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Application of Mathematical Methods in Financial Economics
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Application of Mathematical Methods in Financial Economics

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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 57674

Special Issue Editors

Prof. Dr. Román Ferrer

E-Mail Website
Guest Editor
Dpto. Economía Financiera y Actuarial, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
Interests: financial markets; time series; wavelet analysis; energy finance
Prof. Dr. Rafael Benítez

E-Mail Website
Guest Editor
Dpto. Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
Interests: nonlinear analysis; wavelets; time series; numerical analysis; integral equations
Prof. Dr. Vicente J. Bolós

E-Mail Website
Guest Editor
Dpto. Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
Interests: nonlinear analysis; wavelets; time series; numerical analysis

Special Issue Information

Dear Colleagues,

Advanced mathematical tools and methods are becoming more and more necessary in the field of financial economics to provide a better characterization of the complex relationships between economic and financial time series. However, there is often a considerable gap between the state-of-the-art mathematical techniques and the mainstream research in financial economics, particularly that conducted by non-mathematicians.

The purpose of this Special Issue is to contribute to close this gap by providing a collection of articles that illustrate the applicability of novel mathematical tools and methods to a wide range of topics in financial economics, including, among others, portfolio management, risk management, portfolio optimization, relationships among financial markets and among financial and commodity markets, information flows across markets, cryptocurrencies and financial markets, green finance and financial risks.

Prof. Dr. Román Ferrer
Prof. Dr. Rafael Benítez
Prof. Dr. Vicente J. Bolós
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Risk management
  • Portfolio management
  • Portfolio optimization
  • Financial risks
  • Quantitative finance
  • Interdependence among markets
  • Financial time series
  • Wavelet analysis
  • Nonlinear models
  • Forecasting and uncertainty

Published Papers (22 papers)

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Research

23 pages, 3807 KiB  
Article
Quantile Dependence between Crude Oil Returns and Implied Volatility: Evidence from Parametric and Nonparametric Tests
by Bechir Raggad and Elie Bouri
Mathematics 2023, 11(3), 528; https://0-doi-org.brum.beds.ac.uk/10.3390/math11030528 - 18 Jan 2023
Cited by 4 | Viewed by 1368
Abstract
We examine the daily dependence and directional predictability between the returns of crude oil and the Crude Oil Volatility Index (OVX). Unlike previous studies, we apply a battery of quantile-based techniques, namely the quantile unit root test, the causality-in-quantiles test, and the cross-quantilogram [...] Read more.
We examine the daily dependence and directional predictability between the returns of crude oil and the Crude Oil Volatility Index (OVX). Unlike previous studies, we apply a battery of quantile-based techniques, namely the quantile unit root test, the causality-in-quantiles test, and the cross-quantilogram approach. Our main results show evidence of significant bi-directional predictability that is quantile-dependent and asymmetric. A significant positive Granger causality runs from oil (OVX) returns to OVX (oil) returns when both series are in similar lower (upper) quantiles, as well as in opposite quantiles. The Granger causality from OVX returns to oil returns is only significant during periods of high volatility, although it is not always positive. The findings imply that the forward-looking estimate of oil volatility, reflecting the sentiment of oil market participants, should be considered when studying price variations in the oil market, and that crude oil returns can be used to predict oil implied volatility during bearish market conditions. Therefore, the findings have implications regarding predictability under various conditions for oil market participants. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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17 pages, 733 KiB  
Article
Risk-Taking, Financial Knowledge, and Risky Investment Intention: Expanding Theory of Planned Behavior Using a Moderating-Mediating Model
by Abu Elnasr E. Sobaih and Ibrahim A. Elshaer
Mathematics 2023, 11(2), 453; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020453 - 14 Jan 2023
Cited by 9 | Viewed by 4568
Abstract
This research examines the impact of financial knowledge on risky investment intention via the lens of the theory of planned behavior (TPB). The research developed a comprehensive model to test the mediation effect of the three TPB antecedents on the link between financial [...] Read more.
