In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The regular set of measures play fundamental role for the description of incomplete markets. In the partial case, the description of the regular set of measures is presented. The notion of completeness of the regular set of measures have the important significance for the simplification of the proof of the optional decomposition for super-martingales. Using this notion, the important inequalities for some random values are obtained. These inequalities give the simple proof of the optional decomposition of the majorized super-martingales. The description of all local regular super-martingales relative to the regular set of measures is presented. It is proved that every majorized super-martingale relative to the complete set of measures is a local regular one. In the case, as evolution of a risk asset is given by the discrete geometric Brownian motion, the financial market is incomplete and a new formula for the fair price of super-hedge is founded.
Identifying meaningful relationships between the price movements of financial assets is a challenging but important problem in a variety of financial applications. However with recent research, particularly those using machine learning and deep learning techniques, focused mostly on price forecasting, the literature investigating the modelling of asset correlations has lagged somewhat. To address this, inspired by recent successes in natural language processing, we propose a neural model for training stock embeddings, which harnesses the dynamics of historical returns data in order to learn th…
An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually directly related to the degree of clustering of large fluctuations within the financial time series. We also introduce an index to quantitatively measure the clustering behaviour of fluctuations in these time series and show that big losses in financial markets usually lump more severely than big gains. We further give examples to demonstrate that comparing to conv…
We characterize the collective phenomena of a liquid market. By interpreting the behavior of a no-arbitrage N asset market in terms of a particle system scenario, (thermo)dynamical-like properties can be extracted from the asset kinetics. In this scheme the mechanisms of the particle interaction can be widely investigated. We test the verisimilitude of our construction on two-decade stock market daily data (DAX30) and show the result obtained for the interaction potential among asset pairs.
We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return - entropy system. For empirical in…
The Chinese University of Hong Kong（香港中文大学）；Tencent AI Lab（腾讯人工智能实验室）；City University of Hong Kong（香港城市大学）
We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time series. It combines the merits of a popular sequential neural network model, i.e., LSTM, with a novel parametric quantile function that we construct to represent the conditional distribution of asset returns. Our model also captures individually the serial dependences of higher moments, rather than just the volatility. Across a wide range of asset classes, t…
The collective phenomena of a liquid market is characterized in terms of a particle system scenario. This physical analogy enables us to disentangle intrinsic features from purely stochastic ones. The latter are the result of environmental changes due to a `heat bath' acting on the many-asset system, quantitatively described in terms of a time dependent effective temperature. The remaining intrinsic properties can be widely investigated by applying standard methods of classical many body systems. As an example, we consider a large set of stocks traded at the NYSE and determine the correspondin…
University of Oxford（牛津大学）；Saïd Business School（赛德商学院）
This research paper explores the performance of Machine Learning (ML) algorithms and techniques that can be used for financial asset price forecasting. The prediction and forecasting of asset prices and returns remains one of the most challenging and exciting problems for quantitative finance and practitioners alike. The massive increase in data generated and captured in recent years presents an opportunity to leverage Machine Learning algorithms. This study directly compares and contrasts state-of-the-art implementations of modern Machine Learning algorithms on high performance computing (HPC…
The bubble is a controversial and important issue. Many methods which based on the rational expectation have been proposed to detect the bubble. However, for some developing countries, epically China, the asset markets are so young that for many companies, there are no dividends and fundamental value, making it difficult (if not impossible) to measure the bubbles by existing methods. Therefore, we proposed a simple but effective statistical method and three statistics (that is, C, U, V) to capture and quantify asset price bubbles, especially in immature emerging markets. To present a clear exa…
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic vari…
On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experiment, we add a diagnostic of a new bubble developing on a fourth asset.
This is the third installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 27 bubbles in 27 different global assets; for 25 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that document of the original analysis on 2 May 2011.
Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as …
This is the second installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 7 bubbles in 7 different global assets; for 4 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that document of the original analysis on 1 November 2010.
