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arXiv2009

World stock market: more sizeable trend reversal likely in February/March 2010

Based on our "finance-prediction-oriented" methodology which involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble" we analyze the 2009 world stock market (here represented by the SP500, Hang Seng and WIG) development. We identify elements that indicate the third decade of September 2009 as a time limit for the present bull market phase which is thus to be followed by a significant correction. In this context we also interpret the Chinese stock market index SSE. The third decade of September 2009 was accompanied with a stock market correction typically within the range of 4-5% worldwide. Taking into account the market patterns that followed the time of delivering the previous scenario we present an updated scenario whose critical time corresponds to October 28, 2009. Assuming quite evident (as of November 12, 2009) termination of the correction due to the above critical time we extend - consistently with our methodology - the stock market forecasting scenario. The corresponding expected SP500 future trend is shown in Fig. 5 and it supports a potential average continuation of increases to as far into the future as the turn of February/March 2010. We also indicate the log-periodic patterns on the gold market and they point to the end of November 2009 as the time when the trend reversal - likely local however - is expected to begin.

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arXiv2009

Hidden Noise Structure and Random Matrix Models of Stock Correlations

We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise band is composed of multiple subbands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering. We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription.

q-fin.RM↗

arXiv2010

Econophysics: Empirical facts and agent-based models

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words Economics and Physics, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modelling), econometrics of financial bubbles and crashes, etc. In the first part of the review, we discuss on the emergence of Econophysics. Then we present empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged stylized facts which describe the returns of financial assets- fat tails, volatility clustering, autocorrelation, etc.- and recall that some of these properties are directly linked to the way time is taken into account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrating this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Finally, contributions to the study of correlations of assets such as random matrix theory and graph theory are presented. In the second part of the review, we deal with models in Econophysics through the point of view of agent-based modelling. Amongst a large number of multi-agent-based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioural finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that are extensively presented here. Second, kinetic theory models designed to explain some empirical facts on wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.

q-fin.GN↗

arXiv2009

Financial bubbles analysis with a cross-sectional estimator

We highlight a very simple statistical tool for the analysis of financial bubbles, which has already been studied in [1]. We provide extensive empirical tests of this statistical tool and investigate analytically its link with stocks correlation structure.

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arXiv2009

Wavelet Based Volatility Clustering Estimation of Foreign Exchange Rates

We have presented a novel technique of detecting intermittencies in a financial time series of the foreign exchange rate data of U.S.- Euro dollar(US/EUR) using a combination of both statistical and spectral techniques. This has been possible due to Continuous Wavelet Transform (CWT) analysis which has been popularly applied to fluctuating data in various fields science and engineering and is also being tried out in finance and economics. We have been able to qualitatively identify the presence of nonlinearity and chaos in the time series of the foreign exchange rates for US/EURO (United States dollar to Euro Dollar) and US/UK (United States dollar to United Kingdom Pound) currencies. Interestingly we find that for the US-INDIA(United States dollar to Indian Rupee) foreign exchange rates, no such chaotic dynamics is observed. This could be a result of the government control over the foreign exchange rates, instead of the market controlling them.

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arXiv2009

A general "bang-bang" principle for predicting the maximum of a random walk

Let $(B_t)_{0\leq t\leq T}$ be either a Bernoulli random walk or a Brownian motion with drift, and let $M_t:=\max\{B_s: 0\leq s\leq t\}$, $0\leq t\leq T$. This paper solves the general optimal prediction problem \sup_{0\leqτ\leq T}\sE[f(M_T-B_τ)], where the supremum is over all stopping times $τ$ adapted to the natural filtration of $(B_t)$, and $f$ is a nonincreasing convex function. The optimal stopping time $τ^*$ is shown to be of "bang-bang" type: $τ^*\equiv 0$ if the drift of the underlying process $(B_t)$ is negative, and $τ^*\equiv T$ is the drift is positive. This result generalizes recent findings by S. Yam, S. Yung and W. Zhou [{\em J. Appl. Probab.} {\bf 46} (2009), 651--668] and J. Du Toit and G. Peskir [{\em Ann. Appl. Probab.} {\bf 19} (2009), 983--1014], and provides additional mathematical justification for the dictum in finance that one should sell bad stocks immediately, but keep good ones as long as possible.

math.PR↗

arXiv2009

Financial Applications of Random Matrix Theory: a short review

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum and its various generalisations, random SVD, free matrices, largest eigenvalue statistics, etc.) as well as some concrete applications to portfolio optimisation and out-of-sample risk estimation.

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arXiv2009

Multifractal analysis and instability index of prior-to-crash market situations

We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates. These spectra have properties that typify the prior-to-crash market situation. Any of these spectra entail elaborate processing of the raw signal data. With the unprocessed raw data we obtain an instability index, also with properties that typify the prior-to-crisis market situation. Both spectra and the instability index agree in characterizing such crashes, and in giving an early warning of them.

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arXiv2009

Nonparametric methods for volatility density estimation

Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuous time processes and discrete time models will be discussed. The key insight for the analysis is a transformation of the volatility density estimation problem to a deconvolution model for which standard methods exist. Three type of nonparametric density estimators are reviewed: the Fourier-type deconvolution kernel density estimator, a wavelet deconvolution density estimator and a penalized projection estimator. The performance of these estimators will be compared. Key words: stochastic volatility models, deconvolution, density estimation, kernel estimator, wavelets, minimum contrast estimation, mixing

stat.ME↗

arXiv2010

The Financial Bubble Experiment: advanced diagnostics and forecasts of bubble terminations

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.

