Study leading-order asymptotics for VIX option prices in Bergomi models.
problem Understanding VIX option pricing in Bergomi models.
method Analytical approach to derive leading-order asymptotics for VIX option prices in Bergomi models.
result Closed-form solutions for VIX option prices in Bergomi models are derived.
Study shows stock price is a martingale if volatility's driving Brownian motion is negatively correlated with the stock.
problem Determining the martingale property of stock prices in fractional stochastic volatility models.
method Analyzed a class of fractional stochastic volatility models, including the rough Bergomi model, focusing on the correlation between stock and volatility.
result The stock price is a true martingale if and only if the correlation between the driving Brownian motions of the stock and the volatility is nonpositive.
We simplify a complex volatility model to make it easier to price options.
problem The rough Bergomi model's non-Markovian nature complicates option pricing.
method We approximate the rBergomi model with a Bergomi model that is Markovian.
result The rBergomi model can be effectively approximated by a Markovian model.
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.
The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve ge…
Proposes a new model for equity options calibration.
problem Calibration of joint SPX/VIX options.
method Replaces fractional Brownian motion with grey Brownian motion.
result Shows potential advantages and calibration results for new model.
Paper estimates Hurst parameter from implied volatilities.
problem Estimating Hurst parameter from implied volatilities.
method Uses covariance between asset return and realized volatility, and applies limit theorems for stochastic volatility models.
result Direct relation between covariance and slope of at-the-money implied volatility established.
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.
We study the small-time behaviour of the rough Bergomi model, introduced by Bayer, Friz and Gatheral (2016), and prove a large deviations principle for a rescaled version of the normalised log stock price process, which then allows us to characterise the small-time behaviour of the implied volatility.
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.
Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models
problem Computing option prices and Greeks for stochastic volatility models
method Matrix approximation using elementary linear algebra
result Option prices and Greeks computed for infinitely many strikes with a finite number of expectations
The article introduces a new interest rate model using Bergomi stochastic volatility.
problem Developing a model for interest rate swaps and swaptions without requiring calibration.
method Forward variance modeling by L. Bergomi applied to co-terminal swap market model.
result The model provides simple PnL formulas and high flexibility in controlling model dynamics.
New methods for volatility modeling using rough paths and signatures.
problem Calibrating implied volatility surfaces in various stochastic models.
method Analytical approximations and signature-based models based on rough path theory.
result Signature-based models achieve comparable accuracy to analytical expansions and can capture more complex dynamics.
The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in e…
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.
A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary.…
Improved volatility models for option pricing with weak error rates.
problem Improving volatility models to fit market data better.
method Developed a weak convergence analysis for the Euler method applied to linear rough volatility models.
result Proved weak convergence rates of 1/2 + H for linear models and 1 for quadratic payoffs.
Derives formula for skew stickiness ratio in asset price and volatility dynamics.
problem Capturing joint dynamics of asset price and volatility.
method Uses Itô-Wentzell and Clark-Ocone formulae to derive representation.
result Derives asymptotics of skew stickiness ratio under stochastic volatility models.
Deep learning solves barrier options with stochastic volatility.
problem Solving barrier options with stochastic volatility.
method Unsupervised deep learning neural networks trained to satisfy PDE and boundary conditions.
result Neural networks accurately price barrier options in a single framework.
Develops a new method for quantizing rough volatility for volatility derivatives pricing.
problem Pricing volatility derivatives in rough volatility models.
method Functional quantization of rough volatility using offline computable quantizers.
result Pricing VIX Futures in the rough Bergomi model shows competitive results.
New method speeds up option pricing for rough Bergomi model.
problem Time-consuming option pricing under rough Bergomi model.
method Hierarchical adaptive sparse grids and quasi Monte Carlo.
result Substantial computational gains over standard Monte Carlo.
Derives a rough SABR formula for short maturities.
problem Modeling volatility smiles under rough volatility.
method Derives an ODE and solves it numerically.
result Develops a very accurate approximation called the rough SABR formula.
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
Efficiently calibrates volatility models using Chebyshev Tensors.
problem Calibrating pricing models efficiently.
method Used Chebyshev Tensors to speed up calibration of the rough Bergomi volatility model.
result Chebyshev Tensors can calibrate the rough Bergomi volatility model 40,000 times more efficiently than brute-force methods.
The paper provides formulas for volatility in various models, including rough volatility.
problem Calibrating SPX and VIX options with rough volatility models.
method Developed explicit formulae using Malliavin calculus for Gaussian processes.
result New insights on joint calibration of SPX and VIX options.