This research examines the impact of financial knowledge on risky investment intention via the lens of the theory of planned behavior (TPB). The research developed a comprehensive model to test the mediation effect of the three TPB antecedents on the link between financial knowledge and risky investment intention. The research investigates the moderating effect of risk-taking on the link between three TPB constructs and risky investment intention. For these purposes, we used a pre-tested survey, was directed to senior university students in public universities in Saudi Arabia. The findings of SmartPLS showed a significant positive influence of financial knowledge on attitudes towards risky investment, subjective norms (SNs), and perceived behavioral control (PBC). Both SNs and PBC have a significant positive influence on risky investment intention. Nonetheless, the personal attitude of students failed to have a significant direct or mediating influence on risky investment intention. Additionally, risk-taking did not have a moderating effect on the link between personal attitude and risky investment intention. Students belong to a risk-adverse culture, which could justify the insignificant impact of their personal attitudes on risky investment intention. On the other side, SNs and PBC have a mediating effect on the link between financial knowledge and risky investment intention. Risk-taking has a moderating effect on the link between SNs, PBC, and risky investment intention. The research extends the use of TPB by validating its assumptions about driving the investment intention of university graduates. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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14 pages, 3358 KiB  
Article
Artificial Intelligence-Based Prediction of Crude Oil Prices Using Multiple Features under the Effect of Russia–Ukraine War and COVID-19 Pandemic
by Hadi Jahanshahi, Süleyman Uzun, Sezgin Kaçar, Qijia Yao and Madini O. Alassafi
Mathematics 2022, 10(22), 4361; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224361 - 20 Nov 2022
Cited by 6 | Viewed by 5621
Abstract
The effect of the COVID-19 pandemic on crude oil prices just faded; at this moment, the Russia–Ukraine war brought a new crisis. In this paper, a new application is developed that predicts the change in crude oil prices by incorporating these two global [...] Read more.
The effect of the COVID-19 pandemic on crude oil prices just faded; at this moment, the Russia–Ukraine war brought a new crisis. In this paper, a new application is developed that predicts the change in crude oil prices by incorporating these two global effects. Unlike most existing studies, this work uses a dataset that involves data collected over twenty-two years and contains seven different features, such as crude oil opening, closing, intraday highest value, and intraday lowest value. This work applies cross-validation to predict the crude oil prices by using machine learning algorithms (support vector machine, linear regression, and rain forest) and deep learning algorithms (long short-term memory and bidirectional long short-term memory). The results obtained by machine learning and deep learning algorithms are compared. Lastly, the high-performance estimation can be achieved in this work with the average mean absolute error value over 0.3786. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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21 pages, 4559 KiB  
Article
Automotive Sector Financial Performance Dynamic Model: Europe vs. Asia Case Study
by Romeo-Victor Ionescu, Monica-Laura Zlati, Valentin-Marian Antohi and Marius-Sorin Dincă
Mathematics 2022, 10(19), 3627; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193627 - 04 Oct 2022
Cited by 1 | Viewed by 2732
Abstract
The current geo-political context brings to light new challenges to the smooth functioning of the global automotive trade, both through the economic boycott of Russian units and the intensified transition to the green economy. The main objective of the research is to quantify [...] Read more.
The current geo-political context brings to light new challenges to the smooth functioning of the global automotive trade, both through the economic boycott of Russian units and the intensified transition to the green economy. The main objective of the research is to quantify the financial efficiency of the global automotive industry in order to determine a general dynamic performance model and quantify the impact of external regional factors on the performance of economic entities in the automotive sector. The current objectives of the study are identifying recent asset developments in the industry, the main performance models in the literature, designing a global financial performance model and other regional dynamic models, validation of these models and dissemination of the model results and proposals. The used methods are of an empirical nature, namely, the literature study, with the authors aiming to identify the main performance models promoted by specialists in the field. We use qualitative-analytical and forecasting methods for dynamic performance modelling, using information from the 2010–2021 financial reports of major car manufacturers. The results of the study highlight the need for performance in relation to the influence of regional factors and performance leaders by economic and financial chapters. The results are useful for both managers of economic entities and supra-regional decision makers in order to establish economic development strategies and policies in view of the transition to the green economy and in the current geopolitical context. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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19 pages, 615 KiB  
Article
Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment
by Junkee Jeon and Geonwoo Kim
Mathematics 2022, 10(15), 2688; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152688 - 29 Jul 2022
Cited by 4 | Viewed by 1143
Abstract
This paper investigates the American strangle option in a mean-reversion environment. When the underlying asset follows a mean-reverting lognormal process, an analytic pricing formula for an American strangle option is explicitly provided. To present the pricing formula, we consider the partial differential equation [...] Read more.
