Paper approximates rough stochastic local volatility models for efficient computation.
problem No unified method for rough stochastic local volatility models.
method Semimartingale and continuous-time Markov chain approximation.
result Fast CTMC algorithm with weak convergence proved.
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers recently. More precisely, given a local volatility surface and a choice of stocha…
The study calibrates VIX and VXX options using a multi-factor model.
problem Calibration failure of VIX and VXX options using stochastic or local volatility models.
method Presented a multi-factor stochastic-local volatility model.
result Joint calibration of VIX and VXX options successfully achieved.
The article reviews how to set stochastic volatility model parameters.
problem Choosing parameters for stochastic volatility models.
method Examines existing literature on various methods.
result Different approaches to setting stochastic volatility parameters.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
Efficient method for lookback option pricing under Markov models.
problem Pricing lookback options under Markov models.
method Model-free representations combined with numerical quadrature and Markov chain approximation.
result Efficient method applicable to various Markov models.
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the …
This paper deals with the exact calibration of semidiscretized stochastic local volatility (SLV) models to their underlying semidiscretized local volatility (LV) models. Under an SLV model, it is common to approximate the fair value of European-style options by semidiscretizing the backward Kolmogorov equation using fi…
We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the linearity-generating unspanned volatility term structure model by Carr et al. (2011) by a…
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV) discretization in the numerical solution of general 1D and 2D forward Kolmogorov eq…
Two methods improve simulation of European call options under Heston model.
problem Efficient simulation of European call options under Heston model.
method Two strongly convergent and positivity-preserving methods for Cox-Ingersoll-Ross process under Lamperti transformation: truncated Euler and backward Euler methods.
result Explicit truncated Euler method is computationally effective and robust under high volatility, while implicit backward Euler method provides high accuracy and stability.
Model prices commodity futures and index options.
problem Deriving accurate prices for derivative contracts on commodity futures and indices.
method Stochastic local volatility model for commodity futures.
result Model accurately recovers prices of derivative claims.
New method for CMS derivatives pricing using Watanabe's expansions.
problem Pricing CMS derivatives under local and stochastic volatility.
method Malliavin's calculus and Watanabe's expansions applied to quadratic payoffs.
result Generic approximations for CMS derivatives pricing under various volatility models.
New method solves SLV models faster using Lie algebra.
problem Local stochastic volatility models.
method Wei-Norman factorization method and Lie algebraic techniques.
result Reduces time-dependent SLV models to autonomous PDEs.
New method for sampling from complex distributions using stochastic localization.
problem Sampling from unnormalized target densities in multi-modal distributions.
method Stochastic Localization via Iterative Posterior Sampling (SLIPS) framework.
result Approximate samples from target distribution and denoiser learned iteratively.
We present a stochastic-local volatility model for derivative contracts on commodity futures able to describe forward-curve and smile dynamics with a fast calibration to liquid market quotes. A parsimonious parametrization is introduced to deal with the limited number of options quoted in the market. Cleared commodity …
We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for…
Develops a functional generalization of Eldan's stochastic localization for optimization and privacy.
problem Sampling under non-Euclidean geometries and optimization in differential privacy.
method Functional generalization of Eldan's stochastic localization, incorporating log-Laplace transform.
result Improves query complexities in zeroth-order differential private convex optimization.
This work extends stochastic localization to joint probability measures for data analysis.
problem Data distributional analysis in high-dimensional probability.
method Unified stochastic localization under Eldan's α-scheme, coupled probability measures via shared Brownian motion.
result Eldan's α-distance as a scalable surrogate for Wasserstein distance.
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most general context -- the impact of stochastic variables on the P&L of a hedged port…
New algorithms improve Bayesian linear regression with spike-and-slab priors.
problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.
New bounds show diffusion models converge nearly linearly in data dimension.
problem Improving convergence bounds for diffusion models.
method Refined discretization of reverse SDE using stochastic localization.
result Linear convergence in data dimension with logarithmic factors.
Paper explores how Rectified Flow adapts to low-dimensional data.
problem Improving sampling efficiency in low-dimensional data.
method Investigates Rectified Flow's adaptation to low-dimensional support and introduces a stochastic version.
result Shows improved sampling efficiency with O(k/ε) complexity. Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
New approach solves utility maximization problems using Delta family.
problem Utility maximization in stochastic control problems.
method Directly solving DP equation with Delta function representation.
result Explicit series representation of value function.
Develops a nonparametric model for arbitrage-free pricing of illiquid derivatives.
problem Modeling joint dynamics of liquid vanilla options for arbitrage-free pricing of illiquid derivatives.
method Derives a state space for prices respecting underlying financial constraints using neural networks and imposes constraints to preserve no-arbitrage conditions.
result Neural SDE models are guaranteed to satisfy a set of linear inequalities and validated with numerical experiments.
