization of the proposed surface in terms of strictly positive “discrete local volatility” variables. This yields, to our knowledge, the first construction of smooth, strictly arbitrage-free option price surfaces while requiring only trivial parameter constraints (positivity). We illustrate the approach using S&P 500 index options

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel, non-parametric method (SANOS) for constructing smooth, strictly arbitrage-free option surfaces using a linear programming formulation. It bridges mathematical rigor and practical trading utility effectively, demonstrating strong visual and empirical calibration performance on S&P 500 options.

Research Flowchart

  flowchart TD
    A[Goal: Smooth, Strictly Arbitrage-Free<br>Option Price Surface Construction] --> B[Inputs: S&P 500 Index Options Quotes<br>with Bid-Ask Spreads]
    B --> C[Methodology: Smooth Generalization of<br>Linear Interpolation Scheme]
    C --> D[Optimization: Linear Program LP Calibration<br>incorporating Bid-Ask Penalties/Constraints]
    D --> E[Parameterization: Reparameterize via<br>Discrete Local Volatility Variables]
    E --> F[Outcomes: Fast, Low-Cost Calibration &<br>Arbitrage-Free Surface with Simple Positivity Constraints]

Cited References (652)

  1. Local variance gamma and explicit calibration to option prices (2017)
  2. Interpolation of data by smooth nonnegative functions (2017)
  3. Functions differentiable on the boundaries of regions (1934)
  4. Étude de quelques algèbres tayloriennes (1958)
  5. Sharp finiteness principles for Lipschitz selections (2018)
  6. Whitney’s extension problem for $C^m$ (2006)
  7. A sharp form of Whitney’s extension theorem (2005)
  8. Whitney’s extension problems and interpolation of data (2009)
and 644 more
  1. Fitting a $C^m$ -smooth function to data. I (2009)
  2. Fitting a $C^m$ -smooth function to data. III (2009)
  3. A generalized sharp Whitney theorem for jets (2005)
  4. Reconstruction and interpolation of manifolds. I: The geometric Whitney problem (2020)
  5. Smooth convex extensions of convex functions (2019)
  6. Explicit formulas for C11 and C1\ensuremath \omega extensions of 1-jets in Hilbert and superreflexive spaces (2018)
  7. Finiteness principles for smooth convex functions (2024) — link
  8. Kirszbraun’s theorem via an explicit formula (2021)
  9. Whitney extension theorems for convex functions of the classes C1 and C1,\ensuremath \omega (2017) — link
  10. A general version of the fundamental theorem of asset pricing (1994) (2006)
  11. Do we really need the Rademacher complexities? (2025) — link
  12. Mimicking the one-dimensional marginal distributions of processes having an It^ o differential (1986) — link
  13. Volatility is rough (2022)
  14. Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing (2000)
  15. Calibration of local stochastic volatility models to market smiles: A Monte-Carlo approach (2009)
  16. Arbitrage-free SVI volatility surfaces (2014)
  17. Generalized arbitrage-free SVI volatility surfaces (2016)
  18. From Implied to Spot Volatilities (2010) — link
  19. Arbitrage-Free Smoothing of the Implied Volatility Surface (2009) — link
  20. The volatility surface: a practitioner’s guide (2011)
  21. Robust replication of volatility derivatives (2008)
  22. Does Net Buying Pressure Affect the Shape of Implied Volatility Functions? (2004) — link
  23. Demand-Based Option Pricing (2009) — link
  24. High-frequency trading in a limit order book (2008)
  25. Option valuation using the fast Fourier transform (1999)
  26. Vola Fitter: Real-Time, Arbitrage-Free Volatility Surfaces for Options Trading (2025)
  27. Instrument Pricing Analytics: Volatility Surfaces Analytics (2025)
  28. IvyDB US: Historical Option Prices and Smoothed Implied Volatility Surfaces (2025)
  29. Arbitrage-Free Parametric Volatility Surfaces and Real-Time Fitting (2017)
  30. The Swiss Army Knife of Options Analytics – Vola Dynamics (2020)
  31. Volatility Surfaces – Analytics (2025)
  32. Instrument Pricing Analytics – Volatility Surfaces and Curves (2020)
  33. Instrument Pricing Analytics: Overview (2025)
  34. OptionMetrics (2025)
  35. OptionMetrics: Historical Options Data (2025)
  36. Historical Options Data Products (2025)
  37. Derivatives for decision makers: strategic management issues (1996)
  38. An Engine, Not a Camera: How Financial Models Shape Markets (2008) — link
  39. The fundamental theorem of asset pricing for unbounded stochastic processes (1998)
  40. Martingales and arbitrage in multiperiod securities markets (1979)
  41. Arbitrage and equilibrium in economies with infinitely many commodities (1981)
  42. On Distributions of Certain Wiener Functionals (1949)
  43. Le R ^o le des Valeurs Boursi `e res pour la R 'e partition la Meilleure des Risques (1953)
  44. Theory of Value: An Axiomatic Analysis of Economic Equilibrium (1959)
  45. Politics (1932)
  46. Tulipmania: Money, Honor, and Knowledge in the Dutch Golden Age (2007)
  47. The Pricing of Options and Corporate Liabilities (1973) — link
  48. E$_ \gamma $-Mixing Time (2024)
  49. Theory of Rational Option Pricing (1973) — link
  50. Expensive martingales (2006)
  51. Arbitrage free implied volatility surfaces (2010)
  52. Operator Deep Smoothing for Implied Volatility — → 2406.11520
  53. An improved estimator for Black-Scholes-Merton implied volatility (2004)
  54. A deep reinforcement learning framework for the financial portfolio management problem (2017) — link
  55. Finbert: Financial sentiment analysis with pre-trained language models (2019) — link
  56. Portfolio Transformer for Attention-Based Asset Allocation (2022) — link
  57. Sentiment analysis of financial news articles using performance indicators (2018)
  58. Evaluating Sentiment Analysis in the Context of Securities Trading. (2016)
  59. An analysis of verbs in financial news articles and their impact on stock price (2010)
  60. Textual analysis in accounting and finance: A survey (2016)
  61. PrivySense: Price Volatility based Sentiment Estimation from Financial News using Machine Learning (2017) — link
  62. Decision support from financial disclosures with deep neural networks and transfer learning (2017)
