Diamonds help compute volatility models efficiently.
problem Computing volatility models in forward variance form.
method Application of diamond trees and forests.
result Efficient computation of volatility models.
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48 results for “forward variance models”
Study variance-optimal hedging of forward curve derivatives under stochastic volatility.
problem Variance-optimal hedging of forward curve derivatives with stochastic volatility.
method Assumes HJM-Musiela dynamics modulated by stochastic covariance, uses Galtchouk-Kunita-Watanabe projection.
result Density of finite-maturity strategies, convergence of finite-rank projections, decomposition of hedging error.
We create precise formulas for VIX option implied volatility.
problem Calibrating VIX option prices in forward variance models.
method Developed closed-form expansions using weak-approximation techniques.
result Explicit formulas for implied volatility with computable correction terms.
A new QHR model extends HR model with a quadratic variance function.
problem Modeling volatility with greater flexibility and stationarity.
method Introducing a quadratic variance function to the HR model, maintaining Markovian property.
result Stationary distribution of the QHR model is Pearson type IV.
New algorithms reduce variance in solving complex mathematical problems.
problem Solving convex-concave saddle point problems, variational inequalities, and inclusions.
method Stochastic variance reduction for extragradient, forward-backward-forward, and forward-reflected-backward methods.
result All proposed methods converge with complexities matching or improving deterministic counterparts.
Affine forward variance modelsq-fin.MF
We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterized by the affine form of their cumulant generating function, which can be obtained as solution of a convolution Riccati equat…
Neural network models accurately price assets in rough Bergomi model.
problem Accurately pricing assets in the rough Bergomi model with hidden parameters.
method Used a neural SDE to learn the forward variance curve, proposing a numerical scheme for simulation.
result The learned forward variance curve calibrates asset prices and option prices simultaneously.
Computing the SSRq-fin.MF
Model-free expression for SSR derived in terms of characteristic function.
problem Calculating the skew-stickiness-ratio (SSR) in financial markets.
method Model-free expression using characteristic function, focusing on diffusion and affine forward variance cases.
result General formula for SSR simplifies and becomes particularly tractable in affine forward variance cases, with a limit of for short-term limit.
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.
New model for pricing volatility derivatives considering rough volatility and jumps.
problem Modeling instantaneous volatility with rough volatility and jumps.
method Generalized fractional Ornstein-Uhlenbeck process with Lévy subordinator and sinusoidal-composite Lévy process.
result Pricing-hedging formulae for power-type derivatives on average forward variance are derived.
We provide approximations for VIX futures and options in forward variance models.
problem Modeling VIX futures and options in forward variance models.
method Weak approximations and explicit formula derivation for VIX futures and options.
result Explicit combinations of Black-Scholes prices and greeks for option price approximations.
New variance-reduction methods solve stochastic composite inclusions.
problem Solving nonmonotone stochastic composite inclusions.
method Developed unbiased and biased variance-reduced estimators for FRBS method.
result Achieved best oracle complexities for finite-sum and expectation settings.
The paper prices energy spread options using a complex stochastic model.
problem Pricing energy spread options with specific stochastic dynamics.
method Uses an exponential Ornstein-Uhlenbeck process driven by variance gamma processes, applying the Esscher transform and FFT method.
result Derives an analytical formula for pricing forwards and spread options.
Optimal investment and risk control strategies for insurers are derived using a time-consistent approach.
problem Optimal investment and risk control for insurers under mean-variance criterion.
method Introducing a deterministic forward auxiliary process to formulate a time-consistent problem.
result Optimal strategy and value function obtained in closed-form for the new problem.
In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Fu…
Develops a multilevel Monte Carlo framework with dropout for efficient uncertainty quantification.
problem Efficiently quantify uncertainty in complex models using dropout.
method Integrates multilevel Monte Carlo with Monte Carlo dropout, creating coupled estimators to reduce variance.
result Demonstrates significant variance reduction and efficiency gains over single-level Monte Carlo dropout.
