Value-at-Risk and its conditional allegory, which takes into account the available information about the economic environment, form the centrepiece of the Basel framework for the evaluation of market risk in the banking sector. In this paper, a new nonparametric framework for estimating this conditional Value-at-Risk is presented. A nonparametric approach is particularly pertinent as the traditionally used parametric distributions have been shown to be insufficiently robust and flexible in most of the equity-return data sets observed in practice. The method extracts the quantile of the conditional distribution of interest, whose estimation is based on a novel estimator of the density of the copula describing the dynamic dependence observed in the series of returns. Real-world back-testing analyses demonstrate the potential of the approach, whose performance may be superior to its industry counterparts.

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize the Bessel-like birth-death process having clear representation by the SDEs. The new process helps to integrate the alternatives of description and to derive the equations for the probability density function (PDF) of the burst and inter-burst duration of the proposed continuous time birth-death processes.

In this paper we introduce an additive two-factor model for electricity futures prices based on Normal Inverse Gaussian L\'evy processes, that fulfills a no-overlapping-arbitrage (NOA) condition. We compute European option prices by Fourier transform methods, introduce a specific calibration procedure that takes into account no-arbitrage constraints and fit the model to power option settlement prices of the European Energy Exchange (EEX). We show that our model is able to reproduce the different levels and shapes of the implied volatility (IV) profiles displayed by options with a variety of delivery periods.

Several systematic studies have suggested that a large fraction of published research is not reproducible. One probable reason for low reproducibility is insufficient sample size, resulting in low power and low positive predictive value. It has been suggested that insufficient sample-size choice is driven by a combination of scientific competition and 'positive publication bias'. Here we formalize this intuition in a simple model, in which scientists choose economically rational sample sizes, balancing the cost of experimentation with income from publication. Specifically, assuming that a scientist's income derives only from 'positive' findings (positive publication bias) and that individual samples cost a fixed amount, allows to leverage basic statistical formulas into an economic optimality prediction. We find that if effects have i) low base probability, ii) small effect size or iii) low grant income per publication, then the rational (economically optimal) sample size is small. Furthermore, for plausible distributions of these parameters we find a robust emergence of a bimodal distribution of obtained statistical power and low overall reproducibility rates, matching empirical findings. Overall, the model describes a simple mechanism explaining both the prevalence and the persistence of small sample sizes. It suggests economic rationality, or economic pressures, as a principal driver of irreproducibility.

We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to dual sets in the representation of coherent risk measures. We provide results that guarantee the existence of a solution and explore the properties of minimizer and minimum as risk and deviation measures, respectively. Empirical illustration is carried out to demonstrate the use of our approach in capital determination.

It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this short paper we prove that Expected Shortfall is a concave risk measure with respect to probability distributions, i. e. Expected Shortfall of a finite mixture of arbitrary risk positions is not lower than the linear combination of Expected Shortfalls of the same risk positions (with the same weights as in the mixture).

In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as in the power market, in which the volume to be traded can only be estimated and becomes more accurate when approaching a specified delivery time. In this paper, we develop a model that accounts for volume uncertainty and we show that a risk-averse trader has benefit in delaying their trades. More precisely, we argue that the optimal strategy is a trade-off between early and late trades in order to balance risk associated with both price and volume. By incorporating a risk term related to the volume to trade, the static optimal strategies suggested by our model avoid the explosion in the algorithmic complexity usually associated with dynamic programming solutions, all the while yielding competitive performance.

We model sectoral production by cascading binary compounding processes. The sequence of processes is discovered in a self-similar hierarchical structure stylized in the economy-wide networks of production. Nested substitution elasticities and Hicks-neutral productivity growth are measured such that the general equilibrium feedbacks between all sectoral unit cost functions replicate the transformation of networks observed as a set of two temporally distant input-output coefficient matrices. We examine this system of unit cost functions to determine how idiosyncratic sectoral productivity shocks propagate into aggregate macroeconomic fluctuations in light of potential network transformation. Additionally, we study how sectoral productivity increments propagate into the dynamic general equilibrium, thereby allowing network transformation and ultimately producing social benefits.

When society maintains a competitive system to promote an abstract goal, competition by necessity relies on imperfect proxy measures. For instance profit is used to measure value to consumers, patient volumes to measure hospital performance, or the Journal Impact Factor to measure scientific value. Here we note that \textit{any proxy measure in a competitive societal system becomes a target for the competitors, promoting corruption of the measure}, suggesting a general applicability of what is best known as Campbell's or Goodhart's Law. Indeed, prominent voices have argued that the scientific reproducibility crisis or inaction to the threat of global warming represent instances of such competition induced corruption. Moreover, competing individuals often report that competitive pressures limit their ability to act according to the societal goal, suggesting lock-in. However, despite the profound implications, we lack a coherent theory of such a process. Here we propose such a theory, formalized as an agent based model, integrating insights from complex systems theory, contest theory, behavioral economics and cultural evolution theory. The model reproduces empirically observed patterns at multiple levels. It further suggests that any system is likely to converge towards an equilibrium level of corruption determined by i) the information captured in the proxy and ii) the strength of an intrinsic incentive towards the societal goal. Overall, the theory offers mechanistic insight to subjects as diverse as the scientific reproducibility crisis and the threat of global warming.

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition sharpens and improves on previous results. We connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Finally, we discuss computation of the test value associated with our condition, providing a Monte Carlo method that is naturally parallelizable.

Our study presents the analysis of stock market data of S&P500 before and after been detrended. The analysis is based on two types of returns, simple return and log-return respectively. Both of them are non-stationary time series. This means that their statistical distribution change over time. Consequently a detrended process is made to neutralize the non-stationary effects. The detrended process is obtained by decomposing the financial time series into a deterministic trend and random fluctuations. We present an alternative method on detrending time series based on the classical moving average (MA) models, where Kurtosis is used to determine the windows size. Then, the dentrending fluctuation analysis (DFA) is use to show that the detrended part is stationary. This is done by considering the autocorrelation of detrended price return and the power spectrum analysis of detrended price.

The art of systematic financial trading evolved with an array of approaches, ranging from simple strategies to complex algorithms all relying, primary, on aspects of time-series analysis. Recently, after visiting the trading floor of a leading financial institution, we noticed that traders always execute their trade orders while observing images of financial time-series on their screens. In this work, we built upon the success in image recognition and examine the value in transforming the traditional time-series analysis to that of image classification. We create a large sample of financial time-series images encoded as candlestick (Box and Whisker) charts and label the samples following three algebraically-defined binary trade strategies. Using the images, we train over a dozen machine-learning classification models and find that the algorithms are very efficient in recovering the complicated, multiscale label-generating rules when the data is represented visually. We suggest that the transformation of continuous numeric time-series classification problem to a vision problem is useful for recovering signals typical of technical analysis.