Method uses trinomial trees to price nontraditional options.
problem Pricing of random-expiry options with early expiry.
method Developed a trinomial tree approach to interpret early expiry.
result The method is free of arbitrage and can be implemented efficiently.
In this paper, we present a new method for calculating the limit of early exercise boundary at expiry. We price American style of general derivative using a formula expressed as a sum of the value of European style of derivative and so called American premium. We use the latter expression to calculate an analytic formu…
We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial marke…
In this paper we generalize and analyze the model for pricing American-style Asian options due to (Hansen and Jorgensen 2000) by including a continuous dividend rate q and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The fi…
We examine the small expiry behaviour of European call options in stock price models of exponential Lévy type. In most cases of interest, we are able to identify the exact small expiry asymptotics. In "complete generality" we are able to show that the time value of the call option has O(τ) decay as τ(time to expiry) go…
In this paper we extend Buchen's method to develop a new technique for pricing of some exotic options with several expiry dates(more than 3 expiry dates) using a concept of higher order binary option. At first we introduce the concept of higher order binary option and then provide the pricing formulae of n-th order b…
Study finds monthly SIPs outperform first-day SIPs in Nifty 50 by 0.5-2.5% annually.
problem Underexplored impact of SIP timing in India's equity market.
method 22-year analysis using multi-layered statistical framework (non-parametric tests, effect size metrics, SSD).
result Monthly SIPs (EXP-SIP) outperform first-day SIPs (FTD-SIP) by 0.5-2.5% annually over short-to-medium-term horizons.
Paper improves American option valuation in complex models.
problem Valuation of American options in time-dependent jump-diffusion models.
method Integral equations and characteristic functions for explicit exercise boundary determination.
result Efficient and accurate pricing method for American options in various models.
The paper presents an approximate formula for European mortgage options pricing.
problem Pricing European mortgage options with accuracy and efficiency.
method Approximation of the underlying price distribution using lognormal distributions and matching moments.
result The proposed formula provides a good approximation with high accuracy compared to Monte Carlo simulations.
A model-free framework extracts risk-neutral densities from short-dated options.
problem Arbitrage and bid-ask spread issues in short-dated options.
method Develops ARIES for filtering static arbitrage and SEDEx for density extraction.
result Robust density extraction across various market conditions and volatility smiles construction.
We consider an American put option under the CEV process. This corresponds to a free boundary problem for a PDE. We show that this free bondary satisfies a nonlinear integral equation, and analyze it in the limit of small ρ = 2r/σ2, where r is the interest rate and σ is the volatility. We use perturbation met…
A neural network method for financial data nowcasting.
problem Financial data nowcasting, especially with variable grid nodes.
method Neural network architecture for variable grid nodes data.
result Outperforms interpolation benchmarks and outlier detection.
Derives new equations for stochastic volatility models.
problem Modeling local-stochastic-volatility models and their derivatives.
method Conditional forward equation, Dupire stochastic PDE, rolling expiry vanilla option SPDE.
result New equations for LSV models and their derivatives.
Derives new equations for volatility models and option pricing.
problem Modeling and pricing options in local-stochastic-volatility models.
method Develops conditional forward equations and Dupire stochastic PDEs.
result Derives new SPDE for vanilla options.
New method calibrates eSSVI volatility surfaces without arbitrage.
problem Sequential calibration of eSSVI surfaces lacks global view and guarantees no arbitrage.
method Global and arbitrage-free parametrization of eSSVI surfaces.
result Faster calibration always guarantees an arbitrage-free fit.
We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options. First and higher order small-time moderate deviation estimates of call prices an…
We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems defined by a class of nonlocal operators that are not stable-like and may have supercritical drift. We give sufficient conditions on the coefficients of the operator to obtain Hölder and Lipschitz con…
We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be null at the maturity of t…
A new framework for SPX and VIX hedging that combines AI and market dynamics.
problem Jointly hedging SPX and VIX exposures under transaction costs and regime shifts.
method Integrates an SSVI-based implied-volatility surface and a Cboe-compliant VIX computation with a control layer that enforces safety as constraints.
result Reduces expected shortfall while suppressing nuisance turnover in a reproducible synthetic environment.
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generaliz…
Early stopping improves logistic regression's calibration and consistency in high dimensions.
problem Improving the statistical performance of gradient descent in overparameterized logistic regression.
method Investigates the effects of early stopping on gradient descent in logistic regression.
result Early-stopped gradient descent is well-calibrated and statistically consistent, while asymptotic gradient descent is not.
New method stops experiments early for harm in diverse groups.
problem Early stopping of experiments for harmful treatment effects in diverse populations.
method Causal machine learning approach (CLASH) for early stopping.
result CLASH effectively stops experiments early for harmful treatment effects in diverse groups.
We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-stri…
A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The main points of this note are the following. First, the presented trading strategy a…
SWIFT method speeds up Heston model calibration for European options.
problem Calibrating the Heston model for European options efficiently.
method Extends SWIFT method to Heston model, simplifying gradient computation.
result Extremely fast calibration, outperforming state-of-the-art methods.
This paper improves neural network predictions with early stopping using conformal calibration.
problem Lack of precise statistical guarantees for neural networks trained with early stopping.
method Conformalized early stopping that combines early stopping with conformal calibration.
result Models provide both accuracy and precise inferences without additional data splits.
Gradient descent with early stopping achieves optimal sparse recovery.
problem Sparse regression with gradient descent and early stopping.
method Gradient descent on depth-N networks with early stopping.
result Implicit sparse regularization occurs with early stopping for general depth N.