Surprisal-Rényi Free Energystat.ML
SRFE clarifies KL divergences without unifying learning frameworks.
problem Inductive biases of KL divergences and their limitations.
method Introducing SRFE, a log-moment-based functional of the likelihood ratio.
result SRFE recovers KL divergences as limits and reveals a mean-variance tradeoff.
We reduce variance in Bures-Wasserstein variational inference.
problem High variance in Monte Carlo approximations of Bures-Wasserstein gradients.
method Control variates to reduce variance in the forward step.
result Proposed estimator reduces variance by orders of magnitude.
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and …
This work explains the structural origins of attention sinks in LLMs.
problem Initial tokens disproportionately monopolize attention scores in LLMs.
method Traced to self-attention's value aggregation process and FFN layer activations.
result Attention sinks form due to variance discrepancy and dimension disparity.
Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Modelscs.LG
VT-DIS improves sampling from Boltzmann distributions with minimal overhead.
problem Bias in Monte Carlo estimates from score-based diffusion models.
method Variance-Tuned Diffusion Importance Sampling (VT-DIS) adapts noise covariance to correct bias.
result VT-DIS achieves effective sample sizes of 80%, 35%, and 3.5% on benchmarks, using less computational budget.
A new model for forward curves captures behavior through a single equation.
problem Modeling forward curves in a complex function space.
method Developed a stochastic partial differential equation with locally state-dependent coefficients.
result The model retains simplicity while capturing entire forward curve behavior.
Survey of SDR methods for high-dimensional regression and embedding.
problem Reducing dimensionality in high-dimensional data.
method Involves both statistical and machine learning approaches, covering inverse and forward regression methods.
result Supervised Kernel Dimension Reduction is equivalent to supervised PCA.
This paper focuses on the pricing of the variance swap in an incomplete market where the stochastic interest rate and the price of the stock are respectively driven by Cox-Ingersoll-Ross model and Heston model with simultaneous Lévy jumps. By using the equilibrium framework, we obtain the pricing kernel and the equival…
A hybrid physics-ML model predicts FO water flux with high accuracy and uncertainty quantification.
problem Challenges in accurately modeling Forward Osmosis water flux due to complex internal mass transfer phenomena.
method Robust Hybrid Physics-ML framework using Gaussian Process Regression (GPR) for uncertainty-aware Jw prediction.
result Achieved a state-of-the-art MAPE of 0.26% and R2 of 0.999 on independent test data.
Hedging under rough volatilityq-fin.MF
Perfect hedging of options with a dynamic portfolio in rough volatility models.
problem Hedging options in rough volatility models.
method Presented a simple but general result showing perfect hedging with a dynamic portfolio of underlying and variance swap.
result Rough volatility models significantly reduce hedging error compared to diffusion-based models.
Develops variance-reduced methods for solving generalized equations.
problem Solving a class of generalized equations, including minimization, minimax, and variational inequalities.
method Integrates accelerated operator splitting, fixed-point methods, and variance reduction techniques.
result Achieves both and convergence rates on the expected squared norm of the FBS residual.
Study improves caplet calibration for 1Y maturity using different models.
problem Calibrate 1Y caplet smile better across strike range.
method Alternative local volatility terms and stochastic volatility models.
result Some models calibrate well to 1Y caplet smile across strike range.
We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that the initial mean variance hedging problem is equivalent to a ne…
Backpropagation-free trunk training improves model performance on various benchmarks.
problem Memory inefficiency and noisy gradient estimates in deep network training.
method Split Forward Gradient (Split-FG) method that splits network into trunk and head, estimating only trunk gradient.
result Split-FG achieves better performance than pure forward-gradient training and backpropagation on various benchmarks.
Introduces a new Lévy process for modeling illiquid markets.
problem Modeling dynamic of assets in illiquid markets.
method Introduces Variance Gamma++ process, a new Lévy process, and provides efficient path simulation algorithms.
result Efficient pricing formula and parameter estimation for European options.
