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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (10 November 2021) | Viewed by 43536

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Prof. Dr. J.E. Trinidad-Segovia

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Department of Economy and Company, University of Almería, La Cañada de San Urbano, Almeria, Spain
Interests: long memory; portfolio theory; fractal dimension
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Miguel Ángel Sánchez-Granero

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Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
Interests: fractal structures; fractal dimension; Hurst exponent; finance; asymmetric topology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to interesting and novel mathematics and mathematical physics research papers with an applicability to financial markets. From the known mathematical models used in physics, to standard or new mathematical theories, theories are considered if they are (newly) applied to financial markets.

Possible topics include, but are not limited to, interdependence among assets or markets, price dynamics and modeling, risk measurement and management, hedging, derivatives pricing, volatility modeling, portfolio management and optimization, factor models, forecasting, cluster analysis, etc.

Prof. Dr. J.E. Trinidad-Segovia
Prof. Dr. Miguel Ángel Sánchez-Granero
Guest Editors

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Keywords

Time series analysis
Financial mathematics
Quantitative finance
Uncertainty
Volatility modeling
Stochastic analysis
Mathematical theory and applications
Mathematical physics

Published Papers (14 papers)

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Research

20 pages, 765 KiB

Open AccessFeature PaperArticle

A Cross-Sectional Analysis of Growth and Profit Rate Distribution: The Spanish Case

by David Vidal-Tomás, Alba Ruiz-Buforn, Omar Blanco-Arroyo and Simone Alfarano

Mathematics 2022, 10(6), 926; https://0-doi-org.brum.beds.ac.uk/10.3390/math10060926 - 14 Mar 2022

Viewed by 1864

Abstract

We analyse the time evolution of the empirical cross-sectional distribution of firms’ profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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20 pages, 4223 KiB

Open AccessArticle

Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading”

by Alejandro Raúl Hernández-Montoya, Carlos Manuel Rodríguez-Martínez, Manuel Enríque Rodríguez-Achach and David Hernández-Enríquez

Mathematics 2022, 10(2), 215; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020215 - 11 Jan 2022

Cited by 1 | Viewed by 1610

Abstract

In this paper a comparative, coarse grained, entropy data analysis of multi-scale log-returns distribution, produced by an ideal “optimal trader” and one thousand “noise traders” performing “bucket shop” trading, by following four different financial daily indices, is presented. A sole optimal trader is assigned to each one of these four analyzed markets, DJIA, IPC, Nikkei and DAX. Distribution of differential entropies of the corresponding multi-scale log-returns of the optimal and noise traders are calculated. Kullback-Leiber distances between the different optimal traders returns distributions are also calculated and results discussed. We show that the entropy of returns distribution of optimal traders for each analyzed market indeed reaches minimum values with respect to entropy distribution of noise traders and we measure this distance in

σ

units for each analyzed market. We also include a discussion on stationarity of the introduced multi-scale log-returns observable. Finally, a practical application of the obtained results related with ranking markets by their entropy measure as calculated here is presented. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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15 pages, 306 KiB

Open AccessEditor’s ChoiceArticle

Assessing the Role of Digital Finance on Shadow Economy and Financial Instability: An Empirical Analysis of Selected South Asian Countries

by Aamir Aijaz Syed, Farhan Ahmed, Muhammad Abdul Kamal and Juan E. Trinidad Segovia

Mathematics 2021, 9(23), 3018; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233018 - 25 Nov 2021

Cited by 23 | Viewed by 4652

Abstract

The advancement in fintech technological development in emerging countries has accelerated the role of digital finance in economic development. Digital finance assists in financial inclusion; however, it may also increase the chances of financial instability due to systematic risks. Emerging countries are also in the clutches of shadow economic growth, which reduces taxable income revenue and creates pressure on financial inclusion prospects. The current study attempts to measure the impact of digital finance on the shadow economic growth and financial stability among the selected South Asian emerging countries. We have used the CUP-FM and CUP-BC estimation methods to measure the above relationship on two model frameworks from 2004 to 2018, with the former measuring the influence of digital finance on the shadow economy and the latter examining the relationship between digital finance and financial stability. In addition, the second-generation unit root test, and the Westerlund cointegration analysis are also employed to confirm the stationarity and cointegration among the variables. The result of the Westerlund’s cointegration confirms a long cointegration between the explanatory and outcome variables. Furthermore, the long-run estimation results conclude that an increase in digital finance helps in reducing the growth of the shadow economy among the selected sample countries. However, it also increases the likelihood of systematic risks and increases financial instability. The study also reveals that the control variables like unemployment and industrial productivity also have a significant influence on financial stability and the shadow economy. The findings will assist readers in comprehending how digital finance influences the shadow economy and promotes financial inclusion and stability in emerging nations. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