  63. Adaptive quantitative trading: An imitative deep reinforcement learning approach (2020)
  64. The Sharpe Ratio (1994)
  65. Foundations of portfolio theory (1991)
  66. Mean-variance investing (2012)
  67. Passive investment strategies and efficient markets (2003)
  68. Profitable momentum trading strategies for individual investors (2015)
  69. Is domain adaptation worth your investment? Comparing BERT and FinBERT on financial tasks (2021)
  70. The Future of Financial Analysis (1963)
  71. A random walk down wall street [by] burton G. Malkiel (1973)
  72. Efficient market hypothesis (1989)
  73. Efficient capital markets: A review of theory and empirical work (1970)
  74. Efficient capital markets: reply (1976)
  75. Efficient capital markets: II (1991)
  76. Market efficiency, long-term returns, and behavioral finance (1998)
  77. Regime changes and financial markets (2012)
  78. Size and value anomalies under regime shifts (2008)
  79. Markov switching models in empirical finance (2011)
  80. A new approach to the economic analysis of nonstationary time series and the business cycle (1989)
  81. Analysis of time series subject to changes in regime (1990)
  82. Regime switching models (2010)
  83. A hybrid learning approach to detecting regime switches in financial markets (2020)
  84. Clustering market regimes using the wasserstein distance (2021) — link
  85. Rcv1: A new benchmark collection for text categorization research (2004)
  86. OpenAI Baselines (2017)
  87. Basel III: an overview (2011)
  88. An empirical investigation of the challenges of real-world reinforcement learning (2020)
  89. Reinforcement learning in financial markets - a survey (2018)
  90. Advances in financial machine learning (2018)
  91. SENTiVENT: enabling supervised information extraction of company-specific events in economic and financial news (2022)
  92. Www'18 open challenge: financial opinion mining and question answering (2018)
  93. Impact of news on the commodity market: Dataset and results (2021)
  94. PIXIU: A Large Language Model, Instruction Data and Evaluation Benchmark for Finance (2023) — link
  95. Hybrid deep sequential modeling for social text-driven stock prediction (2018)
  96. Stock movement prediction from tweets and historical prices (2018)
  97. Accurate Stock Movement Prediction with Self-supervised Learning from Sparse Noisy Tweets (2022)
  98. NIFTY Financial News Headlines Dataset (2024) — link
  99. Finqa: A dataset of numerical reasoning over financial data (2021) — link
  100. Convfinqa: Exploring the chain of numerical reasoning in conversational finance question answering (2022) — link
  101. Chronos: Learning the Language of Time Series (2024) — link
  102. N-BEATS: Neural basis expansion analysis for interpretable time series forecasting (2019) — link
  103. Temporal fusion transformers for interpretable multi-horizon time series forecasting (2021)
  104. Stochastic differential equations in finance (1990)
  105. Stochastic differential equations and applications (2007)
  106. The volatility surface: a practitioner’s guide (2011)
  107. No arbitrage SVI (2022)
  108. The extended SSVI volatility surface (2017)
  109. Deep smoothing of the implied volatility surface (2020)
  110. A two-step framework for arbitrage-free prediction of the implied volatility surface (2023)
  111. Managing smile risk (2002)
  112. A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives (2004)
  113. Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models (2021)
  114. Pricing under rough volatility (2016)
  115. HyperIV: Real-time implied volatility smoothing (2025)
  116. Volatility interpolation (2011)
  117. Prices of state-contingent claims implicit in option prices (1978)
  118. Quantitative fundamental theorem of asset pricing (2025)
  119. Ars magna or The Rules of Algebra (1545)
  120. Put-call symmetry: Extensions and applications (2009)
  121. A note on sufficient conditions for no arbitrage (2005)
  122. A new simple approach for constructing implied volatility surfaces (2010)
  123. A subordinated stochastic process model with finite variance for speculative prices (1973)
  124. Local Martingales, Bubbles and Option Prices (2005)
  125. Conditions on option prices for absence of arbitrage and exact calibration (2007)
  126. The Term Structure of Implied Volatility in Symmetric Models with Applications to Heston (2012)
  127. Arbitrage-free smoothing of the implied volatility surface (2009)
  128. The Volatility Surface: A Practitioner’s Guide (2006)
  129. Arbitrage-free approximation of call price surfaces and input data risk (2012)
  130. Martingales and stochastic integrals in the theory of continuous trading (1981)
  131. Martingales and arbitrage in multiperiod securities markets (1979)
  132. Comparison results for stochastic volatility models via coupling (2010)
  133. Hyp hyp hooray (2008)
  134. An arbitrage-free interpolation of volatilities (2004)
  135. Brownian Motion and Stochastic Calculus (1991)
  136. The moment formula for implied volatility at extreme strikes (2004)
  137. Can the implied volatility surface move by parallel shift? (2010)
  138. Implied Volatility: General Properties and Asymptotics (2009)
  139. Generative Market Equilibrium Models with Stable Adversarial Learning via Reinforcement — → 2504.04300
  140. A consistently well-behaved method of interpolation (1980)
  141. Deep neural network expressivity for optimal stopping problems (2024)
  142. Deep ReLU network expression rates for option prices in high-dimensional, exponential L 'e vy models (2021)
  143. Quasi-explicit calibration of Gatheral’s SVI model (2009)
  144. Operator Deep Smoothing for Implied Volatility — → 2406.11520
  145. A generative adversarial network approach to calibration of local stochastic volatility models (2020)
  146. Arbitrage-free implied volatility surface generation with variational autoencoders (2023)
  147. Variational Autoencoders: A Hands-Off Approach to Volatility (2022)
  148. A Variational Autoencoder Approach to Conditional Generation of Possible Future Volatility Surfaces (2023)
  149. Detecting and repairing arbitrage in traded option prices (2020)
  150. Deep learning based dynamic implied volatility surface (2021)