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We then characterize the time-evolving relationships between the different assets by investigating the correlations b…
University for Continuing Education Krems（克雷姆斯继续教育大学）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；King’s College London（伦敦国王学院）；Centro Ricerche Enrico Fermi（恩里科·费米研究中心）
This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets' dependencies, especially correlational studies, which in our opinion are beneficial for researchers in both fields. In econophysics, these dependencies can be modeled to describe financial markets as evolving complex networks. In particular we show that a useful way to describe dependencies is by means of information filtering networks that are able to retrieve relevant and meaningful …
Bitcoin is a digital financial asset that is devoid of a central authority. This makes it distinct from traditional financial assets in a number of ways. For instance, the total number of tokens is limited and it has not explicit use value. Nonetheless, little is know whether it obeys the same stylized facts found in traditional financial assets. Here we test bitcoin for a set of these stylized facts and conclude that it behaves statistically as most of other assets. For instance, it exhibits aggregational Gaussianity and fluctuation scaling. Moreover, we show by an analogy with natural occurr…
Firm financials are well established as return predictors, being the inspiration for a large set of anomalies in the asset pricing literature. Employing topological data analysis we revisit the question of association between seven of the most commonly studied financial ratios and stock returns. Specifically the TDA Ball Mapper algorithm is applied to visualise the point cloud of financial ratios as an abstract two-dimensional graph readily allowing for identification of interdependencies between factors. These relationships are seldom monotonic, opportunities for investors to profitably explo…
We test for departures from normal and independent and identically distributed (NIID) returns, when returns under the alternative hypothesis are self-affine. Self-affine returns are either fractionally integrated and long-range dependent, or drawn randomly from an L-stable distribution with infinite higher-order moments. The finite sample performance of estimators of the two forms of self-affinity is explored in a simulation study which demonstrates that, unlike rescaled range analysis and other conventional estimation methods, the variant of fluctuation analysis that considers finite sample m…
Traditional machine learning methods have been widely studied in financial innovation. My study focuses on the application of deep learning methods on asset pricing. I investigate various deep learning methods for asset pricing, especially for risk premia measurement. All models take the same set of predictive signals (firm characteristics, systematic risks and macroeconomics). I demonstrate high performance of all kinds of state-of-the-art (SOTA) deep learning methods, and figure out that RNNs with memory mechanism and attention have the best performance in terms of predictivity. Furthermore,…
We demonstrate that future market correlation structure can be predicted with high out-of-sample accuracy using a multiplex network approach that combines information from social media and financial data. Market structure is measured by quantifying the co-movement of asset prices returns, while social structure is measured as the co-movement of social media opinion on those same assets. Predictions are obtained with a simple model that uses link persistence and link formation by triadic closure across both financial and social media layers. Results demonstrate that the proposed model can predi…
In the existing financial literature, entropy based ideas have been proposed in portfolio optimization, in model calibration for options pricing as well as in ascertaining a pricing measure in incomplete markets. The abstracted problem corresponds to finding a probability measure that minimizes the relative entropy (also called $I$-divergence) with respect to a known measure while it satisfies certain moment constraints on functions of underlying assets. In this paper, we show that under $I$-divergence, the optimal solution may not exist when the underlying assets have fat tailed distributions…
The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low frequency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited predictive power in this phenomenological approach and present a stochastic model, based on the scaling symmetry of financial a…
There is more and more empirical evidence that multifractality constitutes another and perhaps the most significant financial stylized fact. A realistic model of the financial dynamics should therefore incorporate this effect. The most promising in this respect is the Multifractal Model of Asset Returns (MMAR) introduced by Mandelbrot in which multifractality is carried by time deformation. In our study we focus on the Lux extension to MMAR and empirical data from Warsaw Stock Exchange. We show that this model is able to reproduce relevant aspects of the real stock market dynamics.
We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution available. Consistency of the proposed estimators is shown under the continuous-time framework that has been developed in our previous work Hayashi and Koike (2018). An empirical application to a quote dataset of the NASDAQ-100 assets identifies two types of lead-lag relationships at …
We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affected by investment based on it. We show that such a feedback on correlations gives rise to an instability when the volume of investment exceeds a critical value. Close to the critical point the model exhibits dynamical correlations very similar to those observed in real markets. …
By monitoring the time evolution of the most liquid Futures contracts traded globally as acquired using the Bloomberg API from 03 January 2000 until 15 December 2014 we were able to forecast the S&P 500 index beating the Buy and Hold trading strategy. Our approach is based on convolution computations of 42 of the most liquid Futures contracts of four basic financial asset classes, namely, equities, bonds, commodities and foreign exchange. These key assets were selected on the basis of the global GDP ranking across countries worldwide according to the lists published by the International Moneta…
This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in …
William & Mary（威廉玛丽学院）；Purdue University（普渡大学）；University of Bath（巴斯大学）；The Alan Turing Institute（阿兰·图灵研究所）；University of Oxford（牛津大学）
Pricing assets has attracted significant attention from the financial technology community. We observe that the existing solutions overlook the cross-sectional effects and not fully leveraged the heterogeneous data sets, leading to sub-optimal performance. To this end, we propose an end-to-end deep learning framework to price the assets. Our framework possesses two main properties: 1) We propose Equity2Vec, a graph-based component that effectively captures both long-term and evolving cross-sectional interactions. 2) The framework simultaneously leverages all the available heterogeneous alpha s…
Reduced-order autoregressive dynamics of a complex financial system: a PCA-based approach
Department of Physics, K. N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran（物理学系，K.N.Toosi技术大学）；Department of Physics, Tehran University, Tehran, Iran（物理学系，德黑兰大学）
The Hong Kong University of Science and Technology（香港科技大学）
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of practitioners' toolboxes. In this paper, we investigate the fundamental problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market times series data. In particular, we present natural justifications, supported by empirical evidence, for the usage of the Laplacian matrix as a model for the p…
MarketGANs: Multivariate financial time-series data augmentation using generative adversarial networks
Department of Mathematics, Sungkyunkwan University, Republic of Korea（淑阳大学数学系）；Department of Financial Engineering, Ajou University, Republic of Korea（东亚大学金融工程系）；Department of FinTech, SKK Business School, Sungkyunkwan University, Republic of Korea（淑阳大学SKK商学院金融科技系）
