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Mathematical and Statistical Methods Applications in Finance

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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 (31 December 2021) | Viewed by 33262

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Prof. Dr. Miltiadis Chalikias

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Department of Accounting and Finance, Univercity of West Attica, Aegaleo, Greece
Interests: mathematical statistics (design of experiments); applied statistics
Special Issues, Collections and Topics in MDPI journals

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Dear Colleagues,

Over recent decades, mathematical and statistical models’ applications in finance have become more and more popular both in a managerial and research context. On the one hand, there are specific aspects of mathematics with a high impact on finance, such as the models dealing with portfolio theory, capital pricing and risk management. On the other hand, statistical models have many applications in finance as well, such as linear and non-linear time series or statistical tools. The aim of this Special Issue is to bridge the gap between the classical models of mathematics and statistics and their applications in real cases of finance. Authors can submit their contributions concerning applications or developments of mathematical and statistical models in finance topics such as risky assets, discrete time market models, portfolio management, forward and future contracts, option pricing, stochastic interest rates, portfolio theory, capital pricing, risk-neural probabilities, financial multiperiod markets, ARMA process, ARIMA processes, seasonal models, maximum likelihood estimation, quasi-maximum likelihood, Kernel estimators in time series, dynamical systems, stochastic integrals, stochastics differential equations, classical arbitrage theory, Fourier methods, stochastic interest rate models, and discrete time approximation.

It is my pleasure to invite authors to contribute to this Special Issue by submitting research articles that will be subject to rigorous peer review aiming to contribute to the development of the relevant research field.

Dr. Miltiadis Chalikias
Guest Editor

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

Mathematical models
Statistical models
Finance
Financial mathematics
Portfolio theory
Risk management
Linear time series
Non-linear time series

Published Papers (12 papers)

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Research

24 pages, 1073 KiB

Open AccessArticle

High-Frequency Quote Volatility Measurement Using a Change-Point Intensity Model

by Zhicheng Li and Haipeng Xing

Mathematics 2022, 10(4), 634; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040634 - 18 Feb 2022

Cited by 1 | Viewed by 1716

Abstract

Quote volatility is important in determining the cost of demand in a high frequency (HF) order market. This paper proposes a new model to measure quote volatility based on the point process and price-change duration. Specifically, we built a change-point intensity (CPI) model to describe the dynamics of price-change events for a given level of threshold. The instantaneous volatility of quote price can be calculated at any time according to price-change intensities. Based on this, we can quantify the cost of demanding liquidity for traders with different trading latency by using integrated variances. Furthermore, we use the autoregressive conditional intensity (ACI) model proposed by Russell (1999) as a benchmark comparison. The results suggest that our model has better performance of both in-sample fitness and out-of-sample prediction. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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25 pages, 2570 KiB

Open AccessFeature PaperArticle

Do Commodities React More to Time-Varying Rare Disaster Risk? A Comparison of Commodity and Financial Assets

by Peng Chen and Ting Huang

Mathematics 2022, 10(3), 445; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030445 - 29 Jan 2022

Cited by 1 | Viewed by 1975

Abstract

Using a rare disaster risk database from almost the last one hundred years, we examine the differences in the reaction of asset prices to rare disaster risk between commodity and financial assets. We first employ time-varying parameter VAR (TVP-VAR) models to investigate the role of rare disaster risk in the price dynamics of major asset markets. The results indicate that disaster risk generally has a more intense and persistent impact on crude oil and stock markets when compared to gold and bond markets. However, the role of rare disaster risk differs substantially between commodity and financial assets, as well as between the short and long term. Moreover, when using a nonparametric causality-in-quantiles method to detect causal relationships, we provide evidence of the nonlinear causality effect of rare disaster risks on asset volatilities, and not their returns, except for crude oil. In addition, we demonstrate that augmenting a diversified portfolio of stock or bonds with gold can significantly increase its risk-adjusted performance. The findings have important implications for investors as well as policymakers. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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18 pages, 2857 KiB

Open AccessArticle

Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19

by Chih-Wen Hsiao, Ya-Chuan Chan, Mei-Yu Lee and Hsi-Peng Lu

Mathematics 2021, 9(21), 2719; https://0-doi-org.brum.beds.ac.uk/10.3390/math9212719 - 26 Oct 2021

Cited by 3 | Viewed by 1901

Abstract

In this paper, we provide a mathematical and statistical methodology using heteroscedastic estimation to achieve the aim of building a more precise mathematical model for complex financial data. Considering a general regression model with explanatory variables (the expected value model form) and the error term (including heteroscedasticity), the optimal expected value and heteroscedastic model forms are investigated by linear, nonlinear, curvilinear, and composition function forms, using the minimum mean-squared error criterion to show the precision of the methodology. After combining the two optimal models, the fitted values of the financial data are more precise than the linear regression model in the literature and also show the fitted model forms in the example of Taiwan stock price index futures that has three cases: (1) before COVID-19, (2) during COVID-19, and (3) the entire observation time period. The fitted mathematical models can apparently show how COVID-19 affects the return rates of Taiwan stock price index futures. Furthermore, the fitted heteroscedastic models also show how COVID-19 influences the fluctuations of the return rates of Taiwan stock price index futures. This methodology will contribute to the probability of building algorithms for computing and predicting financial data based on mathematical model form outcomes and assist model comparisons after adding new data to a database. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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21 pages, 2660 KiB

