Related papers: Roughness of the Implied Volatility
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…
We consider properties of the measurement intensity $\rho$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a…
Time scales of turbulent strain activity, denoted as the strain persistence times of first and second order, are obtained from time-dependent expectation values and correlation functions of lagrangian rate-of-strain eigenvalues taken in…
Robust estimators and different filtering techniques are proposed and their impact on the determination of a wide range of turbulence quantities is analysed. High-frequency water level measurements in a stepped spillway are used as a case…
We propose a new framework for measuring connectedness among financial variables that arises due to heterogeneous frequency responses to shocks. To estimate connectedness in short-, medium-, and long-term financial cycles, we introduce a…
In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent…
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…
We consider two kinds of stochastic volatility models. Both kinds of models contain a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We discuss discrete time models where for instance a…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
This study delves into the intricate realm of risk evaluation within the domain of specific financial derivatives, notably options. Unlike other financial instruments, like bonds, options are susceptible to broader risks. A distinctive…
In this paper the accuracy and robustness of quality measures for the assessment of machine learning models are investigated. The prediction quality of a machine learning model is evaluated model-independent based on a cross-validation…
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion of Hurst index $H \in (0,1/2)$. We obtain results on the rate of…
Recently, varextropy has been introduced as a new dispersion index and a measure of information. In this article, we derive the generating function of extropy and present its infinite series representation. Furthermore, we propose new…
To model and quantify the variability in plasticity and failure of additively manufactured metals due to imperfections in their microstructure, we have developed uncertainty quantification methodology based on pseudo marginal likelihood and…
Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for…
In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of…