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arXiv2011

Financial Risks and the Pension Protection Fund: Can it Survive Them?

This paper discusses the financial risks faced by the UK Pension Protection Fund (PPF) and what, if anything, it can do about them. It draws lessons from the regulatory regimes under which other financial institutions, such as banks and insurance companies, operate and asks why pension funds are treated differently. It also reviews the experience with other government-sponsored insurance schemes, such as the US Pension Benefit Guaranty Corporation, upon which the PPF is modelled. We conclude that the PPF will live under the permanent risk of insolvency as a consequence of the moral hazard, adverse selection, and, especially, systemic risks that it faces.

q-fin.RM↗

arXiv2011

A sharp analysis on the asymptotic behavior of the Durbin-Watson statistic for the first-order autoregressive process

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated to the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. It allows us to establish the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic. Finally, we propose a new bilateral statistical test for residual autocorrelation.

math.ST↗

arXiv2011

Density Approximations for Multivariate Affine Jump-Diffusion Processes

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in credit risk, likelihood inference, and option pricing highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

math.ST↗

arXiv2011

State-Observation Sampling and the Econometrics of Learning Models

In nonlinear state-space models, sequential learning about the hidden state can proceed by particle filtering when the density of the observation conditional on the state is available analytically (e.g. Gordon et al., 1993). This condition need not hold in complex environments, such as the incomplete-information equilibrium models considered in financial economics. In this paper, we make two contributions to the learning literature. First, we introduce a new filtering method, the state-observation sampling (SOS) filter, for general state-space models with intractable observation densities. Second, we develop an indirect inference-based estimator for a large class of incomplete-information economies. We demonstrate the good performance of these techniques on an asset pricing model with investor learning applied to over 80 years of daily equity returns.

stat.ME↗

arXiv2011

Stochastic Price Dynamics Implied By the Limit Order Book

In this paper we present a novel approach to the determination of fat tails in financial data by studying the information contained in the limit order book. In an order-driven market buyers and sellers may submit limit orders, which are executed when the price touches a pre-specified lower, respectively higher, limit-price. We show that, in equilibrium, the collection of all such orders - the limit order book - implies a volatility smile, similar to observations from option pricing in the Black-Scholes model. We also show how a jump-diffusion process can be explicitly inferred to account for the volatility smile.

q-fin.TR↗

arXiv2011

Is there a bubble in LinkedIn's stock price?

Recent academic work has developed a method to determine, in real time, if a given stock is exhibiting a price bubble. Currently there is speculation in the financial press concerning the existence of a price bubble in the aftermath of the recent IPO of LinkedIn. We analyze stock price tick data from the short lifetime of this stock through May 24, 2011, and we find that LinkedIn has a price bubble.

q-fin.RM↗

arXiv2011

Calibration and filtering for multi factor commodity models with seasonality: incorporating panel data from futures contracts

We examine a general multi-factor model for commodity spot prices and futures valuation. We extend the multi-factor long-short model in Schwartz and Smith (2000) and Yan (2002) in two important aspects: firstly we allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volatility factors and secondly we develop an additive structural seasonality model. Then a Milstein discretized non-linear stochastic volatility state space representation for the model is developed which allows for futures and options contracts in the observation equation. We then develop numerical methodology based on an advanced Sequential Monte Carlo algorithm utilising Particle Markov chain Monte Carlo to perform calibration of the model jointly with the filtering of the latent processes for the long-short dynamics and volatility factors. In this regard we explore and develop a novel methodology based on an adaptive Rao-Blackwellised version of the Particle Markov chain Monte Carlo methodology. In doing this we deal accurately with the non-linearities in the state-space model which are therefore introduced into the filtering framework. We perform analysis on synthetic and real data for oil commodities.

q-fin.CP↗

arXiv2011

Large Vector Auto Regressions

One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an \textit{integrated} solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an \textit{oracle} under such scenarios. The tuning parameters are chosen via a data driven "rolling scheme" method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators.

stat.ML↗

arXiv2011

Dynamic Large Spatial Covariance Matrix Estimation in Application to Semiparametric Model Construction via Variable Clustering: the SCE approach

To better understand the spatial structure of large panels of economic and financial time series and provide a guideline for constructing semiparametric models, this paper first considers estimating a large spatial covariance matrix of the generalized $m$-dependent and $β$-mixing time series (with $J$ variables and $T$ observations) by hard thresholding regularization as long as ${\log J \, \cx^*(\ct)}/{T} = \Co(1)$ (the former scheme with some time dependence measure $\cx^*(\ct)$) or $\log J /{T} = \Co(1)$ (the latter scheme with some upper bounded mixing coefficient). We quantify the interplay between the estimators' consistency rate and the time dependence level, discuss an intuitive resampling scheme for threshold selection, and also prove a general cross-validation result justifying this. Given a consistently estimated covariance (correlation) matrix, by utilizing its natural links with graphical models and semiparametrics, after "screening" the (explanatory) variables, we implement a novel forward (and backward) label permutation procedure to cluster the "relevant" variables and construct the corresponding semiparametric model, which is further estimated by the groupwise dimension reduction method with sign constraints. We call this the SCE (screen - cluster - estimate) approach for modeling high dimensional data with complex spatial structure. Finally we apply this method to study the spatial structure of large panels of economic and financial time series and find the proper semiparametric structure for estimating the consumer price index (CPI) to illustrate its superiority over the linear models.