  151. Pricing with a smile (1994)
  152. Simulation of implied volatility surfaces via tangent L 'e vy models (2017)
  153. Volgan: a generative model for arbitrage-free implied volatility surfaces (2024)
  154. Certified monotonic neural networks (2020)
  155. Constrained monotonic neural networks (2023)
  156. Scalable monotonic neural networks (2024)
  157. Some filtering results in R iemann manifolds (1977)
  158. Designing universal causal deep learning models: The geometric (Hyper)transformer (2023) — link
  159. Volatility and Dividends - Volatility Modelling with Cash Dividends and Simple Credit Risk (2008) — link
  160. Discrete Local Volatility for Large Time Steps (Extended Version) (2015) — link
  161. Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks (2022)
  162. Augmented dickey fuller test (2011)
  163. Riemannian Lp center of mass: existence, uniqueness, and convexity (2011)
  164. On the support of Wiener functionals. Asymptotic problems in probability theory: Wiener functionals and asymptotics (Sanda/Kyoto, 1990), 3–34 (1993)
  165. Stanford Alpaca: An Instruction-following LLaMA model (2023)
  166. Alpaca: A strong, replicable instruction-following model (2023)
  167. PAC-Bayesian bounds for randomized empirical risk minimizers (2008)
  168. On the properties of variational approximations of Gibbs posteriors (2016)
  169. Optimal projection filters with information geometry (2023)
  170. Arrows of Time for Large Language Models (2024) — link
  171. Layer normalization (2016) — link
  172. Kalman filtering of generalized Vasicek term structure models (1999)
  173. Neural Machine Translation by Jointly Learning to Align and Translate (2016) — link
  174. Fundamentals of stochastic filtering (2009) — link
  175. Computation of conditional expectations with guarantees (2023) — link
  176. Lectures on spaces of nonpositive curvature (1995) — link
  177. Th' e orie des op' e rations lin' e aires (1955)
  178. An inverse matrix adjustment arising in discriminant analysis (1951) — link
  179. Fixed point theorems for metric spaces with a conical geodesic bicombing (2018)
  180. Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions (2014)
  181. Markov processes on manifolds of maps (1976) — link
  182. Exploring the Impact of Instruction Data Scaling on Large Language Models: An Empirical Study on Real-World Use Cases (2023) — link
  183. Training verifiers to solve math word problems (2021) — link
  184. Evaluating large language models trained on code (2021) — link
  185. Gaia: a benchmark for general ai assistants (2023) — link
  186. Measuring Massive Multitask Language Understanding (2021)
  187. Existence of optimal strategies based on specified information, for a class of stochastic decision problems (1970)
  188. Exact finite-dimensional filters for certain diffusions with nonlinear drift (1981)
  189. Scaling Learning Algorithms Towards AI (2007)
  190. Stochastic filtering with applications in finance (2010)
  191. A note on reverse P insker inequalities (2019) — link
  192. Multimodal datasets: misogyny, pornography, and malignant stereotypes (2021)
  193. Manifolds of negative curvature (1969) — link
  194. Exponential integrability and transportation cost related to logarithmic S obolev inequalities (1999) — link
  195. On the opportunities and risks of foundation models (2021)
  196. Time series analysis: forecasting and control (2015)
  197. Rank analysis of incomplete block designs: I. The method of paired comparisons (1952)
  198. A differential geometric approach to nonlinear filtering: the projection filter (1998)
  199. Language Models are Few-Shot Learners (2020)
  200. Sparks of artificial general intelligence: Early experiments with GPT-4 (2023)
  201. Filtering for stochastic processes with applications to guidance (2005)
  202. Smooth densities for solutions to stochastic differential equations with jumps (2009)
  203. Financial equilibrium with asymmetric information and random horizon (2018)
  204. Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates (1993)
  205. Efficient approximation of high-dimensional functions with neural networks (2021)
  206. PaLM : Scaling language modeling with pathways. 2022 (2022)
  207. Patch-level routing in mixture-of-experts is provably sample-efficient for convolutional neural networks (2023)
  208. Turing Completeness of Bounded-Precision Recurrent Neural Networks (2021) — link
  209. The design of robust approximations to the stochastic differential equations of nonlinear filtering (1978)
  210. Parameter estimation in commodity markets: A filtering approach (2007)
  211. Stochastic calculus and applications (2015) — link
  212. Generalised correlated batched bandits via the ARC algorithm with application to dynamic pricing (2022) — link
  213. I-divergence geometry of probability distributions and minimization problems (1975)
  214. The pile: An 800gb dataset of diverse text for language modeling (2020) — link
  215. Linear and non-linear filtering in mathematical finance: a review (2011)
  216. Embeddable M arkov matrices (2010) — link
  217. Pathwise nonlinear filtering for nondegenerate diffusions with noise correlation (1987) — link
  218. Deep learning for financial sentiment analysis on finance news providers (2016)
  219. Introducing DBRX: A New State-of-the-Art Open LLM (2024)
  220. Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions (2011)
  221. GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series (2019)
  222. On the approximation of functions by tanh neural networks (2021)
  223. Local Lipschitz constant of exponential map for Hadamard manifolds — link
  224. Nonlinear filtering: Interacting particle resolution (1997)
  225. Mean field simulation for M onte C arlo integration (2013)
  226. BERT : Pre-training of Deep Bidirectional Transformers for Language Understanding (2019) — link
  227. Constructive approximation (1993)
  228. Particle filtering (2003)
  229. Implications of the Dodd-Frank act (2012)
  230. Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus (2021) — link
  231. Direct preference optimization: Your language model is secretly a reward model (2023) — link
