Related papers: Volatility estimation from a view point of entropy
Properties of mixed fractional Brownian motion has been discussed by Cheridito (2001) and Zili (2006). We have proposed an estimator of volatility parameter for a model driven by MFBM. In our article we have shown that the estimator has…
Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
The principal aim of this Comment is to correct those entropic uncertainty relations that are presented in a paper by Massar [arXiv:quant-ph/0703036v2 (current version)], concerning two approaches to a study of the noise produced by POVM's.…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
Realization of uncertainty of prices is captured by volatility, that is the tendency of prices to vary along a period of time. This is generally measured as standard deviation of daily returns. In this paper we propose and investigate the…
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet…
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…
This paper presents the Fourier-Malliavin Volatility (FMVol) estimation library for MATLAB. This library includes functions that implement Fourier- Malliavin estimators (see Malliavin and Mancino (2002, 2009)) of the volatility and…
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…
We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an It\^o semimartingale with jumps and general…
The Cartier-Perrin theorem, which was published in 1995 and is expressed in the language of nonstandard analysis, permits, for the first time perhaps, a clear-cut mathematical definition of the volatility of a financial asset. It yields as…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…
This paper proposes a new pathwise sensitivity estimator for chaotic SDEs. By introducing a spring term between the original and perturbated SDEs, we derive a new estimator by importance sampling. The variance of the new estimator increases…
In an era when derivatives is getting popular, risk management has gradually become the core content of modern finance. In order to study how to accurately estimate the volatility of the S&P 500 index, after introducing the theoretical…
We introduce a new model of financial market with stochastic volatility driven by an arbitrary H\"older continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the…
In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all…
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…
We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete…