Research articles for the 2020-03-22

Asymptotics for Small Nonlinear Price Impact: a PDE Approach to the Multidimensional Case
Erhan Bayraktar,Thomas Caye,Ibrahim Ekren

We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear second order PDE related to an ergodic control problem and a linear parabolic PDE. We illustrate our result on a multivariate geometric Brownian motion price model.

Coronavirus and oil price crash
Claudiu Albulescu

Coronavirus (COVID-19) creates fear and uncertainty, hitting the global economy and amplifying the financial markets volatility. The oil price reaction to COVID-19 was gradually accommodated until March 09, 2020, when, 49 days after the release of the first coronavirus monitoring report by the World Health Organization (WHO), Saudi Arabia floods the market with oil. As a result, international prices drop with more than 20% in one single day. Against this background, the purpose of this paper is to investigate the impact of COVID-19 numbers on crude oil prices, while controlling for the impact of financial volatility and the United States (US) economic policy uncertainty. Our ARDL estimation shows that the COVID-19 daily reported cases of new infections have a marginal negative impact on the crude oil prices in the long run. Nevertheless, by amplifying the financial markets volatility, COVID-19 also has an indirect effect on the recent dynamics of crude oil prices.

Entropy-Norm space for geometric selection of strict Nash equilibria in n-person games
A. B. Leoneti,G. A. Prataviera

Motivated by empirical evidence that individuals within group decision making simultaneously aspire to maximize utility and avoid inequality we propose a criterion based on the entropy-norm pair for geometric selection of strict Nash equilibria in n-person games. For this, we introduce a mapping of an n-person set of Nash equilibrium utilities in an Entropy-Norm space. We suggest that the most suitable group choice is the equilibrium closest to the largest entropy-norm pair of a rescaled Entropy-Norm space. Successive application of this criterion permits an ordering of the possible Nash equilibria in an n-person game accounting simultaneously equality and utility of players payoffs. Limitations of this approach for certain exceptional cases are discussed. In addition, the criterion proposed is applied and compared with the results of a group decision making experiment.

Fast Pricing of Energy Derivatives with Mean-reverting Jump-diffusion Processes
Nicola Cufaro Petroni,Piergiacomo Sabino

Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and fast methodologies for the simulation of the spot price dynamics modeled as the exponential of the sum of an Ornstein-Uhlenbeck and an independent pure jump process, where the latter one is driven by a compound Poisson process with (bilateral) exponentially distributed jumps. These methodologies are finally applied to the pricing of Asian options, gas storages and swings under different combinations of jump-diffusion market models, and the apparent computational advantages of the proposed procedures are emphasized.

Gender bias in the Erasmus students network
Luca De Benedictis,Silvia Leoni

The Erasmus Program (EuRopean community Action Scheme for the Mobility of University Students), the most important student exchange program in the world, financed by the European Union and started in 1987, is characterized by a strong gender bias. Girls participate to the program more than boys. This work quantifies the gender bias in the Erasmus program between 2008 and 2013, using novel data at the university level. It describes the structure of the program in great details, carrying out the analysis across fields of study, and identifies key universities as senders and receivers. In addition, it tests the difference in the degree distribution of the Erasmus network along time and between genders, giving evidence of a greater density in the female Erasmus network with respect to the one of the male Erasmus network.

Graham's Formula for Valuing Growth Stocks
Andreas A. Aigner,Walter Schrabmair

Benjamin Graham introduced a very simple formula for valuing a growth stock in 1962. How does it work and why? What is a sensible way to calculate this across many stocks and provide a scoring system to compare stocks amongst each other? We are presenting a methodology here which is put into practice.

Kernel density decomposition with an application to the social cost of carbon
Richard S.J. Tol

A kernel density is an aggregate of kernel functions, which are itself densities and could be kernel densities. This is used to decompose a kernel into its constituent parts. Pearson's test for equality of proportions is applied to quantiles to test whether the component distributions differ from one another. The proposed methods are illustrated with a meta-analysis of the social cost of carbon. Different discount rates lead to significantly different Pigou taxes, but not different growth rates. Estimates have not varied over time. Different authors have contributed different estimates, but these differences are insignificant. Kernel decomposition can be applied in many other fields with discrete explanatory variables.