This paper investigates the American strangle option in a mean-reversion environment. When the underlying asset follows a mean-reverting lognormal process, an analytic pricing formula for an American strangle option is explicitly provided. To present the pricing formula, we consider the partial differential equation (PDE) for American strangle options with two optimal stopping boundaries and use Mellin transform techniques to derive the integral equation representation formula arising from the PDE. A Monte Carlo simulation is used as a benchmark to validate the formula’s accuracy and efficiency. In addition, the numerical examples are provided to demonstrate the effects of the mean-reversion on option prices and the characteristics of options with respect to several significant parameters. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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25 pages, 5457 KiB  
Article
Fourier Integral Operator Model of Market Liquidity: The Chinese Experience 2009–2010
by Peter B. Lerner
Mathematics 2022, 10(14), 2459; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142459 - 14 Jul 2022
Viewed by 1155
Abstract
This paper proposes and motivates a dynamical model of the Chinese stock market based on linear regression in a dual state-space connected to the original state-space of correlations between the volume-at-price buckets by a Fourier transform. We apply our model to the price [...] Read more.
This paper proposes and motivates a dynamical model of the Chinese stock market based on linear regression in a dual state-space connected to the original state-space of correlations between the volume-at-price buckets by a Fourier transform. We apply our model to the price migration of orders executed by Chinese brokerages in 2009–2010. We use our brokerage tapes to conduct a natural experiment assuming that tapes correspond to randomly assigned, informed, and uninformed traders. Our analysis demonstrates that customers’ orders were tightly correlated—in the highly nonlinear sense of prediction by the neural networks—with Chinese market sentiment, significantly correlated with the returns of the Chinese stock market, and exhibited no correlations with the yield of the bellwether bond of the Bank of China. We did not notice any spike of illiquidity transmitting from the US Flash Crash in May 2010 to trading in China. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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16 pages, 372 KiB  
Article
A Modified Black-Scholes-Merton Model for Option Pricing
by Paula Morales-Bañuelos, Nelson Muriel and Guillermo Fernández-Anaya
Mathematics 2022, 10(9), 1492; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091492 - 30 Apr 2022
Cited by 6 | Viewed by 3036
Abstract
Financial derivatives have grown in importance over the last 40 years with futures and options being actively traded on a daily basis throughout the world. The need to accurately price such financial instruments has, thus, also increased, which has given rise to several [...] Read more.
Financial derivatives have grown in importance over the last 40 years with futures and options being actively traded on a daily basis throughout the world. The need to accurately price such financial instruments has, thus, also increased, which has given rise to several mathematical models among which is that of Black, Scholes, and Merton whose wide acceptance is partly justified by its ability to price derivatives in mature and well-developed markets. For instruments traded in emerging markets, however, the accurateness of the BSM model is unproven and new proposals need be made to face the pricing challenge. In this paper we develop a model, inspired in conformable calculus, providing greater flexibilities for these markets. After developing the theoretical aspects of the model, we present an empirical application. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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26 pages, 5713 KiB  
Article
Is Promoting Green Finance in Line with the Long-Term Market Mechanism? The Perspective of Chinese Commercial Banks
by Kai Zhang and Xinmiao Zhou
Mathematics 2022, 10(9), 1374; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091374 - 20 Apr 2022
Cited by 7 | Viewed by 2267
Abstract
Green finance is a sustainable force in promoting green development. China’s social financing structure determines the key role that green credit plays in sustainable development. Under the dual pressure of future economic downturn and huge capital gaps, it is worth exploring whether to [...] Read more.