18 pages, 1058 KiB

Open AccessArticle

Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis

by Cristiana Vaz, Rui Pascoal and Helder Sebastião

Mathematics 2021, 9(17), 2088; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172088 - 29 Aug 2021

Cited by 2 | Viewed by 1605

Abstract

Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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31 pages, 4719 KiB

Open AccessArticle

An RFM Model Customizable to Product Catalogues and Marketing Criteria Using Fuzzy Linguistic Models: Case Study of a Retail Business

by Rocío G. Martínez, Ramon A. Carrasco, Cristina Sanchez-Figueroa and Diana Gavilan

Mathematics 2021, 9(16), 1836; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161836 - 04 Aug 2021

Cited by 8 | Viewed by 4993

Abstract

In the field of strategic marketing, the recency, frequency and monetary (RFM) variables model has been applied for years to determine how solid a database is in terms of spending and customer activity. Retailers almost never obtain data related to their customers beyond their purchase history, and if they do, the information is often out of date. This work presents a new method, based on the fuzzy linguistic 2-tuple model and the definition of product hierarchies, which provides a linguistic interpretability giving business meaning and improving the precision of conventional models. The fuzzy linguistic 2-tuple RFM model, adapted by the product hierarchy thanks to the analytical hierarchical process (AHP), is revealed to be a useful tool for including business criteria, product catalogues and customer insights in the definition of commercial strategies. The result of our method is a complete customer segmentation that enriches the clusters obtained with the traditional fuzzy linguistic 2-tuple RFM model and offers a clear view of customers’ preferences and possible actions to define cross- and up-selling strategies. A real case study based on a worldwide leader in home decoration was developed to guide, step by step, other researchers and marketers. The model was built using the only information that retailers always have: customers’ purchase ticket details. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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23 pages, 4782 KiB

Open AccessArticle

Study of the Behavior of Cryptocurrencies in Turbulent Times Using Association Rules

by José Benito Hernández C., Andrés García-Medina and Miguel Andrés Porro V.

Mathematics 2021, 9(14), 1620; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141620 - 09 Jul 2021

Cited by 1 | Viewed by 1989

Abstract

We studied the effects of the recent financial turbulence of 2020 on the cryptocurrency market, taking into account both prices and volumes from December 2019 to July 2020. Time series were transformed into transaction matrices, and the Apriori algorithm was applied to find the association rules between different currencies, identifying whether the price or the volume of the currencies compose the rules. We divided the data set into two subsets and found that before the decline in cryptocurrency prices, the association rules were generally formed by these prices and that, then, the volumes of the transactions dominated to form the association rules. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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26 pages, 422 KiB

Open AccessArticle

Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations

by Jaume Masoliver, Miquel Montero and Josep Perelló

Mathematics 2021, 9(14), 1589; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141589 - 06 Jul 2021

Cited by 4 | Viewed by 2291

Abstract

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution, specially when extreme situations occur (pandemics, global wars, etc.). When, between jumps, the dynamical evolution is governed by an Ornstein–Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continuous time random walk. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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18 pages, 306 KiB

Open AccessArticle

Herd Behavior in Venture Capital Market: Evidence from China

by Ruijun Zhang, Xiaotong Yang, Nian Li and Muhammad Asif Khan

Mathematics 2021, 9(13), 1509; https://0-doi-org.brum.beds.ac.uk/10.3390/math9131509 - 28 Jun 2021