Stochastic LWTA networks resist adversarial attacks while maintaining accuracy.
problem Adversarial robustness of neural networks.
method Replaced ReLU with stochastic LWTA activations, trained with Variational Bayesian and PGD.
result Stochastic LWTA networks achieve state-of-the-art robustness against adversarial attacks.
It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin…
A new method for generating SPX and VIX risk scenarios using perturbed optimal transport.
problem Generating accurate risk estimates for SPX and VIX without full recalibration.
method A joint optimal transport calibration with perturbation methodology for sensitivities, combined with Skew Stickiness Ratio dynamics.
result The proposed method produces accurate risk estimates relative to full recalibration and is computationally faster.
PEMC uses ML to enhance Monte Carlo simulations, reducing variance and runtime.
problem Computational inefficiency in Monte Carlo simulations for complex tasks.
method Prediction-Enhanced Monte Carlo (PEMC) framework that uses ML surrogates as predictors.
result PEMC provides unbiased evaluations with reduced variance and runtime compared to standard Monte Carlo.
This work combines machine learning with physical models to solve inverse problems efficiently.
problem Solving inverse problems in the presence of missing physics and recovering parameters.
method Variational autoencoding with a physically structured decoder network and stochastic local approximations.
result The method accelerates inference for Bayesian inverse problems and acts as a regularizer encoding prior physical information.
Exact relationships found between ATM slope, volatility swap, and zero vanna.
problem Understanding relationships between implied volatilities and swaps.
method Analyzes exact relationships between ATM slope, volatility swap, and zero vanna.
result Exact relationships between ATM slope, volatility swap, and zero vanna.
Study local volatility from rough volatility models, finding new skew rule.
problem Understanding local volatility from rough volatility models.
method Analyzing asymptotic behavior of local volatility surface generated by rough stochastic volatility models.
result New skew rule: ratio of implied and local vol skews tends to 1/(H + 3/2).
Enhanced volatility forecasting using options data and rough volatility model.
problem Improving realized volatility forecasting accuracy.
method Infer spot volatility from options data using rough stochastic volatility model, accelerate estimation with deep learning, benchmark against traditional models.
result Augmented HAR-RV-RHeston model outperforms traditional models in daily and long-term forecasting.
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…
Volatility models must be rough to match market skew.
problem Inconsistent non-rough volatility models with power law volatility skew.
method Asymptotic expansion and continuous price dynamics analysis.
result Volatility must be rough to align with market skew.
Study on estimating volatility of volatility using Fourier methods and provides insights into volatility dynamics.
problem Estimating the volatility of volatility (vol-of-vol) accurately and efficiently.
method Used Fourier methodology to estimate integrated volatility of volatility, bias-corrected and without bias-correction, comparing their asymptotic properties and accuracy.
result The bias-corrected estimator reaches the optimal rate n1/4, while the uncorrected estimator has a slower rate and smaller asymptotic variance. Extends Heston model with local volatility for better fit to market volatilities.
problem Fitting stochastic volatility models to market volatilities.
method Adds local volatility term to rough-Heston model, preserving stylized results.
result Provides a proper extrapolation scheme for calibration.
The paper values perpetual callable American volatility options using a mean-reverting volatility model.
problem Valuation of callable American volatility put options.
method Modeling volatility dynamics as a mean-reverting 3/2 process and proposing a pricing formula.
result The value of perpetual callable American volatility put options is discussed under given conditions.
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. …
In this paper, Malliavin calculus is applied to arrive at exact formulas for the difference between the volatility swap strike and the zero vanna implied volatility for volatilities driven by fractional noise. To the best of our knowledge, our estimate is the first to derive the rigorous relationship between the zero v…
Paper extends Poincaré's work to stochastic differential equations.
problem Existence of first integrals in stochastic differential equations.
method Introduce two definitions of local first integrals for SDEs.
result Stochastic version of Poincaré non-integrability theorem.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Study large deviations in fractional volatility models with non-Gaussian volatility.
problem Large deviations in fractional volatility models with non-Gaussian volatility.
method Established a small-noise large deviation principle for log-price.
result Logarithmic call price asymptotics for large strikes in a special case.
Estimates volatility of volatility and leverage effect using high-frequency options data.
problem Estimating volatility of volatility and leverage effect from high-frequency options data.
method Model-free estimators using characteristic function of price increments and spot volatility.
result Developed feasible inference methods for estimating volatility of volatility and leverage effect.
New deep learning model robust to adversarial attacks using stochastic LWTA units.
problem Adversarial robustness in deep learning networks.
method Introduces deep networks with stochastic LWTA activations, combining them with Bayesian non-parametric tools.
result Achieves high robustness to adversarial perturbations, outperforming state-of-the-art methods.