Green finance is a sustainable force in promoting green development. China’s social financing structure determines the key role that green credit plays in sustainable development. Under the dual pressure of future economic downturn and huge capital gaps, it is worth exploring whether to continue promoting green credit that conforms to the long-term market mechanism. From the perspective of Chinese commercial banks, this paper analyzes whether promoting green credit is compatible with the incentives and their profit maximization goals. To this end, the research in this paper is based on the following three aspects: (1) Based on financial analysis, this paper reveals the different pricing of green industries in the capital market and credit market and explains the mechanism through which green credit policies improve the operating conditions of commercial banks; (2) combined with the conclusions from the literature and financial analysis, the influence of different index types on the modeling results is analyzed, and it is determined that the main reasons causing a decline in the return on assets are the excessive expansion of capital and the decline in internal resource-use efficiency; (3) a data envelopment model (more accurately, SBM-DDF) with undesirable outputs is established to dynamically analyze the operating efficiency of Chinese commercial banks, and the role of green credit in improving efficiency is studied. The main conclusions of this paper are as follows: if Chinese commercial banks increase their proportion of green credit, they can not only increase their profit scale but also improve and optimize the allocation of their internal resources, thus improving their operating efficiency. The main sample of this study comprises 43 commercial banks in China from 2007 to 2020. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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14 pages, 347 KiB  
Article
Tracking a Well Diversified Portfolio with Maximum Entropy in the Mean
by Argimiro Arratia, Henryk Gzyl and Silvia Mayoral
Mathematics 2022, 10(4), 557; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040557 - 11 Feb 2022
Cited by 2 | Viewed by 1460
Abstract
In this work we address the following problem: Having chosen a well diversified portfolio, we show how to improve on its return, maintaining the diversification. In order to achieve this boost on return we construct a neighborhood of the well diversified portfolio and [...] Read more.
In this work we address the following problem: Having chosen a well diversified portfolio, we show how to improve on its return, maintaining the diversification. In order to achieve this boost on return we construct a neighborhood of the well diversified portfolio and find a portfolio that maximizes the return in that neighborhood. For that we use the method of maximum entropy in the mean to find a portfolio that yields any possible return up to the maximum return within the neighborhood. The implicit bonus of the method is that if the benchmark portfolio has acceptable risk and diversification, the portfolio of maximum return in that neighborhood will also have acceptable risk and diversification. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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32 pages, 962 KiB  
Article
Real Economy Effects on Consumption-Based CAPM
by Dandan Zheng, Shusheng Ding, Tianxiang Cui and Huan Jin
Mathematics 2022, 10(3), 360; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030360 - 25 Jan 2022
Cited by 1 | Viewed by 2799
Abstract
The consumption-based capital asset pricing model (CCAPM) is an attractive research field in finance, and extant studies have examined the impacts of different factors towards traditional CCAPM, intending to improve the model from the practical perspective. In this paper, we comprehensively scrutinize the [...] Read more.
The consumption-based capital asset pricing model (CCAPM) is an attractive research field in finance, and extant studies have examined the impacts of different factors towards traditional CCAPM, intending to improve the model from the practical perspective. In this paper, we comprehensively scrutinize the real economy effects on the CCAPM by comprising expenditure on durable, expenditure on non-durable goods, services, and real estate four factors. Our study pays great attention to the real economy effect on the CCAPM based on two types of portfolios. By employing both time-series and cross-sectional analysis, our empirical results suggest that the real economy factors can help traditional CCAPM to produce better asset pricing results. Particularly, incorporating the real estate component into the CCAPM model can improve its explanation power on the stock market risk. Our results are potentially useful for investors, portfolios managers and policy makers towards the CCAPM. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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23 pages, 23294 KiB  
Article
The Nexus between Sovereign CDS and Stock Market Volatility: New Evidence
by Laura Ballester, Ana Mónica Escrivá and Ana González-Urteaga
Mathematics 2021, 9(11), 1201; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111201 - 25 May 2021
Cited by 3 | Viewed by 1864
Abstract
This paper extends the studies published to date by performing an analysis of the causal relationships between sovereign CDS spreads and the estimated conditional volatility of stock indices. This estimation is performed using a vector autoregressive model (VAR) and dynamically applying the Granger [...] Read more.
This paper extends the studies published to date by performing an analysis of the causal relationships between sovereign CDS spreads and the estimated conditional volatility of stock indices. This estimation is performed using a vector autoregressive model (VAR) and dynamically applying the Granger causality test. The conditional volatility of the stock market has been obtained through various univariate GARCH models. This methodology allows us to study the information transmissions, both unidirectional and bidirectional, that occur between CDS spreads and stock volatility between 2004 and 2020. We conclude that CDS spread returns cause (in the Granger sense) conditional stock volatility, mainly in Europe and during the sovereign debt crisis. This transmission dynamic breaks down during the COVID-19 period, where there are high bidirectional relationships between the two markets. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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20 pages, 2094 KiB  
Article
Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold
by Mehmet Balcilar, Riza Demirer and Festus V. Bekun
Mathematics 2021, 9(8), 915; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080915 - 20 Apr 2021
Cited by 2 | Viewed by 2130
Abstract
This paper introduces a new methodology to estimate time-varying alphas and betas in conditional factor models, which allows substantial flexibility in a time-varying framework. To circumvent problems associated with the previous approaches, we introduce a Bayesian time-varying parameter model where innovations of the [...] Read more.