Open AccessArticle

Contribution of the Optimization of Financial Structure to the Real Economy: Evidence from China’s Financial System Using TVP-VAR Model

by Xiaoye Liu, Kedong Yin and Yun Cao

Mathematics 2021, 9(18), 2232; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182232 - 11 Sep 2021

Cited by 5 | Viewed by 2054

Abstract

How the financial structure promotes the development of real economy has always been a research topic in academia. By analyzing the characteristics of China’s financial system, this paper constructs the Finance Structure Index (FSI) from the perspectives of structural efficiency, financing structure and industry structure, and interprets the trend of the FSI. Based on the quarterly data of China from 2004 to 2020, this paper constructs a time-varying parameter-vector autoregression (TVP-VAR) model to study the dynamic impact of finance structure on the growth and optimization of the structure of the real economy. The empirical analysis results show that the response of the real economy has time-varying characteristics. Early on, financial structure has a promotion effect on the scale of the real economy, but the impact on the structure is not clear. In the middle, the effect of promoting the scale decreases slightly and then rebounds rapidly, while the optimization of the structure is inhibited. Later, it has a significant promoting effect and an obvious time-lag effect. Moreover, the impact of the financial structure is unstable. It is necessary to improve the efficiency and quality of the transmission of the optimization of the financial structure to the real economy. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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20 pages, 2871 KiB

Open AccessArticle

Profiting on the Stock Market in Pandemic Times: Study of COVID-19 Effects on CESEE Stock Markets

by Tihana Škrinjarić

Mathematics 2021, 9(17), 2077; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172077 - 27 Aug 2021

Cited by 2 | Viewed by 2401

Abstract

This research deals with stock market reactions of Central Eastern and South Eastern European (CESEE) markets to the COVID-19 pandemic, via the event study methodology approach. Since the stock markets react quickly to certain announcements, the used methodology is appropriate to evaluate how the aforementioned markets reacted to certain events. The purpose of this research was to evaluate possibilities of obtaining profits on the stock markets during great turbulences, when a majority of the participants panic. More specifically, the contrarian trading strategies are observed if they can obtain gains, although a majority of the markets suffer great losses during pandemic shocks. The contributions to the existing literature of this research are as follows. Firstly, empirical research on CESEE stock markets regarding other relevant topics is still scarce and should be explored more. Secondly, the event study approach of COVID-19 effects utilized in this study has (to the knowledge of the author) not yet been explored on the aforementioned markets. Thirdly, based on the results of CESEE market reactions to specific announcements regarding COVID-19, a simulation of simple trading strategies will be made in order to estimate whether some investors could have profited in certain periods. The results of the study indicate promising results in terms of exploiting other investors’ panicking during the greatest decline of stock market indices. Namely, the initial results, as expected, indicate strong negative effects of specific COVID-19 announcements on the selected stock markets. Secondly, the obtained information was shown to be useful for contrarian strategy in order to exploit great dips in the stock market indices values. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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13 pages, 1938 KiB

Open AccessArticle

Covariance Principle for Capital Allocation: A Time-Varying Approach

by Jilber Urbina, Miguel Santolino and Montserrat Guillen

Mathematics 2021, 9(16), 2005; https://0-doi-org.brum.beds.ac.uk/10.3390/math9162005 - 21 Aug 2021

Cited by 3 | Viewed by 2825

Abstract

The covariance allocation principle is one of the most widely used capital allocation principles in practice. Risks change over time, so capital risk allocations should be time-dependent. In this paper, we propose a dynamic covariance capital allocation principle based on the variance-covariance of risks that change over time. The conditional correlation of risks is modeled by means of a dynamic conditional correlation (DCC) model. Unlike the static approach, we show that in our dynamic capital allocation setting, the distribution of risk capital allocations can be estimated, and the expected future allocations of capital can be predicted, providing a deeper understanding of the stochastic multivariate behavior of risks. The methodology presented in the paper is illustrated with an example involving the investment risk in a stock portfolio. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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15 pages, 498 KiB

Open AccessArticle

Trading Cryptocurrencies as a Pandemic Pastime: COVID-19 Lockdowns and Bitcoin Volume

by Alexander Guzmán, Christian Pinto-Gutiérrez and María-Andrea Trujillo

Mathematics 2021, 9(15), 1771; https://0-doi-org.brum.beds.ac.uk/10.3390/math9151771 - 27 Jul 2021