We extend the model-free formula of [Fukasawa 2012] for E[Ψ(XT)], where XT=logST/F is the log-price of an asset, to functions Ψ of exponential growth. The resulting integral representation is written in terms of normalized implied volatilities. Just as Fukasawa's work provides rigourous ground for Ch…
This paper investigates multiscaling in the rough Bergomi model, finding it primarily due to fat-tailed returns.
problem Understanding multiscaling in the rough Bergomi model to improve financial modelling and risk management.
method Introducing a two-stage statistical testing procedure: first, testing for multiscaling against uniscaling; second, using shuffled surrogates to preserve return distributions.
result Multiscaling in the rough Bergomi model arises primarily from fat-tailed return distributions, not memory effects.
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.
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.
Study on implied volatility of Asian options with stochastic volatility.
problem Understanding the implied volatility of Asian options under stochastic volatility models.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for the implied volatility and skew.
result Developed short-maturity asymptotic formulas for the skew of the implied volatility, which depends on the roughness of the volatility model.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
problem Analyzing implied volatility for European and Asian options under stochastic volatility.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for implied volatility and skew.
result The paper provides a short maturity asymptotic formula for the skew of implied volatility that depends on the roughness of the volatility model.
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
Efficiently simulates and calibrates the rough Bergomi model using Wasserstein distance.
problem High computational complexity in pricing and calibration of the rough Bergomi model.
method Developed a modified-sum-of-exponentials Monte Carlo scheme and a calibration approach based on Wasserstein-1 distance.
result The method achieves high pricing accuracy and improved parameter recovery, optimization stability, and out-of-sample performance.
The paper introduces a new volatility model using Fourier techniques for pricing and hedging.
problem Pricing and hedging of financial derivatives with stochastic volatility.
method A Fourier-based approach to price and hedge European and path-dependent options in a stochastic volatility model.
result The model includes and extends popular volatility models like Stein-Stein, Bergomi, and Heston.
We revisit the ``Smile Dynamics'' problem, which consists in relating the implied leverage (i.e. the correlation of the at-the-money volatility with the returns of the underlying) and the skew of the option smile. The ratio between these two quantities, called ``Skew-Stickiness Ratio'' (SSR) by Bergomi (Smile Dynamics …
Study on implied volatility of Inverse options under stochastic volatility models.
problem Short-time behavior and skew of implied volatility for Inverse European options.
method Malliavin calculus, anticipating Itô's formula, asymptotic analysis.
result Asymptotic formula for skew of implied volatility, extending to Quanto-Inverse options.
Estimates roughness of financial volatility paths using horizontal visibility graphs.
problem Estimating roughness in financial volatility models.
method Introduces L+(t) for first-passage horizons, treating uncensored observations as first-passage times.
result Estimates roughness through a single tail exponent θ, separating rough Bergomi volatility from classical models.
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).
Proposes a neural network for calibrating stochastic volatility models.
problem Calibrating stochastic volatility models with robustness and efficiency.
method Combines grid approach with pointwise two-stage calibration, using random grids for training.
result Validates the approach with empirical and Monte Carlo experiments for rough Bergomi and Heston 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.
A new model adapts Hurst parameter in real-time for volatility forecasting.
problem Capturing volatility dynamics and clustering in financial markets.
method Rough Bergomi model with EWMA-driven time-dependent Hurst parameter.
result Empirical validation shows superior performance in diverse asset classes.
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.
New method calibrates rough stochastic volatility models quickly.
problem Calibrating rough stochastic volatility models is expensive and time-consuming.
method Combines Levenberg-Marquardt with neural networks for fast calibration.
result Neural network approximates implied volatility map efficiently.
Paper shows strong convergence rates for fractional processes using Ornstein-Uhlenbeck representations.
problem Understanding and improving Monte Carlo schemes for fractional volatility models.
method Numerical discretizations of fractional processes using Ornstein-Uhlenbeck representations.
result Strong convergence rates of arbitrarily high polynomial order for fractional processes.
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.
Efficiently calibrates Bergomi models to VIX derivatives using vector quantization.
problem Calibrating Bergomi models to VIX derivatives for accurate pricing.
method Applied vector quantization in mixed Bergomi models for fast and efficient option pricing.
result Calibration of Bergomi models to VIX derivatives is feasible and accurate over daily data.
A hybrid framework for American option pricing under time-varying rough volatility.
problem Pricing American options under time-varying rough volatility.
method Signature method combined with gradient-boosted ensemble for Hurst parameter estimation, regime switch, and Random Fourier Features for acceleration.
result The proposed hybrid framework improves performance over fixed-roughness baselines and reduces duality gaps in some regimes.
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of thre…