This paper introduces a new methodology to estimate time-varying alphas and betas in conditional factor models, which allows substantial flexibility in a time-varying framework. To circumvent problems associated with the previous approaches, we introduce a Bayesian time-varying parameter model where innovations of the state equation have a spike-and-slab mixture distribution. The mixture distribution specifies two states with a specific probability. In the first state, the innovation variance is set close to zero with a certain probability and parameters stay relatively constant. In the second state, the innovation variance is large and the change in parameters is normally distributed with mean zero and a given variance. The latent state is specified with a threshold that governs the state change. We allow a separate threshold for each parameter; thus, the parameters may shift in an unsynchronized manner such that the model moves from one state to another when the change in the parameter exceeds the threshold and vice versa. This approach offers great flexibility and nests a plethora of other time-varying model specifications, allowing us to assess whether the betas of conditional factor models evolve gradually over time or display infrequent, but large, shifts. We apply the proposed methodology to industry portfolios within a five-factor model setting and show that the threshold Capital Asset Pricing Model (CAPM) provides robust beta estimates coupled with smaller pricing errors compared to the alternative approaches. The results have significant implications for the implementation of smart beta strategies that rely heavily on the accuracy and stability of factor betas and yields. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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20 pages, 1966 KiB  
Article
Interdependence between Green Financial Instruments and Major Conventional Assets: A Wavelet-Based Network Analysis
by Román Ferrer, Rafael Benítez and Vicente J. Bolós
Mathematics 2021, 9(8), 900; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080900 - 19 Apr 2021
Cited by 27 | Viewed by 5036
Abstract
This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based [...] Read more.
This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based network approach that allows for assessing the degree of interconnection between green financial products and traditional asset classes across different investment horizons is applied. The empirical results show that green bonds are tightly linked to Treasury and investment-grade corporate bonds, while green stocks are strongly tied to general stocks, regardless of the specific time period and investment horizon considered. However, despite their common climate-friendly nature, there is no a remarkable association between green bonds and green stocks. This means that these green investments constitute basically two independent asset classes, with a distinct risk-return profile and aimed at a different type of investor. Furthermore, green financial products have a weak connection with high-yield corporate bonds and crude oil. These findings can have important implications for investors and policy makers in terms of investment decision, hedging strategies, and sustainability and energy policies. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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20 pages, 581 KiB  
Article
TAC Method for Fitting Exponential Autoregressive Models and Others: Applications in Economy and Finance
by Javier Cabello Sánchez, Juan Antonio Fernández Torvisco and Mariano R. Arias
Mathematics 2021, 9(8), 862; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080862 - 14 Apr 2021
Cited by 3 | Viewed by 1419
Abstract
There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for economic science. The solution of the first problem is as conclusive as it can be: working with the max-norm, [...] Read more.
There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for economic science. The solution of the first problem is as conclusive as it can be: working with the max-norm, we determine which datasets have best approximation by means of exponentials of the form f(t)=b+aexp(kt), we give a necessary and sufficient condition for some a,b,k∈R to be the coefficients that give the best approximation, and we give a best approximation by means of limits of exponentials when the dataset cannot be best approximated by an exponential. For the usual case, we have also been able to approximate the coefficients of the best approximation. As for the second purpose, we show how to approximate the coefficients of exponential models in economic science (this is only applying the R-package nlstac) and also the use of exponential autoregressive models, another well-established model in economic science, by utilizing the same tools: a numerical algorithm for fitting exponential patterns without initial guess designed by the authors and implemented in nlstac. We check one more time the robustness of this algorithm by successfully applying it to two very distant areas of economy: demand curves and nonlinear time series. This shows the utility of TAC (Spanish for CT scan) and highlights to what extent this algorithm can be useful. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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11 pages, 408 KiB  
Article
Grading Investment Diversification Options in Presence of Non-Historical Financial Information
by Clara Calvo, Carlos Ivorra, Vicente Liern and Blanca Pérez-Gladish
Mathematics 2021, 9(6), 692; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060692 - 23 Mar 2021
Cited by 1 | Viewed by 1458
Abstract
Modern portfolio theory deals with the problem of selecting a portfolio of financial assets such that the expected return is maximized for a given level of risk. The forecast of the expected individual assets’ returns and risk is usually based on their historical [...] Read more.
