A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Volatility roughness studied using fractional noise-driven models.
Approximates derivative pricing under fractional stochastic volatility.
Study large deviations in fractional volatility models with non-Gaussian 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…
The paper models cryptocurrency price and volatility with jumps and fractional volatility.
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
Study confirms rough volatility in financial data, independent of microstructure noise.
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 finds roughness in volatility despite diffusive instantaneous volatility.
Study provides LDP for non self-similar stochastic volatility models.
Survey of continuous volatility models, focusing on fractional and rough methods.
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…
New rough stochastic volatility models using log-modulated fractional Brownian motion.
Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are discussed and, using agent-based models, one tr…
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close to that of a fractional Brownian motion with Hurst parameter around 0.1. Motivated by this, we wish to define a natural and re…
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 …
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Br…
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…
The paper introduces a new method to detect rough volatility and market states using fractional derivatives.
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 …
This paper extends Heston model to fractional Brownian motion for option pricing.
Study tests rough fractional volatility model across different time scales, revealing new volatility patterns.
Study models market volatility with persistent and temporary impacts.
The paper introduces a new stochastic volatility model with long-term memory and jumps.
Method predicts LFSM increments from past observations using codifference.
Modeling joint log-volatility dynamics with multivariate fractional Ornstein-Uhlenbeck process.
We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula by Ito's calculus yields a theoretical replicating strategy for the target volatility option, assuming the accessibilities of all variance swaps and swaptions. The same formula also sugges…
Formula for option pricing in a stochastic volatility model with jumps.
Study rough volatility models using path-dependent PDEs and fractional Brownian motions.
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 …
Study on CVA in volatility models, including rough volatility.
This paper revisits the fractional cointegrating relationship between ex-ante implied volatility and ex-post realized volatility. We argue that the concept of corridor implied volatility (CIV) should be used instead of the popular model-free option-implied volatility (MFIV) when assessing the fractional cointegrating r…
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…
Estimates roughness of volatility from discrete variance data.
Study shows how certain stochastic models reach a steady state over time.
Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.
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…
Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.
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…
Improved volatility models for option pricing with weak error rates.
Paper develops a new estimator for rough volatility parameters.
Study approximates rough stochastic volatility models using diffusion processes.
Paper tackles rough volatility estimation from high-frequency data.
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…
mfBm models and forecasts volatility with different Hurst exponents and correlations.
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show i…
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
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 between the driving Brownian motions of the …