arXiv research

Approximates derivative pricing under fractional stochastic volatility.

Study large deviations in fractional volatility models with non-Gaussian volatility.

The paper models cryptocurrency price and volatility with jumps and fractional volatility.

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…

Study provides LDP for non self-similar stochastic volatility models.

New rough stochastic volatility models using log-modulated fractional Brownian motion.

Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

Study approximates rough stochastic volatility models using diffusion processes.

Study shows how certain stochastic models reach a steady state over time.

Study finds roughness in volatility despite diffusive instantaneous volatility.

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

Study confirms rough volatility in financial data, independent of microstructure noise.

Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.

Formula for option pricing in a stochastic volatility model with jumps.

Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

Survey of continuous volatility models, focusing on fractional and rough methods.

This paper extends Heston model to fractional Brownian motion for option pricing.

The paper introduces a new stochastic volatility model with long-term memory and jumps.

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …

We consider the fractional Heston model originally proposed by Comte, Coutin and Renault. Inspired by recent ground-breaking work on rough volatility, which showed that models with volatility driven by fractional Brownian motion with short memory allows for better calibration of the volatility surface and more robust e…

Paper approximates rough stochastic local volatility models for efficient computation.

Estimates roughness of volatility from discrete variance data.

Study rough volatility models using path-dependent PDEs and fractional Brownian motions.

Develops a GMM method to estimate roughness in stochastic volatility models.

Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal paper titled "Volatility is rough" was posted on SSRN in 2014 showing that the log…

Paper tackles rough volatility estimation from high-frequency data.

In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift and fractional diffusion. Since the DO process is a semi-martingale,…

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

Study improves weak error estimates for rough volatility models.

Study on CVA in volatility models, including rough volatility.

Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.

Researchers derive an analytic expression for Gaussian stochastic volatility models.

Study models market volatility with persistent and temporary impacts.

We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part, followed by a reasonable approximation we show that it is possible to cast the proble…

We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale if and only if the correlation $ρ$ between the driving Brownian motions of the …

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…

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes pric…

Volatility roughness studied using fractional noise-driven models.

Paper develops a new estimator for rough volatility parameters.

Proposes a new metric for financial risk based on volatility's local deviations.

The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot…

Modeling joint log-volatility dynamics with multivariate fractional Ornstein-Uhlenbeck process.

Large deviation principles for multivariate stochastic volatility models.

The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.

Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider Europ…