  232. GLaM: Efficient Scaling of Language Models with Mixture-of-Experts (2022)
  233. Estimating and testing exponential-affine term structure models by Kalman filter (1999)
  234. Real analysis and probability (2002)
  235. Linear O perators. I . G eneral T heory (1958)
  236. UCI Machine Learning Repository (2017)
  237. Modern portfolio theory, 1950 to date (1997)
  238. Stochastic differential equations on manifolds (1998) — link
  239. The geometry of filtering (2010) — link
  240. Adaptive nonlinear system identification with echo state networks (2002)
  241. A framework for few-shot language model evaluation (2021) — link
  242. Bartscore: Evaluating generated text as text generation (2021)
  243. Bertscore: Evaluating text generation with bert (2019) — link
  244. Stochastic processes and filtering theory (2007)
  245. Billion-scale similarity search with GPUs (2019)
  246. A sharp form of W hitney’s extension theorem (2005) — link
  247. Scaling instruction-finetuned language models (2022) — link
  248. Principal geodesic analysis for the study of nonlinear statistics of shape (2004)
  249. Stochastic integration by parts and functional It ^o calculus (2016)
  250. Signature-based models: Theory and calibration (2023)
  251. The GARCH option pricing model (1995)
  252. Joint calibration to SPX and VIX options with signature-based models — → 2301.13235
  253. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  254. Venturing into uncharted territory: An extensible implied volatility surface model (2022)
  255. Mass at zero in the uncorrelated SABR model and implied volatility asymptotics (2018)
  256. Pricing credit derivatives under incomplete information: a nonlinear-filtering approach (2010)
  257. A course on rough paths (2020) — link
  258. Pytorch fsdp: experiences on scaling fully sharded data parallel (2023) — link
  259. Neocognitron: A self-organizing neural network model for a mechanism of visual pattern recognition (1982)
  260. Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis (2022) — link
  261. Riemannian geometry (1990)
  262. Consistent recalibration models and deep calibration (2020) — link
  263. Short, colorful, and irreverent! a comparative analysis of new users on wallstreetbets during the gamestop short-squeeze (2022)
  264. Explaining Gamestop Short Squeeze using Intraday Data and Google Searches (2021)
  265. Arbitrage-free SVI volatility surfaces (2013) — link
  266. Convolutional sequence to sequence learning (2017)
  267. Gemini — link
  268. A class of W asserstein metrics for probability distributions (1984) — link
  269. Convergence of stochastic processes (2012)
  270. The generalization error of random features regression: Precise asymptotics and the double descent curve (2022)
  271. Benign overfitting in ridge regression (2023)
  272. Approximation bounds for random neural networks and reservoir systems (2023)
  273. Deep learning (2016)
  274. LASSO reloaded: a variational analysis perspective with applications to compressed sensing (2023)
  275. Generative adversarial networks (2020)
  276. Regret-optimal federated transfer learning for kernel regression with applications in American option pricing — → 2309.04557
  277. Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality (2023)
  278. GPT-NeoX-20B : An Open-Source Autoregressive Language Model (2022) — link
  279. On complete open manifolds of positive curvature (1969) — link
  280. Learning Word Vectors for 157 Languages (2018)
  281. Kalman filtering: Theory and Practice with MATLAB (2014)
  282. Filling riemannian manifolds (1983)
  283. Hyperbolic groups (1987) — link
  284. DeepSeek-Coder: When the Large Language Model Meets Programming–The Rise of Code Intelligence (2024) — link
  285. Forecasting, structural time series models and the Kalman filter (1990)
  286. Lectures on analysis on metric spaces (2001) — link
  287. BPE mb: Tokenization-free Pre-trained Subword Embeddings in 275 Languages (2018)
  288. Analysis, geometry, and modeling in finance (2009)
  289. Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering (2021) — link
  290. Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices (2023) — link
  291. The metric dimension of geometric spaces (2014) — link
  292. The metric dimension of metric manifolds (2015) — link
  293. A Fast Learning Algorithm for Deep Belief Nets (2006)
  294. Bridging the gap between approximation and learning via optimal approximation by relu mlps of maximal regularity (2024) — link
  295. Matrix Analysis (2012) — link
  296. Whack-a-mole learning: Physics-informed deep calibration for implied volatility surface (2024)
  297. Instance-Dependent Generalization Bounds via Optimal Transport (2022) — link
  298. Deep Kalman Filters Can Filter (2023) — link
  299. Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients (2015)
  300. Positivity of the density for rough differential equations (2022)
  301. Stochastic calculus (2005)
  302. Stop Uploading Test Data in Plain Text: Practical Strategies for Mitigating Data Contamination by Evaluation Benchmarks (2023)
  303. Filtering in finance (2003)
  304. Riemannian geometry and geometric analysis (2017) — link
  305. Challenges and Applications of Large Language Models (2023) — link
  306. Stochastic filtering theory (1980)
  307. Understanding the Kalman filter (1983)
  308. A New Approach to Linear Filtering and Prediction Problems (1960) — link
  309. New Results in Linear Filtering and Prediction Theory (1961) — link
  310. Least squares approximation of completely monotonic functions by sums of exponentials (1979)
  311. Bi-Lipschitz approximation by finite-dimensional imbeddings (2011)
  312. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding (2019)
  313. Neural sdes as infinite-dimensional gans (2021)
  314. Introduction to Kalman filter and its applications (2018)
  315. The imbedding problem for finite M arkov chains (1962) — link
  316. A Smooth Model of Decision Making under Ambiguity (2005) — link
  317. Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs (2022) — link
  318. Non-euclidean universal approximation (2020)
  319. Universal Regular Conditional Distributions via Probabilistic Transformers (2023)