Cited by 11 | Viewed by 3170

Abstract

This paper aims to empirically analyze the herd behavior in the VC market in the context of China, including the existence, causes and consequences of herding among venture capitalists. For our empirical analysis, we first construct a herding measure and confirm the existence of herd behavior in the Chinese VC market. Then, we perform OLS/logit regression to examine the causes and consequences of herding among venture capitalists. Our results suggest that herd behavior in the venture capital market are driven by positive signals of essential information and a higher degree of information uncertainty. However, we find no evidence of the influence of feedback trading signals on herding among venture capitalists. Further analysis suggests that a better external information environment would help weaken the herding among venture capitalists, while their reputation concerns might amplify the herding effect. Finally, we examine the economic consequence of the herding and find that the herd behavior of venture capitalists would have an adverse effect on their exit performance. In addition to the enrichment and development of herding theory, our study also provides an essential theoretical frame and policy implications for the steady growth of the venture capital market in emerging economies. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

18 pages, 1343 KiB

Open AccessArticle

Bitcoin and Fiat Currency Interactions: Surprising Results from Asian Giants

by Samet Gunay, Kerem Kaskaloglu and Shahnawaz Muhammed

Mathematics 2021, 9(12), 1395; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121395 - 16 Jun 2021

Cited by 6 | Viewed by 2881

Abstract

This study examines the interaction of Bitcoin with fiat currencies of three developed (euro, pound sterling and yen) and three emerging (yuan, rupee and ruble) market economies. Empirical investigations are executed through symmetric, asymmetric and non-linear causality tests, and Markov regime-switching regression (MRSR) analysis. Results show that Bitcoin has a causal nexus with Chinese yuan and Indian rupee for price and various return components. The MRSR analysis justifies these findings by demonstrating the presence of interaction in contractionary regimes. Accordingly, it can be stated that when markets display a downward trend, appreciation of the Chinese yuan and Indian rupee positively and strongly affects the value of Bitcoin, possibly due to the market timing. The MRSR analysis also exhibits a transition from a tranquil to a crisis regime in March 2020 because of the pandemic. However, a shorter duration spent in the crisis regime in 2020 indicates the limited and relatively less harmful effect of the pandemic on the cryptocurrency market when compared to the turmoil that occurred in 2018. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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23 pages, 379 KiB

Open AccessArticle

Investor Attention and Corporate Innovation Performance: Evidence from Web Search Volume Index of Chinese Listed Companies

by Nian Li, Chunling Li, Runsen Yuan, Muhammad Asif Khan, Xiaoran Sun and Nosherwan Khaliq

Mathematics 2021, 9(9), 930; https://0-doi-org.brum.beds.ac.uk/10.3390/math9090930 - 22 Apr 2021

Cited by 5 | Viewed by 2470

Abstract

Leveraging from the online search index of Chinese listed companies from 2012 to 2018, we empirically test the relationship between investors’ attention and corporate innovation performance for the first time. The main results are as follows: (1) investors’ attention significantly improves listed companies’ innovation performance, which is reflected in the increase of patent applications. This indicates that investors’ active information collection behaviour affects China’s economic development by promoting enterprise innovation. (2) This paper’s conclusion remains intact after a battery of robustness checks, such as alternative measures of key variables and empirical specifications and a series of endogenous treatment. (3) The mechanisms tests show that: “information asymmetry”, “financing constraint”, and “agency cost” are supported. In other words, with the increase of investors’ attention, not only the information asymmetry is reduced, which greatly improved the information environment of the capital market, but also the external financing constraints of enterprises are alleviated. The opportunistic management behaviour is effectively suppressed, thus motivating the corporate innovation incentives and improving the corporate innovation of input, output and quality. (4) Further research shows that investor attention to listed companies also improves the efficiency of capital allocation. This paper’s conclusion shows that investors’ initiative information acquisition behaviour can improve enterprises innovation performance, thus providing a driving force for China’s economic development. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

22 pages, 2648 KiB

Open AccessArticle

Feature Selection in a Credit Scoring Model

by Juan Laborda and Seyong Ryoo

Mathematics 2021, 9(7), 746; https://0-doi-org.brum.beds.ac.uk/10.3390/math9070746 - 31 Mar 2021

