Related papers: Detecting Rough Volatility: A Filtering Approach
The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a…
The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
A technique for on-line estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction.…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical…
High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems…
We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
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…
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…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…
In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with…
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…
Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the…