Early stopping methods reduce unnecessary reasoning steps in LLMs by monitoring uncertainty signals.
problem LLMs sometimes generate unnecessary reasoning steps, especially under uncertainty.
method Statistically principled early stopping methods that monitor uncertainty signals during generation.
result Uncertainty-aware early stopping improves efficiency and reliability in LLM reasoning, especially in math reasoning.
Paper analyzes pricing model for bonds with early redemption.
problem Analyzing pricing of bonds with early redemption features.
method Structural approach for mathematical modeling of bond prices.
result Existence and uniqueness of default and early redemption boundaries proved.
The study reveals optimal early stopping behaviors in deep learning models.
problem Understanding optimal early stopping in deep learning models.
method Theoretical analysis of linear models and experimental validation.
result Two distinct behaviors of optimal early stopping time depending on model dimension relative to dataset features.
This paper reviews early time series classification methods.
problem Minimizing class prediction delay in time-sensitive applications.
method Divided into four categories: prefix based, shapelet based, model based, and miscellaneous approaches.
result Demonstrates reasonable performance in various applications.
This work bounds the run-time of nonconvex optimization with early stopping.
problem Bounding the expected run-time of nonconvex optimization with early stopping.
method Derives conditions for well-defined early stopping based on validation function norms and bounds the expected number of iterations and gradient evaluations.
result Guarantees the validity of early stopping and provides bounds on the expected run-time for various optimization algorithms.
E2CM uses class means for efficient early exits in neural networks.
problem Efficient early exits in neural networks with low computational cost.
method Early Exit Class Means (E2CM) based on class means of samples, without gradient-based training. result E2CM achieves higher accuracy with fixed training time budget and boosts existing early exit schemes. Enhances early-exit neural networks for anytime classification.
problem Lack of guaranteed prediction quality improvement with longer computation time.
method Post-hoc modification based on Product-of-Experts to enforce conditional monotonicity.
result Achieves conditional monotonicity in prediction quality, enabling anytime classification.
Paper introduces a method to control early classification accuracy gaps.
problem Maintaining accuracy in early classification without full input processing.
method Statistical framework for a calibrated stopping rule.
result Reduces up to 94% of timesteps while controlling accuracy gaps.
Continuous-time interpolation of volatility surfaces preserving mixtures and arbitrage-free.
problem Interpolation of volatility surfaces
method Constructing a mixture-preserving, arbitrage-free interpolation
result Lifts Brigo-Mercurio to time-varying weights with additive cost
The paper analyzes early stopping in linear regression and shows it's equivalent to ridge regularization.
problem Understanding the effect of early stopping on linear regression models.
method Characterization of gradient descent dynamics and analysis of excess risk.
result Early stopped solution is equivalent to minimum norm solution for a generalized ridge regularized problem.
We estimate treatment cost-savings from early cancer diagnosis. For breast, lung, prostate and colorectal cancers and melanoma, which account for more than 50% of new incidences projected in 2017, we combine published cancer treatment cost estimates by stage with incidence rates by stage at diagnosis. We extrapolate to…
XAI identifies key time steps for early crop classification.
problem Early crop classification with high accuracy and timeliness.
method Training a baseline model with LRP to identify important time steps.
result Identified a 21st April 2019 to 9th August 2019 timeframe with 0.75% accuracy loss.
System predicts respiratory failure up to 8 hours early.
problem Early detection of respiratory failure in ICU patients.
method Machine learning on ICU patient monitoring data.
result System outperforms traditional clinical decision-making.
Study proposes a new early-warning framework for high-dimensional complex systems.
problem Predicting critical transitions in complex systems like epileptic seizures.
method Integrates manifold learning with stochastic dynamical system modeling, using Schrödinger bridge theory.
result Demonstrates higher sensitivity and robustness in epilepsy prediction.
Paper characterizes early-stage dementia signatures from sensor data.
problem Detecting early-stage dementia from sensor data.
method Developed bespoke behavioural models from longitudinal sensor data.
result Found subtle differences in sleep quality and wandering between dementia patients and controls.
Enhances early risk assessments for pediatric outcomes using contrastive learning.
problem Improving risk assessments in early stages of pediatric development.
method Contrastive multi-modal framework that treats each time window as a distinct modality, training on all available data.
result Consistent improvements in early-stage risk assessments validated on real-world tasks.
Early stopping improves neural networks' performance on binary classification tasks.
problem Improving shallow ReLU networks' performance on binary classification tasks.
method Gradient descent with early stopping on binary classification data.
result Gradient descent with early stopping achieves population risk arbitrarily close to optimal.
The paper accelerates LLM inference by adding early exit heads trained in a self-supervised manner.
problem Inference speed in large language models (LLMs) is slow and resource-intensive.
method Adding self-supervised early exit heads at intermediate transformer layers to stop computation early based on confidence thresholds.
result Entropy provides the most reliable confidence metric for stopping computation early.
Well begun is half done. In the crowdfunding market, the early fundraising performance of the project is a concerned issue for both creators and platforms. However, estimating the early fundraising performance before the project published is very challenging and still under-explored. To that end, in this paper, we pres…
Two new rational formulae for normal implied volatility are presented.
problem Calculating normal implied volatility using iterative methods.
method Two explicit rational formulae that avoid iteration and logarithms.
result Accurate and fast formulae for normal implied volatility.
Early stopping is a well known approach to reduce the time complexity for performing training and model selection of large scale learning machines. On the other hand, memory/space (rather than time) complexity is the main constraint in many applications, and randomized subsampling techniques have been proposed to tackl…