Modern portfolio theory deals with the problem of selecting a portfolio of financial assets such that the expected return is maximized for a given level of risk. The forecast of the expected individual assets’ returns and risk is usually based on their historical returns. In this work, we consider a situation in which the investor has non-historical additional information that is used for the forecast of the expected returns. This implies that there is no obvious statistical risk measure any more, and it poses the problem of selecting an adequate set of diversification constraints to mitigate the risk of the selected portfolio without losing the value of the non-statistical information owned by the investor. To address this problem, we introduce an indicator, the historical reduction index, measuring the expected reduction of the expected return due to a given set of diversification constraints. We show that it can be used to grade the impact of each possible set of diversification constraints. Hence, the investor can choose from this gradation, the set better fitting his subjective risk-aversion level. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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22 pages, 1983 KiB  
Article
An Econometric Approach Regarding the Impact of Fiscal Pressure on Equilibrium: Evidence from Electricity, Gas and Oil Companies Listed on the New York Stock Exchange
by Larissa Batrancea
Mathematics 2021, 9(6), 630; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060630 - 16 Mar 2021
Cited by 47 | Viewed by 2699
Abstract
The matter of fiscal pressure is more current than ever in most countries around the world for various reasons. In the first place, disruptive phenomena such as financial crises put tremendous pressure on worldwide economies. Secondly, high taxes trigger an overall reduction in [...] Read more.
The matter of fiscal pressure is more current than ever in most countries around the world for various reasons. In the first place, disruptive phenomena such as financial crises put tremendous pressure on worldwide economies. Secondly, high taxes trigger an overall reduction in the level of investments aiming at creating stable and well-paid jobs. Thirdly, the income generated by the majority of taxpayers is subject to excessive taxation, which may fuel tax evasion acts. On these grounds, the article is the first empirical research investigating the impact of fiscal pressure on the financial equilibrium of energy companies listed on the New York Stock Exchange. The sample included 88 electricity, gas, and oil companies from around the world, which were analyzed over a time span of 16 years, including the periods before, during, and after the 2008 global financial crisis. The methodology entailed estimating econometric models via Panel Least Squares (cross-section weights) with and without time fixed effects. Empirical results showed that fiscal pressure had a stronger impact on the short-term and long-term equilibrium of electricity and oil companies than on the equilibrium of gas companies. The study can serve as a compass for the managers of energy companies interested in estimating the evolution of company equilibrium state when considering other potential financial downturns. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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25 pages, 1474 KiB  
Article
Smooth Break Detection and De-Trending in Unit Root Testing
by Furkan Emirmahmutoglu, Tolga Omay, Syed Jawad Hussain Shahzad and Safwan Mohd Nor
Mathematics 2021, 9(4), 371; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040371 - 13 Feb 2021
Cited by 12 | Viewed by 2328
Abstract
This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence [...] Read more.
This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence of power comparisons among alternative unit root tests that accommodate smooth or sharp structural breaks. The power experiments demonstrate that the unit root tests utilizing the Fourier function lead to unexpected results. Furthermore, through simulation studies, we investigate the source of such unexpected outcomes. Moreover, we provide the asymptotic distribution of two recently proposed unit root tests, namely Fourier-Augmented Dickey–Fuller (FADF) and Fourier-Kapetanios, Shin and Shell (FKSS), which are not given in the original studies. Lastly, we find that the selection of de-trending function is pivotal for unit root testing with structural breaks. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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13 pages, 318 KiB  
Article
Mean Squared Variance Portfolio: A Mixed-Integer Linear Programming Formulation
by Francisco Fernández-Navarro, Luisa Martínez-Nieto, Mariano Carbonero-Ruz and Teresa Montero-Romero
Mathematics 2021, 9(3), 223; https://0-doi-org.brum.beds.ac.uk/10.3390/math9030223 - 23 Jan 2021
Cited by 9 | Viewed by 2648
Abstract
The mean-variance (MV) portfolio is typically formulated as a quadratic programming (QP) problem that linearly combines the conflicting objectives of minimizing the risk and maximizing the expected return through a risk aversion profile parameter. In this formulation, the two objectives are expressed in [...] Read more.