A new aggregation strategy improves GNN performance and learning dynamics.
problem Improving expressivity and learning dynamics of GNNs.
method Proposes a variance-preserving aggregation function (VPA) for GNNs.
result VPA leads to increased predictive performance and improved learning dynamics.
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to and asymptotically optimal .
Unified analysis for deterministic samplers in diffusion models.
problem Challenges in analyzing deterministic samplers for diffusion models.
method Unified convergence analysis framework.
result Achieved polynomial iteration complexity for DDIM-type samplers.
Valuing FF contracts in time-dependent models
problem Valuing American options and Flexible Forwards contracts
method Recursive Riccati solution and Volterra equation
result FF contracts priced faster than traditional methods
Investigates time-inconsistent portfolio selection under MMV preferences.
problem Time-inconsistent optimal strategies for MMV preferences.
method Nash equilibrium controls for MMV and MV preferences, solving FBSDE and HJB equations.
result MMV optimal strategies lead to higher investment amounts than MV strategies, narrowing over time.
Mean-field game of mean-variance portfolio management with peer-based relative risk aversionq-fin.MF
New MFG model for MV portfolio management with peer-based risk aversion.
problem Time-inconsistent mean-variance portfolio management with peer-based risk aversion.
method Mean-field game, smooth regularization, fixed-point arguments, convergence analysis.
result Existence of mean-field equilibrium in time-inconsistent MFG.
Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal…
The paper analyzes insurance risks using stochastic models.
problem Interest rate and variance risks in unit-linked insurance policies.
method General stochastic volatility models and stochastic interest rates are used to price unit-linked life insurance contracts.
result A perfect hedging strategy is provided and compared with the Black-Scholes model.
Variational inference improves training of generative flow networks.
problem Training generative flow networks efficiently and accurately.
method Define variational objectives in terms of KL divergences and optimize convex combinations.
result Variational inference methods can reduce the variance of gradients in training generative flow networks.
Improves predictions by integrating forward-looking views into dynamic factor models.
problem Poor forecasts from historical data when dynamics change.
method Combines historical data with forward-looking views using a dynamic factor model.
result Derives optimal portfolio strategies influenced by both myopic and intertemporal factors.
New insights into how randomization affects greedy model selection.
problem Understanding the impact of feature subsampling on greedy model selection.
method Investigated greedy forward selection with feature subsampling, proving effects on bias and variance.
result Ensembling with feature subsampling reduces both bias and variance, unlike convex base learners.
This paper tackles variance issues in GNN training by proposing a method to reduce both embedding and gradient variances.
problem High variance in estimating stochastic gradients in GNN training, especially in large graphs.
method The paper proposes a decoupled variance reduction strategy that employs approximate gradient information to adaptively sample nodes with minimal variance.
result The proposed method achieves faster convergence and better generalization compared to existing sampling methods.
We propose a feed-forward inference method applicable to belief and neural networks. In a belief network, the method estimates an approximate factorized posterior of all hidden units given the input. In neural networks the method propagates uncertainty of the input through all the layers. In neural networks with inject…
Develops a new calculus for stochastic processes with occupation flows.
problem Analyzing the behavior of stochastic processes with occupation flows.
method Itô calculus for occupied processes, Feynman-Kac approach.
result Unified Markovian lifts for pricing financial derivatives.
Readouts for Echo-state Networks Built using Locally Regularized Orthogonal Forward Regressionstat.ML
Echo state network (ESN) is viewed as a temporal non-orthogonal expansion with pseudo-random parameters. Such expansions naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the variance of the tea…
Pricing Bermudan swaptions with few exercise dates using analytic methods.
problem Pricing Bermudan swaptions with few exercise dates
method Analytic decomposition and backward induction under rolling forward measures
result Pricing formulas with decomposition and boundary linearity
Derives variance kernel for reaction boundary in financial models.
problem Separating components in financial volatility models.
method Operational-time variance kernel, damped Abel response kernel, closed asymptotic form.
result Operational variance has a closed asymptotic form involving various parameters.