Cited by 22 | Viewed by 5071

Abstract

This paper proposes different classification algorithms—logistic regression, support vector machine, K-nearest neighbors, and random forest—in order to identify which candidates are likely to default for a credit scoring model. Three different feature selection methods are used in order to mitigate the overfitting in the curse of dimensionality of these classification algorithms: one filter method (Chi-squared test and correlation coefficients) and two wrapper methods (forward stepwise selection and backward stepwise selection). The performances of these three methods are discussed using two measures, the mean absolute error and the number of selected features. The methodology is applied for a valuable database of Taiwan. The results suggest that forward stepwise selection yields superior performance in each one of the classification algorithms used. The conclusions obtained are related to those in the literature, and their managerial implications are analyzed. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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33 pages, 9707 KiB

Open AccessArticle

A Local Spatial STIRPAT Model for Outdoor NO_x Concentrations in the Community of Madrid, Spain

by José-María Montero, Gema Fernández-Avilés and Tiziana Laureti

Mathematics 2021, 9(6), 677; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060677 - 22 Mar 2021

Cited by 7 | Viewed by 2575

Abstract

Air pollution control is one of the main challenges facing modern societies. Consequently, the estimation of population, affluence, and technology impacts on air pollution concentrations (STIRPAT modeling) has become the cornerstone of environmental decision-making. Spatial effects are not usually included in STIRPAT modeling of air pollution. However, space matters: accounting for spatial dependencies significantly improves the accuracy of estimates and forecasts, especially (or only) when dealing with small information units rather than with large ones (countries, large regions, provinces in China, counties and states in the USA, etc.). The latter scale is typical in the literature on air pollution due to the difficulties in finding data on its drivers at a true local scale. Accordingly, this paper has a double objective. The first is the estimation of a spatial panel data STIRPAT model, with the spatial units being both very small and also highly autonomous, developed municipalities. The second is to examine whether an environmental Kuznets curve relationship exists between income per capita and NO_x concentrations. A case study has been carried out in the Autonomous Community of Madrid, Spain, at the municipal level. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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19 pages, 848 KiB

Open AccessArticle

Volatility Co-Movement in Stock Markets

by María Nieves López-García, Miguel Angel Sánchez-Granero, Juan Evangelista Trinidad-Segovia, Antonio Manuel Puertas and Francisco Javier De las Nieves

Mathematics 2021, 9(6), 598; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060598 - 11 Mar 2021

Cited by 5 | Viewed by 3201

Abstract

The volatility and log-price collective movements among stocks of a given market are studied in this work using co-movement functions inspired by similar functions in the physics of many-body systems, where the collective motions are a signal of structural rearrangement. This methodology is aimed to identify the cause of coherent changes in volatility or price. The function is calculated using the product of the variations in volatility (or price) of a pair of stocks, averaged over all pair particles. In addition to the global volatility co-movement, its distribution according to the volatility of the stocks is also studied. We find that stocks with similar volatility tend to have a greater co-movement than stocks with dissimilar volatility, with a general decrease in co-movement with increasing volatility. On the other hand, when the average volatility (or log-price) is subtracted from the stock volatility (or log-price), the co-movement decreases notably and becomes almost zero. This result, interpreted within the background of many body physics, allows us to identify the index motion as the main source for the co-movement. Finally, we confirm that during crisis periods, the volatility and log-price co-movement are much higher than in calmer periods. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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20 pages, 1224 KiB

Open AccessArticle

Statistical Arbitrage in Emerging Markets: A Global Test of Efficiency

by Karen Balladares, José Pedro Ramos-Requena, Juan Evangelista Trinidad-Segovia and Miguel Angel Sánchez-Granero

Mathematics 2021, 9(2), 179; https://0-doi-org.brum.beds.ac.uk/10.3390/math9020179 - 18 Jan 2021

Cited by 6 | Viewed by 3807

Abstract

In this paper, we use a statistical arbitrage method in different developed and emerging countries to show that the profitability of the strategy is based on the degree of market efficiency. We will show that our strategy is more profitable in emerging ones and in periods with greater uncertainty. Our method consists of a Pairs Trading strategy based on the concept of mean reversion by selecting pair series that have the lower Hurst exponent. We also show that the pair selection with the lowest Hurst exponent has sense, and the lower the Hurst exponent of the pair series, the better the profitability that is obtained. The sample is composed by the 50 largest capitalized companies of 39 countries, and the performance of the strategy is analyzed during the period from 1 January 2000 to 10 April 2020. For a deeper analysis, this period is divided into three different subperiods and different portfolios are also considered. Full article

(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)

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