Investigates Merton's portfolio problem in a rough stochastic environment with Volterra Heston model.
problem Optimizing investment strategies in a non-Markovian, non-semimartingale stochastic environment.
method Solves the portfolio optimization problem using the martingale optimality principle and auxiliary random process.
result Derives semi-closed form solutions for optimal strategies under power and exponential utilities.
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.
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.
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.
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. Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.
problem Merton's portfolio optimization in a fake stationary Volterra-Heston model.
method Stochastic factor solution to a Riccati BSDE, combined with martingale optimality principle.
result Derives semi-closed form optimal strategies and value function.
Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price volatility: both fast-time scale on the order of days and slow-scale on the order of…
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.
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.
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-M…
Robots learn to navigate rough terrain using reinforcement learning.
problem Generalizing robot behavior to new, unseen rough terrains.
method PPMC RL Training Algorithm
result Robots achieve 100% success rate in learning new rough terrain maps.
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.
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.
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.
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. 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 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.
Framework for training stochastic spiking neural networks with rough signals.
problem Training stochastic spiking neural networks with noisy spike timing and dynamics.
method Rough path theory and signature kernels for gradient computation.
result Pathwise gradients of SSNNs' trajectories and event times exist and satisfy a recursive relation.
Unified approach to stochastic control, filtering, and stopping using rough paths.
problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.
Universal approximation for stochastic processes using Brownian motion.
problem Approximating stochastic processes with linear functionals.
method Establishing Lp-type universal approximation theorems for rough path spaces. result Linear functionals on the signature of time-extended Brownian motion can approximate any p-integrable stochastic process. 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.
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.
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.
Investigates optimal investment strategies in financial markets with jumps.
problem Optimal portfolio selection for investors in multi-asset financial markets with jumps.
method Uses martingale optimality principle and Riccati backward stochastic differential equations with jumps.
result Derives semi-closed form optimal strategies and value function for Merton's problem.
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 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.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
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…
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.
Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
Paper explores rough path theory for frictionless markets, linking NCFL to unbiased rough integrators.
problem Tackles the limits of rough path theory in frictionless markets.
method Investigates the capacity of rough path theory to support No Free Lunch markets.
result Establishes a 'Rough Kreps-Yan' theorem linking NCFL to unbiased rough integrators.
A new neural network model simulates financial markets without assuming underlying dynamics.
problem Modeling financial time series without assuming underlying dynamics.
method Neural network based generative model using a parsimonious Variational Autoencoder framework.
result Works reliably in small data environments, providing a new performance evaluation metric.
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.
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.
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).
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.
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.
Efficient simulation scheme for rough Heston model reduces computational cost.
problem Accurate and efficient simulation of the rough Heston model for option pricing.
method Weak simulation scheme based on Markovian approximations of the rough Heston process.
result The new scheme exhibits second order weak convergence with linear computational cost.
Foundation for robust finance using rough path theory.
problem Mathematical models of financial markets under Knightian uncertainty.
method Introducing Property (RIE) for càdlàg paths, proving existence of rough integrals, verifying admissibility of trading strategies.
result Existence and stability of rough path integrals for non-gradient integrands.
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.
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.
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.
Estimates roughness of stochastic processes without assuming specific models.
problem Estimating roughness of stochastic processes without assuming specific models.
method Using Faber-Schauder coefficients and martingales, we provide a method to estimate the roughness exponent of stochastic processes.
result The roughness exponent can be estimated without assuming specific models, providing a strong consistency result for the Gladyshev estimators.
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.
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.
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.
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.