P-hacking in clinical trials and how incentives shape the distribution of results across phases
Jérôme Adda,Christian Decker,Marco Ottaviani

Clinical research should conform to high standards of ethical and scientific integrity, given that human lives are at stake. However, economic incentives can generate conflicts of interest for investigators, who may be inclined to withhold unfavorable results or even tamper with data in order to achieve desired outcomes. To shed light on the integrity of clinical trial results, this paper systematically analyzes the distribution of p-values of primary outcomes for phase II and phase III drug trials reported to the registry. First, we detect no bunching of results just above the classical 5% threshold for statistical significance. Second, a density discontinuity test reveals an upward jump at the 5% threshold for phase III results by small industry sponsors. Third, we document a larger fraction of significant results in phase III compared to phase II. Linking trials across phases, we find that early favorable results increase the likelihood of continuing into the next phase. Once we take into account this selective continuation, we can explain almost completely the excess of significant results in phase III for trials conducted by large industry sponsors. For small industry sponsors, instead, part of the excess remains unexplained.

Portfolio Choice with Small Temporary and Transient Price Impact
Ibrahim Ekren,Johannes Muhle-Karbe

We study portfolio selection in a model with both temporary and transient price impact introduced by Garleanu and Pedersen (2016). In the large-liquidity limit where both frictions are small, we derive explicit formulas for the asymptotically optimal trading rate and the corresponding minimal leading-order performance loss. We find that the losses are governed by the volatility of the frictionless target strategy, like in models with only temporary price impact. In contrast, the corresponding optimal portfolio not only tracks the frictionless optimizer, but also exploits the displacement of the market price from its unaffected level.

Power Assisted Trend Following
Andreas A. Aigner,Walter Schrabmair

'The trend is your friend' is a common saying, the difficulty lies in determining if and when you are in a trend. Is the trend strong enough to trade? When does the trend reverse and how are you going to determine this? We will try and answer at least some of these questions here. We are deriving a novel indicator to measure the power of a trend using digital signal processing techniques, separating the Signal from the Noise. We apply these to examples as well as real data and evaluate the accuracy of these and the relation to PNL performance of the 'Volatility Index' trend following algorithm devised by J. Welles Wilder Jr. in 1978.

Predicting Stock Returns with Batched AROW
Rachid Guennouni Hassani,Alexis Gilles,Emmanuel Lassalle,Arthur Dénouveaux

We extend the AROW regression algorithm developed by Vaits and Crammer in [VC11] to handle synchronous mini-batch updates and apply it to stock return prediction. By design, the model should be more robust to noise and adapt better to non-stationarity compared to a simple rolling regression. We empirically show that the new model outperforms more classical approaches by backtesting a strategy on S\&P500 stocks.

Robust portfolio optimization with multi-factor stochastic volatility
Ben-Zhang Yang,Xiaoping Lu,Guiyuan Ma,Song-Ping Zhu

This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without derivative trading. To illustrate the effects of ambiguity, we compare our optimal robust strategy with some strategies that ignore the information of uncertainty, and provide the corresponding welfare analysis. The effects of derivative trading to the optimal portfolio selection are also discussed by considering alternative strategies. Our study is further extended to the cases with jump risks in asset price and correlated volatility factors, respectively. Numerical experiments are provided to demonstrate the behavior of the optimal portfolio and utility loss.

Total systemic risk statistics
Fei Sun

Systemic risk is a critical factor not only for financial markets but also for risk management. In this paper, we consider a special class of risk statistics, named total systemic risk statistics. Our result provides a new approach for dealing with systemic risk. By further developing the properties related to total systemic risk statistics, we are able to derive dual representation for such risk.