This study simplifies rough Heston model's conditional density equation.
problem Analyzing rough volatility in financial models.
method Pathwise transformation and Fokker-Planck formulation of conditional density equation.
result Transformed equation yields deterministic PDE with path-dependent coefficients.
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).
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.
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.
New method for pricing European options in rough LSV models.
problem Pricing European options in non-Markovian local stochastic volatility models.
method Conditional LSV dynamics, rough path theory, rough partial differential equations (RPDEs).
result Established a PDE pricing method for non-Markovian models.
New algorithm calibrates stochastic volatility models without errors.
problem Calibration errors in stochastic volatility models.
method Monte Carlo based LSV calibration algorithm for all models.
result Closed-form and exact calibration method with variance reduction.
Paper develops a new estimator for rough volatility parameters.
problem Estimating rough volatility parameters from high-frequency data.
method Develops a semiparametric estimator for H in rough volatility models. result The estimator achieves optimal convergence rate in minimax sense.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of min(3α−1,1) for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model. Study approximates rough stochastic volatility models using diffusion processes.
problem High computational cost in simulating rough stochastic volatility models.
method Approximates stochastic Volterra equations with an N-dimensional diffusion process.
result Approximations converge strongly with superpolynomial rate in N.
We expand volatility models for rough stochastic volatility.
problem Modeling rough stochastic volatility.
method Vol-of-vol expansion for potentially infinite dimensional models.
result Explicit representations of push-down Malliavin weights.
New method analyzes volatility models for option prices, especially in rough volatility.
problem Analyzing option prices in rough volatility models.
method Introducing a new methodology to analyze stochastic volatility models, focusing on asymptotics and numerics.
result Detailed expansion and numerical evidence for implied volatility in rough volatility models.
Study finds roughness in volatility despite diffusive instantaneous volatility.
problem Determining the roughness of volatility in financial assets.
method Non-parametric method based on normalized p-th variation for estimating roughness of sample paths. result Realized volatility exhibits rough behavior with a significantly smaller Hurst exponent than instantaneous volatility.
A fast calibration method for rough volatility models with jumps.
problem Calibrating stochastic volatility models to market data efficiently.
method Structure-preserving approach: split pricing formula, precompute data-independent integrals, and approximate market-dependent remainder with neural networks.
result Calibration achieves high accuracy and speed, and a pure-jump rough volatility model adequately captures VIX dynamics.
This paper improves simulation methods for rough Volterra stochastic volatility models.
problem Inefficient techniques in Monte-Carlo simulations for rough Volterra volatility models.
method Comparison and modification of three simulation methods: Cholesky, Hybrid, and rDonsker schemes.
result Suggests modifications to improve simulation accuracy and efficiency.
Enhances swaption modeling with rough stochastic volatility.
problem Modeling swaption volatility in post-LIBOR markets.
method Introduces rough stochastic volatility into FMM and rigorously justifies the freezing approximation.
result Establishes a new framework connecting FMM to rough Bergomi for forward swap rates.
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
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.
New rough stochastic volatility models using log-modulated fractional Brownian motion.
problem Analyzing rough stochastic volatility models over the range 0≤H<1/2. method Introducing log-modulated fractional Brownian motion (log-fBm) to handle H=0 and analyze over the full range. result Obtained skew asymptotics of log(1/T)−pTH−1/2 as To0 for H≥0, no flattening of skew as Ho0. Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.
problem Computing Greeks under rough Volterra stochastic volatility models.
method Malliavin calculus techniques, extending integration by parts to non-square integrable functionals.
result Formulas for computing Greeks (Delta, Gamma, Rho, Vega) under various rough Volterra SV models.
Study improves weak error estimates for rough volatility models.
problem Efficient numerical schemes for non-Markovian stochastic processes with rough volatility.
method Analyzes weak rates for a class of stochastic processes with rough stochastic volatility.
result Weak rate is of order min{3H+0.5, 1} for a large class of test functions.
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized facts of the entire implied volatility surface, including extr…
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.
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough vola…
Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.
problem Estimating Hurst parameter of rough stochastic volatility models from discrete observations.
method Extends a scale-invariant estimator to a general nonlinear function.
result Consistent estimation of Hurst parameter for a wide class of rough stochastic volatility models.
Estimates roughness of volatility from discrete variance data.
problem Estimating roughness exponent of stochastic volatility from discrete observations of integrated variance.
method Pathwise estimator based on fractional Brownian motion with drift.
result Strong consistency theorems for rough volatility models.
Model captures rough volatility and jump clustering in stock vol dynamics.
problem Capturing the joint evolution of S&P 500 and VIX implied vol smiles.
method Rough Hawkes Heston model with affine Volterra dynamics, power kernel, and exponential jump law.
result Model accurately captures S&P 500 and VIX implied vol smiles with low power kernel.
Study provides LDP for non self-similar stochastic volatility models.
problem Analyzing non self-similar stochastic volatility models.
method Short-time large deviation principle (LDP) for models with Volterra process.
result Derives consequences for option prices, implied volatility surfaces, and skew.