The mean-variance (MV) portfolio is typically formulated as a quadratic programming (QP) problem that linearly combines the conflicting objectives of minimizing the risk and maximizing the expected return through a risk aversion profile parameter. In this formulation, the two objectives are expressed in different units, an issue that could definitely hamper obtaining a more competitive set of portfolio weights. For example, a modification in the scale in which returns are expressed (by one or percent) in the MV portfolio, implies a modification in the solution of the problem. Motivated by this issue, a novel mean squared variance (MSV) portfolio is proposed in this paper. The associated optimization problem of the proposed strategy is very similar to the Markowitz optimization, with the exception of the portfolio mean, which is presented in squared form in our formulation. The resulting portfolio model is a non-convex QP problem, which has been reformulated as a mixed-integer linear programming (MILP) problem. The reformulation of the initial non-convex QP problem into an MILP allows for future researchers and practitioners to obtain the global solution of the problem via the use of current state-of-the-art MILP solvers. Additionally, a novel purely data-driven method for determining the optimal value of the hyper-parameter that is associated with the MV and MSV approaches is also proposed in this paper. The MSV portfolio has been empirically tested on eight portfolio time series problems with three different estimation windows (composing a total of 24 datasets), showing very competitive performance in most of the problems. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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21 pages, 560 KiB  
Article
Non-Linear Interdependencies between International Stock Markets: The Polish and Spanish Case
by Francisco Jareño, Ana Escribano and Monika W. Koczar
Mathematics 2021, 9(1), 6; https://0-doi-org.brum.beds.ac.uk/10.3390/math9010006 - 22 Dec 2020
Cited by 3 | Viewed by 1855
Abstract
This research analyzes non-linear interdependencies between the Polish (WIG20) and the Spanish (IBEX 35) stock market returns with some other relevant international stock market returns, such as the German (DAX-30), the British (FTSE-100), the American (S&P 500) and the Chinese (SSE Composite) stock [...] Read more.
This research analyzes non-linear interdependencies between the Polish (WIG20) and the Spanish (IBEX 35) stock market returns with some other relevant international stock market returns, such as the German (DAX-30), the British (FTSE-100), the American (S&P 500) and the Chinese (SSE Composite) stock markets. In addition, this research focuses on the impact of the stage of the economy on these interdependencies, in concrete, on the influence of the 2008 Global Financial Crisis. To that end, we use a nonlinear autoregressive distributed lag (NARDL) approach in the sample period between January 1998 to December 2018. Our results show positive interdependencies between the Polish and the Spanish stock markets with the international reference stock markets analyzed in this research, as well as significant long-run relations between most of the stock markets. Furthermore, the Polish and the Spanish stock market returns may similarly react to positive and negative changes in international stock market returns, evidencing strong short-run asymmetry. In addition, both countries show great persistence in response to both positive and negative changes in stock market returns in the other mayor international markets. Finally, the NARDL model proposed in this research would show good explanatory power, mainly to changes in the international stock market returns, except for the Chinese market. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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23 pages, 5939 KiB  
Article
Construction and Analysis of Actuarial Model of the Influence of Personal Tax Deferred Commercial Pension Insurance on Personal Pension Wealth in China
by Wenguang Yu, Fei Wang, Qianshun Sang, Qi Wang, Yixin Gao, Yujuan Huang, Xinliang Yu, Jinrui Xiao, Huilin Zhu and Chaoran Cui
Mathematics 2020, 8(12), 2124; https://0-doi-org.brum.beds.ac.uk/10.3390/math8122124 - 27 Nov 2020
Cited by 1 | Viewed by 2051
Abstract
Taking mortality distribution, surrender value, and tax relief factors into consideration, the authors construct an actuarial model for the influence of personal income tax deferred commercial pension insurance on changes in personal pension wealth and adopts a numerical simulation to deliver the corresponding [...] Read more.