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arXiv2009

Empirical asset pricing with nonlinear risk premia

In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our framework guarantees existence of weak solutions of the nonlinear SDEs under the physical measure, thus allowing to work with nonlinear models for the real world dynamics not considered in the literature so far. It emerges that the additional flexibility in the time series modelling is econometrically relevant: a nonlinear stochastic volatility diffusion model for the joint time series of the S&P 100 and the VXO implied volatility index data shows superior forecasting power over the standard specifications for implied and realized variance forecasting.

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arXiv2009

Sign and amplitude representation of the forex networks

We decompose the exchange rates returns of 41 currencies (incl. gold) into their sign and amplitude components. Then we group together all exchange rates with a common base currency, construct Minimal Spanning Trees for each group independently, and analyze properties of these trees. We show that both the sign and the amplitude time series have similar correlation properties as far as the core network structure is concerned. There exist however interesting peripheral differences that may open a new perspective to view the Forex dynamics.

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arXiv2009

The StressVaR: A New Risk Concept for Superior Fund Allocation

In this paper we introduce a novel approach to risk estimation based on nonlinear factor models - the "StressVaR" (SVaR). Developed to evaluate the risk of hedge funds, the SVaR appears to be applicable to a wide range of investments. Its principle is to use the fairly short and sparse history of the hedge fund returns to identify relevant risk factors among a very broad set of possible risk sources. This risk profile is obtained by calibrating a collection of nonlinear single-factor models as opposed to a single multi-factor model. We then use the risk profile and the very long and rich history of the factors to asses the possible impact of known past crises on the funds, unveiling their hidden risks and so called "black swans". In backtests using data of 1060 hedge funds we demonstrate that the SVaR has better or comparable properties than several common VaR measures - shows less VaR exceptions and, perhaps even more importantly, in case of an exception, by smaller amounts. The ultimate test of the StressVaR however, is in its usage as a fund allocating tool. By simulating a realistic investment in a portfolio of hedge funds, we show that the portfolio constructed using the StressVaR on average outperforms both the market and the portfolios constructed using common VaR measures. For the period from Feb. 2003 to June 2009, the StressVaR constructed portfolio outperforms the market by about 6% annually, and on average the competing VaR measures by around 3%. The performance numbers from Aug. 2007 to June 2009 are even more impressive. The SVaR portfolio outperforms the market by 20%, and the best competing measure by 4%.

q-fin.RM↗

arXiv2009

Statistical Regularities of Equity Market Activity

Equity activity is an essential topic for financial market studies. To explore its statistical regularities, we comprehensively examine the trading value, a measure of the equity activity, of the 3314 most-traded stocks in the U.S. equity market and find that (i) the trading values follow a log-normal distribution; (ii) the standard deviation of the growth rate of the trading value obeys a power-law with the initial trading value, and the power-law exponent beta=0.14. Remarkably, both features hold for a wide range of sampling intervals, from 5 minutes to 20 trading days. Further, we show that all the 3314 stocks have long-term correlations, and their Hurst exponents H follow a normal distribution. Furthermore, we find that the Hurst exponent depends on the size of the company. We also show that the relation between the scaling in the growth rate and the long-term correlation is consistent with beta=1-H, similar to that found recently on human interaction activity by Rybski and collaborators.

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arXiv2009

Gain/loss asymmetry in time series of individual stock prices and its relationship to the leverage effect

Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We establish that this so-called gain/loss asymmetry is present also for individual stocks and show that the phenomenon is closely linked to the well-known leverage effect -- in the EGARCH model and a modified retarded volatility model, the same parameter that governs the magnitude of the leverage effect also governs the gain/loss asymmetry.

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arXiv2011

Causal Links Between US Economic Sectors

In this paper, we perform a comparative segmentation and clustering analysis of the time series for the ten Dow Jones US economic sector indices between 14 February 2000 and 31 August 2008. From the temporal distributions of clustered segments, we find that the US economy took one and a half years to recover from the mid-1998-to-mid-2003 financial crisis, but only two months to completely enter the present financial crisis. We also find the oil & gas and basic materials sectors leading the recovery from the previous financial crisis, while the consumer goods and utilities sectors led the descent into the present financial crisis. On a macroscopic level, we find sectors going earlier into a crisis emerge later from it, whereas sectors going later into the crisis emerge earlier. On the mesoscopic level, we find leading sectors experiencing stronger and longer volatility shocks, while trailing sectors experience weaker and shorter volatility shocks. In our shock-by-shock causal-link analysis, we also find shorter delays between corresponding shocks in more closely related economic sectors. In addition, our analysis reveals evidences for complex sectorial structures, as well as nonlinear amplification in the propagating volatility shocks. From a perspective relevant to public policy, our study suggests an endogeneous sectorial dynamics during the mid-2003 economic recovery, in contrast to strong exogeneous driving by Federal Reserve interest rate cuts during the mid-2007 onset. Most interestingly, we find for the sequence of closely spaced interest rate cuts instituted in 2007/2008, the first few cuts effectively lowered market volatilities, while the next few cuts counter-effectively increased market volatilities. Subsequent cuts evoked little response from the market.

q-fin.GN↗

arXiv2009

Resilience of Volatility

The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is suggested of the emergence of significant serial autocorrelations in volatility and squared returns. It is shown that when non-stationarity is eliminated, the autocorrelations substantially reduce and become statistically insignificant. The causes of non-Gaussian nature of the probability of returns distribution are considered. For both stock and currency markets data samples, it is shown that removing the non-stationary component substantially reduces the kurtosis of distribution, bringing it closer to the Gaussian one. A statistical criterion is proposed for controlling the degree of smoothing of the empirical values of volatility. The hypothesis of smooth, non-stochastic nature of volatility is put forward, and possible causes of volatility shifts are discussed.

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arXiv2009

Homogeneous Volatility Bridge Estimators

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process, and in its close value, for a given time interval. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass and Parkinson estimators.

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