A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper studies bundles over surfaces and constructs invariants.
4D theorem for disks, generalizing previous work.
The paper studies mapping class groups of nontrivial fiber bundles.
New smoothing techniques for topological surfaces in 4-manifolds.
New method for classifying disk embeddings in 4-manifolds.
In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-…
The paper solves isotopy problems on 4-manifolds and classifies symplectic structures.
The level crossing and inverse statistics analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, , where is the average waiting time for observing the level again. We estimate the probability , which provides us the probab…
We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index…
Computes homotopy groups of embedding spaces of arcs or circles in 4-manifolds.
Effects connected with the world globalization affect also the financial markets. On a way towards quantifying the related characteristics we study the financial empirical correlation matrix of the 60 companies which both the Deutsche Aktienindex (DAX) and the Dow Jones (DJ) industrial average comprised during the year…
The probability distribution of log-returns for financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of time series on futures. We show that the t-distribution with gives a ni…
New method allows backtesting of systemic risk forecasts.
This paper contributes to the literature on international stock market comovements and contagion. The novelty of our approach lies in application of wavelet tools to high-frequency financial market data, which allows us to understand the relationship between stock markets in a time-frequency domain. While major part of…
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the …
A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intradaily structures in the financial time-series. The present study is based on the high-frequency Deutsche Aktie…
We analyze the financial crash in 2008 for different financial markets from the point of view of log-periodic function model. In particular, we consider Dow Jones index, DAX index and Hang Seng index. We shortly discuss the possible relation of the theory of critical phenomena in physics to financial markets.
This case study tests the possibility of prediction for "success" (or "winner") components of four stock & shares market indices in a time period of three years from 02-Jul-2009 to 29-Jun-2012.We compare their performance ain two time frames: initial frame three months at the beginning (02/06/2009-30/09/2009) and the f…
We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma pr…
We have applied the Zipf method to extract the exponent for seven financial indices (DAX, FTSE; DJIA, NASDAQ, S&P500; Hang-Seng and Nikkei 225), after having translated the signals into a text based on two letters. We follow considerations based on the signal Hurst exponent and the notion of a time dependent Zipf …
A brief historical perspective is first given concerning financial crashes, - from the 17th till the 20th century. In modern times, it seems that log periodic oscillations are found before crashes in several financial indices. The same is found in sand pile avalanches on Sierpinski gaskets. A discussion pertains to the…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index (), the Renyi exponents based on the box counting algorithm for the graph () and the generalized Hurst ex…
In this paper we study automatically recognized trends and investigate their statistics. To do that we introduce the notion of a wavelength for time series via cross correlation and use this wavelength to calibrate the 1-2-3 trend indicator of Maier-Paape [Automatic One Two Three, Quantitative Finance, 2013] to automat…
lCARE improves EVaR model for time-varying tail risk by localizing parameters.
In Biology, all motor enzymes operate on the same principle: they trap favourable brownian fluctuations in order to generate directed forces and to move. Whether it is possible or not to copy one such strategy to play the market was the starting point of our investigations. We found the answer is yes. In this paper we …
Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price velocity and price acceleration, we construct a general classification of the possible patterns characterizing the deviation or defects from the random walk market state and its time-translationa…
We review a cochain-free treatment of the classical van Kampen obstruction θto embeddability of an n-polyhedron into R^{2n} and consider several analogues and generalizations of θ, including an extraordinary lift of θwhich in the manifold case has been studied by J.-P. Dax. The following results are obtained. - The mod…
We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index alpha > 3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on high-frequency recordings of …
We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide stable solutions. The heuristic solutions are compared to optimization results o…
Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice…
In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentu…
The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales.…
In this paper we explore the specific role of randomness in financial markets, inspired by the beneficial role of noise in many physical systems and in previous applications to complex socio- economic systems. After a short introduction, we study the performance of some of the most used trading strategies in predicting…
We compare correlations and coherent structures in nuclei and financial markets. In the nuclear physics part we review giant resonances which can be interpreted as a coherent structure embedded in chaos. With similar methods we investigate the financial empirical correlation matrix of the DAX and Dow Jones. We will sho…
Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the draw d…
With the daily and minutely data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. Based on a retarded volatility model, we may eliminate or generate the return-volatility correlation of the time series, while other characteristics, such as the…
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents usually vary with the strength of the large vo…
The Heston model optimizes portfolio management based on real market data.
We develop a method that relates the truncated cumulant-function of the fourth order with the Lévian cumulant-function. This gives us explicit formulas for the Lévy-parameters, which allow a real-time analysis of the state of a random-motion. Cumbersome procedures like maximum-likelihood or least-square methods are unn…
We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents usually vary with the strength of the lar…
This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that r…
Complete obstruction found for 2-spheres in 5-manifolds to be isotopic.
This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures …
From the stock markets of six countries with high GDP, we study the stock indices, S&P 500 (NYSE, USA), SSE Composite (SSE, China), Nikkei (TSE, Japan), DAX (FSE, Germany), FTSE 100 (LSE, Britain) and NIFTY (NSE, India). The daily mean growth of the stock values is exponential. The daily price fluctuations about the me…
We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for th…
In this work we introduce two variants of multivariate Hawkes models with an explicit dependency on various queue sizes aimed at modeling the stochastic time evolution of a limit order book. The models we propose thus integrate the influence of both the current book state and the past order flow. The first variant cons…
Study reveals 2020 stock crashes were mostly endogenous, not exogenous.
Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models. Based on finite sample variances, confidence inte…