Taking mortality distribution, surrender value, and tax relief factors into consideration, the authors construct an actuarial model for the influence of personal income tax deferred commercial pension insurance on changes in personal pension wealth and adopts a numerical simulation to deliver the corresponding changes in personal pension wealth to different initial insured age and different initial insured annual salary. In order to better measure the security level of the commercial pension insurance, the model for the net replacement rate of pension of the commercial pension insurance was further constructed. The results show that the effect of participating in the personal income tax deferred commercial pension insurance on the present value of personal pension wealth depends on the combined action of the initial insured age and the initial annual salary. Under the same insured age, because men retire later and work longer than women, men can obtain a higher accumulation of personal pension wealth than women. For insured persons with different income levels, high-income groups can obtain higher personal pension wealth growth, and although low-income groups cannot obtain higher personal pension wealth growth, they can obtain a significant increase in the pension replacement rate by participating in the insurance, thereby better guaranteeing their living standards after retirement. Regardless of the income level, tax relief can be obtained once participating in the insurance, but the value may vary. The optimal tax-saving age for men is 23 years old, and for women 25 years old. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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17 pages, 3541 KiB  
Article
Role of Economic Policy Uncertainty in the Connectedness of Cross-Country Stock Market Volatilities
by Mudassar Hasan, Muhammad Abubakr Naeem, Muhammad Arif, Syed Jawad Hussain Shahzad and Safwan Mohd Nor
Mathematics 2020, 8(11), 1904; https://0-doi-org.brum.beds.ac.uk/10.3390/math8111904 - 31 Oct 2020
Cited by 9 | Viewed by 2147
Abstract
The implied volatility index is a forward-looking indicator of fear among stock market participants. We examine the extent to which the connectedness of fear among global stock markets is driven by the cross-country connectedness of economic policy uncertainty (EPU). We use data on [...] Read more.
The implied volatility index is a forward-looking indicator of fear among stock market participants. We examine the extent to which the connectedness of fear among global stock markets is driven by the cross-country connectedness of economic policy uncertainty (EPU). We use data on stock market fear and EPU indices for 13 countries, which spans from January 2011 to December 2018. To measure the connectedness among stock market fear and EPU of our sample countries, we employ two connectedness models. A cross-sectional regression model is further employed to ascertain the extent to which EPU connectedness between two countries explains the connectedness of fear between their stock markets, while controlling for bilateral linkage and country-specific factors. We find that EPU connectedness between any two partner countries significantly drives the connectedness of fear between their stock markets. The driving potential not only holds for short- and long-term connectedness, but also after controlling for bilateral linkages (bilateral trade, geographical distance, common language) and country-specific (trade and financial openness of the transmitter country) factors indicating robustness in our results. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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28 pages, 816 KiB  
Article
Industry Risk Factors and Stock Returns of Malaysian Oil and Gas Industry: A New Look with Mean Semi-Variance Asset Pricing Framework
by Mohammad Enamul Hoque and Soo-Wah Low
Mathematics 2020, 8(10), 1732; https://0-doi-org.brum.beds.ac.uk/10.3390/math8101732 - 09 Oct 2020
Cited by 7 | Viewed by 2278
Abstract
This study employs a mean semi-variance asset pricing framework to examine the influence of risk factors on stock returns of oil and gas companies. This study also examines how downside risk is priced in stock performance. The time-series estimations expose that market, size, [...] Read more.
This study employs a mean semi-variance asset pricing framework to examine the influence of risk factors on stock returns of oil and gas companies. This study also examines how downside risk is priced in stock performance. The time-series estimations expose that market, size, momentum, oil, gas, and exchange rate have significant impacts on oil and gas stock returns, but effects are heterogeneous depending on an individual stock. The two-stage cross-section estimations provide new insights about investors’ risk-return trade-off when facing downside risks. The results show that downside risk exposures to market, momentum, oil, and exchange rate factors are negatively priced in the Malaysian oil and gas stocks. This implies that investors are penalized for their downside exposure to these risk factors, and such inference is consistent with the risk preference explanation of prospect theory. Liquefied natural gas (LNG) is the only risk factor found to be positively priced in the returns of oil and gas stocks. Additionally, we find a negative relationship between LNG factor and total risk. This suggests that as the risk exposure to LNG increases, the total risk decreases, implying that the LNG risk factor is an idiosyncratic risk and not a systematic risk factor. Such interpretation is consistent with the correlation result, which shows no association between LNG and the market risk factor. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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