  320. Universal approximation theorems for differentiable geometric deep learning (2022)
  321. An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning (2023) — link
  322. Quality at a Glance: An Audit of Web-Crawled Multilingual Datasets (2022) — link
  323. The convenient setting of global analysis (1997) — link
  324. Structured inference networks for nonlinear state space models (2017)
  325. Exponential families of stochastic processes (1997)
  326. Existence of densities of solutions of stochastic differential equations by Malliavin calculus (2010)
  327. Jensen’s inequality on convex spaces (2014) — link
  328. Lag-llama: Towards foundation models for time series forecasting (2023) — link
  329. Optimal trading strategy for an investor: the case of partial information (1998)
  330. The curse of dimensionality in operator learning (2023) — link
  331. Simple and extended Kalman filters: an application to term structures of commodity prices (2004)
  332. Linear algebra and its applications (2007)
  333. Fisher-Rao geometry of Dirichlet distributions (2021)
  334. Statistical manifolds are statistical models (2005) — link
  335. Deduplicating Training Data Makes Language Models Better (2022) — link
  336. Introduction to smooth manifolds (2013)
  337. Stochastic flows of diffeomorphisms (1984) — link
  338. BART : Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension (2020) — link
  339. Merge, Then Compress: Demystify Efficient SM oE with Hints from Its Routing Policy (2024) — link
  340. Holistic evaluation of language models (2022)
  341. Matrix power means and the K archer mean (2012) — link
  342. Statistics for Finance (2016) — link
  343. Sequential calibration of options (2008)
  344. Fast Simultaneous Calibration and Quadratic Hedging under Parameter Uncertainty (2014)
  345. Statistics of random processes: General theory (1977)
  346. Roberta: A robustly optimized bert pretraining approach (2019)
  347. PAC-Bayes bounds for meta-learning with data-dependent prior (2021) — link
  348. Deepseek-v3 technical report (2024) — link
  349. Deepseek-v2: A strong, economical, and efficient mixture-of-experts language model (2024) — link
  350. Local Lipschitzness of parameterization of Gaussians in Wasserstein space (2020) — link
  351. A random matrix approach to neural networks (2018) — link
  352. Long short-term memory (1997)
  353. Individual choice behavior: A theoretical analysis (2005)
  354. Linearized filtering of affine processes using stochastic R iccati equations (2020) — link
  355. Data Contamination: From Memorization to Exploitation (2022) — link
  356. Statistical and Machine Learning forecasting methods: Concerns and ways forward (2018)
  357. The M6 forecasting competition: Bridging the gap between forecasting and investment decisions (2023) — link
  358. Random Toeplitz matrices: The condition number under high stochastic dependence (2021)
  359. Exponential relu neural network approximation rates for point and edge singularities (2023)
  360. Portfolio selection: efficient diversification of investments (1968)
  361. Geodesic convolutional neural networks on riemannian manifolds (2015)
  362. Lectures on discrete geometry (2002) — link
  363. Uniform approximation of completely monotone functions by exponential sums (1978)
  364. Handbook of Markov decision processes: methods and applications (2012)
  365. Learning to learn by gradient descent by gradient descent (2016)
  366. Learning to learn without gradient descent by gradient descent (2017)
  367. Deep vs. shallow networks: An approximation theory perspective (2016)
  368. Completely monotonic functions (2001)
  369. Conditional generative adversarial nets (2014) — link
  370. Evaluation of sentiment analysis in finance: from lexicons to transformers (2020)
  371. Deepseekmoe: Towards ultimate expert specialization in mixture-of-experts language models (2024) — link
  372. Megablocks: Efficient sparse training with mixture-of-experts (2023)
  373. Adaptive mixtures of local experts (1991)
  374. Mixtral of experts (2024) — link
  375. Hierarchical mixtures of experts and the EM algorithm (1994)
  376. Outrageously large neural networks: The sparsely-gated mixture-of-experts layer (2017) — link
  377. Mixture-of-experts meets instruction tuning: A winning combination for large language models (2023) — link
  378. Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity (2022)
  379. Mixture-of-experts with expert choice routing (2022)
  380. Unified Training of Universal Time Series Forecasting Transformers (2024) — link
  381. Optimal hedging and parameter uncertainty (2007) — link
  382. Functional I to calculus and applications (2010)
  383. Functional I t^ o calculus (2019) — link
  384. CLUES: few-shot learning evaluation in natural language understanding (2021)
  385. Topology (2000)
  386. Poincar' e inequalities, embeddings, and wild groups (2011) — link
  387. The imbedding problem for R iemannian manifolds (1956) — link
  388. Restricted Riemannian geometry for positive semidefinite matrices (2023)
  389. Neural ordinary differential equations (2018)
  390. Nonlinear filtering in riemannian manifolds (1984)
  391. Lipschitz algebras (2018)
  392. NeuralForecast : User friendly state-of-the-art neural forecasting models. (2022) — link
  393. Density for solutions to stochastic differential equations with unbounded drift (2019)
  394. GPT-4 Technical Report (2023) — link
  395. GPT-4 Technical Report (2023)
  396. Discrete-time signal processing. Vol. 2 (2001)
  397. Training language models to follow instructions with human feedback (2022)
  398. What In-Context Learning “Learns” In-Context: Disentangling Task Recognition and Task Learning (2023) — link
  399. Provable memorization via deep neural networks using sub-linear parameters (2021)
  400. On the difficulty of training recurrent neural networks (2013)
  401. Parameter-efficient transfer learning for NLP (2019)
  402. Gpt3. int8 (): 8-bit matrix multiplication for transformers at scale (2022)
  403. Lora: Low-rank adaptation of large language models (2021) — link
  404. Prefix-tuning: Optimizing continuous prompts for generation (2021) — link
  405. Qlora: Efficient finetuning of quantized llms (2023) — link