Study confirms rough volatility in financial data, independent of microstructure noise.
problem Characterizing volatility in financial markets, especially rough volatility.
method Used range-based volatility estimators to confirm findings from fractional behavior.
result Log-volatility behaves like fractional Brownian motion with an even lower Hurst exponent.
New study finds actual volatility is rougher than previously thought.
problem Determining if volatility is rough based on log realized volatility data.
method Developed a quasi-likelihood estimator for fractional stochastic volatility model.
result Volatility is indeed rougher than previously estimated.
The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.
problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.
Develops a GMM method to estimate roughness in stochastic volatility models.
problem Estimating roughness in stochastic volatility models with fractional Brownian motion.
method GMM approach for log-normal models with integrated variance and noisy realized variance.
result Consistent and asymptotically normal parameter estimator with bias correction.
Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.
problem Modeling rough volatility with correlated stochastic processes.
method Developed a method to lift Brownian motion and rough paths, applying it to fractional Brownian motion to model rough volatility.
result Calibrated a new rough volatility model to market data.
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the origin. Another classic stylistic feature often assumed for the volatility is that it …
Analyzes how rough volatility affects stock pricing and risk premium.
problem Impact of non-deterministic volatility risk on stock pricing.
method Rough volatility model under historical measure, analysis of stochastic volatility risk.
result Impact of non-deterministic volatility risk on pricing is significant.
Extends pricing methods for index options under rough volatility.
problem Pricing and hedging of index options under non-Markovian dynamics.
method Extension of large deviations methods to non-local volatility dynamics, specifically rough volatility.
result Validates the approach for pricing index options under rough volatility.
Paper offers a new method for pricing financial derivatives under rough stochastic volatility models.
problem Challenges in pricing financial derivatives, especially vanilla options, for rough stochastic volatility models.
method Developed a decomposition formula and prediction law for European option pricing under general Gaussian Volterra processes.
result Explicit semi-closed approximation formula for rough fractional volatility models, significantly improving computational efficiency.
Study on CVA in volatility models, including rough volatility.
problem Calculating CVA in fractional and rough volatility models.
method General representation formula, specialized for volatility models, numerical and theoretical error analysis.
result Roughness influences the claim's price, and provides accurate approximations.
New methods price American options in rough volatility models.
problem Pricing American options under rough volatility.
method Integrating deep-signature and signature-kernel learning into optimal stopping problem solutions.
result Performance comparison in rough Heston and rough Bergomi models.
Investigates portfolio selection under rough volatility model, showing quadratic efficient frontier.
problem Mean-variance portfolio selection under rough volatility models.
method Constructs an auxiliary stochastic process to solve Riccati-Volterra equation for optimal strategy.
result MV efficient frontier is quadratic, influenced by roughness and volatility of volatility.
The paper analyzes robustness and sensitivity of rough Volterra stochastic volatility models.
problem Analyzing the robustness and sensitivity of stochastic volatility models.
method Statistical tests and empirical analysis on Apple Inc. equity options.
result Comparison of different models' robustness and sensitivity to option data structure.
Paper tackles rough volatility estimation from high-frequency data.
problem Estimating historical volatility from high-frequency asset price data.
method Uses fractional Brownian motion representation and particle methods for filtering and parameter estimation.
result Demonstrates efficient estimation of rough volatility using standard techniques.
Survey of continuous volatility models, focusing on fractional and rough methods.
problem Stylized facts driving continuous volatility modeling.
method Historical development and fractional/rough methods.
result Characterization of landmark models and recent advances.
Comparison results for rough and non-rough Heston models, tighter bounds on moment explosion times.
problem Comparing Heston models with and without roughness.
method Comparison principle for non-linear Volterra integral equations.
result Tighter bounds on moment explosion times for rough Heston models.
The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.
problem Arbitrage in implied volatility calculations.
method Analytical proofs for BBF, SABR, and rough SABR formulas under specific models.
result These formulas offer asymptotically arbitrage-free approximations of implied volatility.
Study small-time CLTs for stochastic Volterra equations with various kernels.
problem Understanding the behavior of stochastic Volterra equations with different kernels.
method Proved convergence of finite-dimensional distributions, functional CLT, and limit theorems for smooth transformations.
result Derived asymptotic pricing formulae for digital calls in rough volatility models.
Researchers derive an analytic expression for Gaussian stochastic volatility models.
problem Analyzing rich autocorrelation structures and persistence in financial markets.
method Two different analytic derivations of the joint characteristic function.
result First analytic formulae for option pricing in rough volatility models.
The paper develops methods to price options under rough volatility models using BSPDEs.
problem Pricing options in models with non-Markovian dynamics.
method Backward stochastic partial differential equations (BSPDEs) and deep learning for numerical approximations.
result Existence and uniqueness of weak solutions for general nonlinear BSPDEs.
The non-Markovian nature of rough volatility processes makes Monte Carlo methods challenging and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker's approximation of Brownian motion to the f…