Related papers: Volatility made observable at last
Beta-sorted portfolios -- portfolios comprised of assets with similar covariation to selected risk factors -- are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little…
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…
Crashes have fascinated and baffled many canny observers of financial markets. In the strict orthodoxy of the efficient market theory, crashes must be due to sudden changes of the fundamental valuation of assets. However, detailed empirical…
Financial markets across all asset classes are known to exhibit trends. These trends have been exploited by traders for decades. Here, we empirically measure when trends revert, based on 30 years of daily futures prices for equity indices,…
Better representation of the uncertainty in a data visualisation is a focus of recent research activity. A problem with the current literature is that there is a lack of clarity about the definition of uncertainty and what it means to…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…
This paper conducts an extensive analysis of Bitcoin return series, with a primary focus on three volatility metrics: historical volatility (calculated as the sample standard deviation), forecasted volatility (derived from GARCH-type…
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…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
Time-varying volatility is an inherent feature of most economic time-series, which causes standard correlation estimators to be inconsistent. The quadrant correlation estimator is consistent but very inefficient. We propose a novel…
Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…
Recent research has documented a significant rise in the volatility (e.g., expected squared change) of individual incomes in the U.S. since the 1970s. Existing measures of this trend abstract from individual heterogeneity, effectively…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
Fluctuation theorems show how coarse graining transforms microscopic symmetry into observable irreversibility. Here we ask whether an analogous symmetrybased diagnostic can be constructed for financial markets. At the microscopic level,…
Upon employing a natural time window of fixed length sliding through a time series, an explicit interrelation between the variability $\beta$ of the variance $\kappa_1$($=< \chi^2 > - < \chi >^2$) of natural time $\chi$ and events'…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…
A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…