  406. A Riemannian framework for tensor computing (2006)
  407. On the Turing Completeness of Modern Neural Network Architectures (2019) — link
  408. Deep Contextualized Word Representations (2018) — link
  409. The fisher–rao distance between multivariate normal distributions: Special cases, bounds and applications (2020)
  410. The analysis of permutations (1975)
  411. Universal Approximation with Deep Narrow Networks (2020) — link
  412. Sharp Analysis of a Simple Model for Random Forests (2021) — link
  413. Optimizing Optimizers: Regret-optimal gradient descent algorithms (2021) — link
  414. Black-Box Variational Inference for Stochastic Differential Equations (2018) — link
  415. From Sparse to Soft Mixtures of Experts (2024) — link
  416. Foundations of hyperbolic manifolds ([2019] \copyright 2019) — link
  417. Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer (2020)
  418. Retrieval-augmented generation for large language models: A survey (2023) — link
  419. Searching for activation functions (2017) — link
  420. Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks (2019) — link
  421. Simple statistical gradient-following algorithms for connectionist reinforcement learning (1992)
  422. Statistical methods for financial engineering (2013)
  423. Convergence rates for empirical measures of M arkov chains in dual and W asserstein distances (2022) — link
  424. Training a helpful and harmless assistant with reinforcement learning from human feedback (2022) — link
  425. A general language assistant as a laboratory for alignment (2021) — link
  426. Training language models to follow instructions with human feedback, 2022 (2022)
  427. Learning to summarize with human feedback (2020)
  428. Fine-tuning language models from human preferences (2019) — link
  429. Dimensions, embeddings, and attractors (2011)
  430. PACOH: Bayes-optimal meta-learning with PAC-guarantees (2021)
  431. Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practice (2023)
  432. Active ranking of experts based on their performances in many tasks (2023)
  433. SAM former: Unlocking the Potential of Transformers in Time Series Forecasting with Sharpness-Aware Minimization and Channel-Wise Attention (2024) — link
  434. Bloom: A 176b-parameter open-access multilingual language model (2022)
  435. Short-term variations and long-term dynamics in commodity prices (2000)
  436. Exponential-Wrapped Distributions on Symmetric Spaces (2022) — link
  437. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix (1950)
  438. Megatron-lm: Training multi-billion parameter language models using model parallelism (2019)
  439. Characterization of the variation spaces corresponding to shallow neural networks (2023)
  440. Optimal stopping rules (1978)
  441. Implicit neural representations with periodic activation functions (2020)
  442. Particle filtering on Riemannian manifolds (2006)
  443. MPNet: Masked and Permuted Pre-training for Language Understanding (2020)
  444. GlobalBench : A Benchmark for Global Progress in Natural Language Processing (2023)
  445. Algebraic topology (1989)
  446. S parse TSF : Modeling Long-term Time Series Forecasting with 1k Parameters (2024) — link
  447. Beyond the imitation game: Quantifying and extrapolating the capabilities of language models (2022)
  448. Optimum nonlinear systems which bring about a separation of a signal with constant parameters from noise (1959)
  449. Application of the Markov processes theory to optimal filtering (1960)
  450. Compound Hawkes processes in limit order books (2019)
  451. Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer (2020) — link
  452. Wasserstein geometry of G aussian measures (2011) — link
  453. Ul2: Unifying language learning paradigms (2022) — link
  454. TF–IDF (2010) — link
  455. Geodesic regression and the theory of least squares on Riemannian manifolds (2013)
  456. Caltrans Performance Measurement System (PeMS) (2023)
  457. Ensemble Modeling for Time Series Forecasting: an Adaptive Robust Optimization Approach (2023) — link
  458. Periodicity and stochastic trends in economic time series (1996)
  459. Graph Deep Learning for Time Series Forecasting (2023) — link
  460. Are Language Models Actually Useful for Time Series Forecasting? (2024) — link
  461. Are transformers effective for time series forecasting? (2023)
  462. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting (2022)
  463. Film: Frequency improved legendre memory model for long-term time series forecasting (2022)
  464. FITS: Modeling Time Series with $10 k $ Parameters (2024)
  465. The capacity and robustness trade-off: Revisiting the channel independent strategy for multivariate time series forecasting (2024)
  466. Position: What Can Large Language Models Tell Us about Time Series Analysis (2024) — link
  467. Generative time series forecasting with diffusion, denoise, and disentanglement (2022)
  468. Review of Time Series Forecasting Methods and Their Applications to Particle Accelerators (2022) — link
  469. Large language models are zero-shot time series forecasters (2024)
  470. Log neural controlled differential equations: The lie brackets make a difference (2024) — link
  471. Robust recurrent neural networks for time series forecasting (2023)
  472. The Rise of Diffusion Models in Time-Series Forecasting (2024) — link
  473. Language Models Still Struggle to Zero-shot Reason about Time Series (2024) — link
  474. Micn: Multi-scale local and global context modeling for long-term series forecasting (2023)
  475. A time series is worth 64 words: Long-term forecasting with transformers (2022) — link
  476. Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and forecasting (2021)
  477. Long-term forecasting with tide: Time-series dense encoder (2023) — link
  478. Timesnet: Temporal 2d-variation modeling for general time series analysis (2023)
  479. Transformers in Time Series: A Survey (2023) — link
  480. Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting (2021)
  481. Time-series generative adversarial networks (2019)
  482. Informer: Beyond efficient transformer for long sequence time-series forecasting (2021)
  483. Weak convergence and empirical processes with applications to statistics (2023) — link
  484. Stochastic calculus, filtering, and stochastic control (2007)
  485. Attention is All you Need (2017)
  486. Graph attention networks (2017) — link
  487. Memory capacity of neural networks with threshold and rectified linear unit activations (2020)
  488. Vicuna: An Open-Source Chatbot Impressing GPT-4 with 90%* ChatGPT Quality (2023) — link
  489. Efficient Memory Management for Large Language Model Serving with PagedAttention (2023)
  490. GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding (2019)
  491. SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems (2019)
  492. Text Embeddings by Weakly-Supervised Contrastive Pre-training (2022)
  493. Self-Instruct: Aligning Language Models with Self-Generated Instructions (2023) — link
  494. Finetuned Language Models are Zero-Shot Learners (2022)
  495. Chain-of-thought prompting elicits reasoning in large language models (2022)
  496. Emergent abilities of large language models (2022)
  497. The Kalman filter in finance (1995)
  498. Dumb Money (2024\mydate) — link
  499. Bounds for eigenvalues using traces (1980) — link
  500. No free lunch theorems for optimization (1997)
  501. Risk-neutral generative networks — → 2405.17770
  502. XLNet: Generalized Autoregressive Pretraining for Language Understanding (2019)
  503. Optimal approximation of continuous functions by very deep ReLU networks (2018)
  504. The phase diagram of approximation rates for deep neural networks (2020)
  505. Teacher Guided Training: An Efficient Framework for Knowledge Transfer (2022) — link
  506. On the optimal filtering of diffusion processes (1969)
  507. Zephyr: Direct distillation of lm alignment (2023) — link
  508. Feedback particle filter on riemannian manifolds and matrix lie groups (2017)
  509. Opt: Open pre-trained transformer language models (2022) — link
  510. A survey of large language models (2023)
  511. Theory of deep convolutional neural networks: Downsampling (2020) — link
  512. On the operator norm of random rectangular T oeplitz matrices (2013)
  513. A few remarks on the operator norm of random T oeplitz matrices (2010) — link
  514. A fixed-point approach to barycenters in W asserstein space (2016) — link
  515. An efficient M onte C arlo scheme for Z akai equations (2023) — link
  516. Information geometry (2017) — link
  517. Econometric analysis of realized volatility and its use in estimating stochastic volatility models (2002) — link
  518. Optimal investment under partial information (2010) — link
  519. Distances de L ' e vy et extensions des th' e orem`es de la limite centrale et de G livenko- C antelli (1993)
  520. Informative geometry of probability spaces (1986)
  521. Comparison theorems in R iemannian geometry (1975)
  522. On the structure of complete manifolds of nonnegative curvature (1972) — link
  523. On a robust version of the integral representation formula of nonlinear filtering (2005) — link
  524. Variational Autoencoders: A Hands-Off Approach to Volatility. (2022)
  525. Regression shrinkage and selection via the lasso (1996)
  526. The lasso method for variable selection in the Cox model (1997)
  527. On model selection consistency of Lasso (2006)
  528. Arbitrage-free implied volatility surface generation with variational autoencoders (2023)
  529. Matrix analysis (2012)
  530. Approximating L 'evy processes with completely monotone jumps (2016) — link
  531. Fisher information distance: a geometrical reading (2015) — link
  532. Deep neural networks, generic universal interpolation, and controlled ODE s (2020) — link
  533. Information projections revisited (2003) — link
  534. Ten lectures on wavelets (1992) — link
  535. Nonlinear approximation and (deep) R e LU networks (2022) — link
  536. Computational problems in nonlinear filtering (1980) — link
  537. On a multiplicative functional transformation arising in nonlinear filtering theory (1980) — link
  538. Fast empirical mode decompositions of multivariate data based on adaptive spline-wavelets and a generalization of the H ilbert- H uang-transformation ( HHT ) to arbitrary space dimensions (2010) — link
  539. Differential properties of spaces of symmetric real matrices (2019)
  540. The F r' e chet distance between multivariate normal distributions (1982) — link
  541. Concentration of measure for the analysis of randomized algorithms (2009) — link
  542. The existence of regular conditional probabilities: necessary and sufficient conditions (1985) — link
  543. Consistency problems for H eath- J arrow- M orton interest rate models (2001) — link
  544. Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering (2012) — link
  545. Unscented K alman filtering on R iemannian manifolds (2013) — link
  546. Optimal approximation with sparsely connected deep neural networks (2019) — link
  547. Geometric mean flows and the C artan barycenter on the W asserstein space over positive definite matrices (2017) — link
  548. Log-majorization and L ie- T rotter formula for the C artan barycenter on probability measure spaces (2017) — link
  549. Extensions of L ipschitz mappings into a H ilbert space (1984) — link
  550. Deep arbitrage-free learning in a generalized HJM framework via arbitrage-regularization (2020)
  551. Small transformers compute universal metric embeddings (2023)
  552. Deep Kalman Filters (2015) — link
  553. Toponogov’s triangle comparison theorem in model spaces of nonconstant curvature (1997) — link
  554. A robust discrete state approximation to the optimal nonlinear filter for a diffusion (1979)
  555. Fisher- R ao geometry of D irichlet distributions (2021) — link
  556. Statistics of random processes. I (2001)
  557. Statistics of random processes. II (2001)
  558. Exponentials of symmetric matrices through tridiagonal reductions (1998) — link
  559. Computing the logarithm of a symmetric positive definite matrix (1998) — link
  560. On the generalized distance in statistics (1936) — link
  561. Regression on fixed-rank positive semidefinite matrices: a R iemannian approach (2011)
  562. Rademacher and G aussian complexities: risk bounds and structural results (2002) — link
  563. Functional I t^ o calculus and stochastic integral representation of martingales (2013) — link
  564. Nearly-tight VC -dimension and pseudodimension bounds for piecewise linear neural networks (2019)
  565. Optimal stable nonlinear approximation (2022) — link
  566. Lipschitz widths (2023) — link
  567. Equivalence of approximation by convolutional neural networks and fully-connected networks (2020) — link
  568. Metric entropy limits on recurrent neural network learning of linear dynamical systems (2022) — link
  569. Every separable B anach space is isometric to a space of continuous nowhere differentiable functions (1995) — link
  570. On filtering with observation in a manifold: reduction to a classical filtering problem (2013) — link
  571. Scale-sensitive dimensions, uniform convergence, and learnability (1997)
  572. Benign overfitting in linear regression (2020)
  573. A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression (2023) — link
  574. A comprehensive analysis on the learning curve in kernel ridge regression (2024)
  575. Beyond Benign Overfitting in Nadaraya-Watson Interpolators (2025) — link
  576. Generalisation and benign over-fitting for linear regression onto random functional covariates (2025) — link
  577. Some explicit formulae in a problem on ``disorder’’ (1965)
  578. The top eigenvalue of the random T oeplitz matrix and the sine kernel (2013) — link
  579. Isometrical embeddings of separable B anach spaces into the set of nowhere approximatively differentiable and nowhere H " o lder functions (2000) — link
  580. TBD (X)
  581. Nhits: Neural hierarchical interpolation for time series forecasting (2023)
  582. Optimal transport (2009) — link
  583. Some applications of stochastic differential equations to optimal nonlinear filtering (1964)
  584. On early stopping in gradient descent learning (2007) — link
  585. Universality of deep convolutional neural networks (2020) — link
  586. Stability of $\varepsilon$ -isometric embeddings into B anach spaces of continuous functions (2017) — link
  587. Stochastic finance (2016) — link
  588. Good debt or bad debt: Detecting semantic orientations in economic texts (2014)
  589. Convergence of Heston to SVI (2011)
  590. Self-instruct: Aligning language model with self generated instructions (2022) — link
  591. Rao’s distance measure (1981)
  592. Approximate nonlinear filtering by projection on exponential manifolds of densities (1999) — link
  593. Convex analysis and monotone operator theory in H ilbert spaces (2017) — link
  594. Robust filtering: correlated noise and multidimensional observation (2013) — link
  595. Some applications of stochastic differential equations to optimal nonlinear filtering (1964)
  596. Stochastic Finance: An Introduction in Discrete Time (2002) — link
  597. Foundations of modern probability (2021) — link
  598. Deep kalman filters (2015) — link
  599. LLaMA : Open and efficient foundation language models (2023)
  600. Deep network approximation for smooth functions (2021) — link
  601. Entropy-regularized 2-Wasserstein distance between Gaussian measures (2022) — link
  602. Energy futures prices: term structure models with Kalman filter estimation (2002)
  603. Mistral 7B (2023) — link
  604. Bernstein functions (2012) — link
  605. The stochastic behavior of commodity prices: Implications for valuation and hedging (1997)
  606. Probability measures on metric spaces of nonpositive curvature (2003) — link
  607. The entropic measure transform (2020) — link
  608. Robust filtering: correlated noise and multidimensional observation (2013) — link
  609. Deep hedging (2019) — link
  610. The Vanna-Volga method for implied volatilities (2007)
  611. Deep hedging: learning to remove the drift (2022) — link
  612. Stochastic Models of Implied Volatility Surfaces (2002) — link
  613. Volatility Markets: Consistent Modeling, Hedging, and Practical Implementation of Variance Swap Market (2009) — link
  614. Strassen’s theorem for biased convex order (2025) — link
  615. Machine Learning Methods for Pricing Financial Derivatives (2024) — link
  616. The Neural Black–Scholes Formula: A Whitney Extension Theorem for Mathematical Finance
  617. Lognormal-Mixture Dynamics and Calibration to Market Volatility Smiles (2002) — link
  618. A Mixed-Up Smile (2000) — link
  619. Multi-Asset Spot and Option Market Simulation (2021) — link
  620. Simulation of Arbitrage-Free Implied Volatility Surfaces (2023) — link
  621. VolGAN: A Generative Model for Arbitrage-Free Implied Volatility Surfaces (2024) — link
  622. Arbitrage-Free Neural-SDE Market Models (2023) — link
  623. Tangent Levy market models (2012) — link
  624. Calibration of Local Stochastic Volatility Models to Market Smiles: A Monte Carlo Approach (2009)
  625. The Fine Structure of Asset Returns: An Empirical Investigation (2002) — link
  626. Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in thePHLX Deutschemark Options (1993) — link
  627. Equity Hybrid Derivatives (2007)
  628. Infinite Dimensional Analysis: A Hitchhiker’s Guide (2006) — link
  629. Markov-Komposition und eine Anwendung auf Martingale. (1972) — link
  630. Nonnegative matrices in the mathematical sciences / Abraham Berman, Robert J. Plemmons. (1994)
  631. Arbitrage-Free Parametric Volatility Surfaces and Real-Time Fitting (2017) — link
  632. Tools for Options Trading in a Crazy World — link
  633. Monotone Piecewise Cubic Interpolation (1980)
  634. Deep hedging: learning to remove the drift (2022) — link
  635. Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures (2022) — link
  636. Clamping Down on Arbitrage (2014) — link
  637. Option-Implied Risk Aversion Estimates (2004)
  638. On Estimating the Risk-Neutral Probability Distribution Implied by Option Prices (1995)
  639. The equity option volatility smile: an implicit finite-difference approach (1997) — link
  640. An Arbitrage-Free Interpolation of Volatilities (2004)
  641. Volatility Surfaces and Log-Normal Mixture: Crafting the Perfect Arbitrage-Free Calibration (2023) — link
  642. Detecting and Repairing Arbitrage in Traded Option Prices (2020) — link
  643. Convex Volatility Interpolation (2026)
  644. Differential Machine Learning (2021) — link

6 of 652 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.