相关论文: From constant to rough: A survey of continuous vol…

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…

The quadratic rough Heston model provides a natural way to encode Zumbach effect in the rough volatility paradigm. We apply multi-factor approximation and use deep learning methods to build an efficient calibration procedure for this model.…

In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the…

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried…

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of…

The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…

Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst…

The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential-affine transform formulas.

We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…

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…

The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…

Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data.…

We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with…

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities…

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to…

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily…

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…

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…

Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among…

The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the…