stat.ML↗

arXiv2013

Maximum entropy distribution of stock price fluctuations

The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk characterized by a stochastic diffusion coefficient and constrained to a given value of the expected volatility, taking in this way into account the information provided by the existence of an option market. This model is validated by a comprehensive comparison with observed distributions of both price return and diffusion coefficient. Expected volatility is the only parameter in the model and can be obtained by analysing option prices. We give an analytic formulation of the probability density function for price returns which can be used to extract expected volatility from stock option data. This distribution is of high practical interest since it should be preferred to a Gaussian when dealing with the problem of pricing derivative financial contracts.

q-fin.ST↗

arXiv2011

The Second Wave of the Global Crisis? A Log-Periodic Oscillation Analysis of Commodity Price Series

This article continues our analysis of the gold price dynamics that was published in December 2010 (abs/1012.4118) and forecasted the possibility of the "burst of the gold bubble" in April - June 2011. Our recent analysis suggests the possibility of one more substantial fluctuation before the final collapse in July 2011. On the other hand, in early 2011 we detected a number of other commodity bubbles and forecasted the start of their collapse in May - June 2011. We demonstrate that this collapse has actually begun, which in conjunction with the forthcoming burst of the gold bubble suggests that the World System is entering a bifurcation zone bearing rather high risks of the second wave of the global financial-economic crisis. Indeed, on the one hand, it is obvious that such a collapse may lead to huge losses or even bankruptcies of many of the major participants of exchange games and their dependent firms and banks. Therefore, the immediate market reaction is likely to be entirely negative. Negative impact on the market could well be amplified by numerous publications in the media and business press, drawing analogies with the events of the early 1980s and earlier similar events, as well as by losses of shareholders of bankrupt companies. On the other hand, investments in gold also lead to the diversion of funds from stock market investments and to the reduction in the production of goods and services. If at the time of the collapse some promising areas of investment appear in the developed and / or developing countries, the investment can move to those markets, which, on the contrary, could contribute to the production of new goods and services and accelerate the way out of the crisis. It is also obvious that the decline of the oil (and other energy/mineral resources) prices may contribute to acceleration of world economic growth rates and world economic recovery.

q-fin.ST↗

arXiv2011

Models for the impact of all order book events

We propose a general framework to describe the impact of different events in the order book, that generalizes previous work on the impact of market orders. Two different modeling routes can be considered, which are equivalent when only market orders are taken into account. One model posits that each event type has a temporary impact (TIM). The "history dependent impact" model (HDIM), on the other hand, assumes that only price-changing events have a direct impact, itself modulated by the past history of all events through an "influence matrix" that measures how much, on average, an event of a given type affects the immediate impact of a price-changing event of the same sign in the future. We find in particular that aggressive market orders tend to reduce the impact of further aggressive market orders of the same sign (and increase the impact of aggressive market orders of opposite sign). We discuss the relative merits of TIM and HDIM, in particular concerning their ability to reproduce accurately the price diffusion pattern. We find that in spite of theoretical inconsistencies, TIM appears to fare better than HDIM when compared to empirical data. We ascribe this paradox to an uncontrolled approximation used to calibrate HDIMs, calling for further work on this issue.

q-fin.TR↗

arXiv2013

The effect of round-off error on long memory processes

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both estimators are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic (i.e. non Gaussian) long memory process and we apply the result to discretized processes.

q-fin.ST↗

arXiv2011

Time-Bridge Estimators of Integrated Variance

We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the well-known realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an Itô stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies.

q-fin.ST↗

arXiv2011

Statistical Methods for Estimating the non-random Content of Financial Markets

q-fin.ST↗

arXiv2011

About the non-random Content of Financial Markets

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 is too small to be detected using traditional time series analysis. However, we show in the following that this difference between real financial time series and random walks, as small as it is, is detectable using modern statistical multivariate analysis, with several triggers encoded in trading systems. This kind of analysis are based on methods widely used in nuclear physics, with large samples of data and advanced statistical inference. Considering the movements of the Euro future contract at high frequency, we show that a part of the non-random content of this series can be inferred, namely the trend-following content depending on volatility ranges. Of course, this is not a general proof of statistical inference, as we focus on one particular example and the generality of the process can not be claimed. Therefore, we produce other examples on a completely different markets, largely uncorrelated to the Euro future, namely the DAX and Cacao future contracts. The same procedure is followed using a trading system, based on the same ingredients. We show that similar results can be obtained and we conclude that this is an evidence that some invariants, as encoded in our system, have been identified. They provide a kind of quantification of the non-random content of the financial markets explored over a 10 years period of time.

q-fin.ST↗

arXiv2011

Estimation in Functional Regression for General Exponential Families

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam's theory of asymptotic equivalence, is used to eliminate the bias caused by the non-linearity of exponential family models.

math.ST↗

arXiv2011

Eigenvector dynamics: theory and some applications

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (${\bf H}_0$ is then the Hamiltonian) and risk control (in which case ${\bf H}_0$ is the assets return correlation matrix). We specialize our results for the case of a Gaussian Orthogonal ${\bf H}_0$, or when ${\bf H}_0$ is a correlation matrix. We illustrate the usefulness of our framework using financial data.

cond-mat.stat-mech↗