Cited by 25 | Viewed by 5234

Abstract

This paper examines the impact of COVID-19 lockdowns on Bitcoin trading volume. Using data from Apple mobility trends and several time-series econometric models, we find that investors became active participants during the COVID-19 pandemic period and traded more bitcoins on days with low mobility associated with lockdown mandates. These results remain robust after controlling for stocks and gold returns, the VIX index, and the level of attention and sentiment toward Bitcoin, as measured by Google search frequencies and the tone of Tweets discussing Bitcoin. These results suggest that when individual investors have ample free time on their hands, they trade cryptocurrencies as a pastime and use the Bitcoin market as a form of entertainment. Moreover, our results have important implications concerning investors’ herding behavior and overconfidence leading to noise trader risks and bubbles typically accompanied by high trading volume in cryptocurrency markets. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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22 pages, 1062 KiB

Open AccessArticle

Teaching CAPM for a Pre-Finance Graduate Program at the STEM Undergraduate Level: Linear Algebra Perspective

by Chi-Lu Peng, Wen-Kuei Chen and An-Pin Wei

Mathematics 2021, 9(14), 1668; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141668 - 15 Jul 2021

Cited by 2 | Viewed by 3028

Abstract

Students considering a masters in Finance Engineering or Artificial Intelligence in Finance are usually required to have an undergraduate background in science, technology, engineering, or mathematics (STEM). STEM students have a good capacity in mathematics and science, but they may not have studied financial theory. To facilitate the classroom teaching of the Capital Asset Pricing Model (CAPM) for STEM students, this paper seeks to expound on the essence of the theory starting at a two-asset framework. Adopting the concepts proposed by Merton (1972), this paper accomplishes the derivation by virtue of basic mathematical tools such as linear algebra, geometry, and statistics except for calculus. We show that the major aspects of Merton’s derivation of the CAPM for a universe of N assets may also be obtained in a two-asset world. Through the methods of this article, students will learn the in-depth theory of CAPM and its hands-on empirical tool. For example, students will realize that even if investors specify different threshold rewards, their different CAPMs will yield identical pricing for assets and portfolios. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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25 pages, 2864 KiB

Open AccessArticle

Alternative Financial Methods for Improving the Investment in Renewable Energy Companies

by José Luis Miralles-Quirós and María Mar Miralles-Quirós

Mathematics 2021, 9(9), 1047; https://0-doi-org.brum.beds.ac.uk/10.3390/math9091047 - 06 May 2021

Cited by 1 | Viewed by 2053

Abstract

Renewable energies have increased in importance in recent years due to the harm caused to the environment by fossil fuels. As a result, renewable energy companies seem to be profitable investment opportunities given their likely substantial future earnings. However, previous empirical evidence has not always agreed about this likely profitability. In addition, the methodologies employed in the existing empirical literature are complicated and not feasible for most investors to use. Therefore, it is proposed an approach which combines the use of performance measures, screening rules, devolatized returns and portfolio strategies, all of which can be implemented by investors. This approach results in high cumulative returns of more than 200% and other positive ratios, even when transaction costs are considered. This should encourage people to invest in these renewable energies and contribute to improving the environment. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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26 pages, 1455 KiB

Open AccessArticle

Spillover and Drivers of Uncertainty among Oil and Commodity Markets

by Muhammad Abubakr Naeem, Saqib Farid, Safwan Mohd Nor and Syed Jawad Hussain Shahzad

Mathematics 2021, 9(4), 441; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040441 - 23 Feb 2021

Cited by 20 | Viewed by 2563

Abstract

The paper aims to examine the spillover of uncertainty among commodity markets using Diebold–Yilmaz approach based on forecast error variance decomposition. Next, causal impact of global factors as drivers of uncertainty transmission between oil and other commodity markets is analyzed. Our analysis suggests that oil is a net transmitter to other commodity uncertainties, and this transmission significantly increased during the global financial crisis of 2008–2009. The use of linear and nonlinear causality tests indicates that the global factors have a causal effect on the overall connectedness, and especially on the spillovers from oil to other commodity uncertainties. Further segregation of transmissions between oil to individual commodity markets indicates that stock market implied volatility, risk spread, and economic policy uncertainty are the influential drivers of connectedness among commodity markets. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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21 pages, 368 KiB

Open AccessArticle

Influence of Bloomberg’s Investor Sentiment Index: Evidence from European Union Financial Sector

by Mariano González-Sánchez and M. Encina Morales de Vega

Mathematics 2021, 9(4), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040297 - 03 Feb 2021

Viewed by 2314

Abstract

A part of the financial literature has attempted to explain idiosyncratic asset shocks through investor behavior in response to company news and events. As a result, there has been an increase in the development of different investor sentiment measurements. This paper analyses whether the Bloomberg investor sentiment index has a causal relationship with the abnormal returns and volume shocks of major European Union (EU) financial companies through a sample of 85 financial institutions over 4 years (2014–2018) on a daily basis. The i.i.d. shocks are obtained from a factorial asset pricing model and ARMA-GARCH-type process; then we checked whether there is both individual and joint causality between the standardized residuals. The results show that the explanatory capacity of the shocks of the firm Bloomberg sentiment index is low, although there is empirical evidence that the effects correspond more to the situation of the financial subsector (banks, real estate, financial services and insurance) than to the company itself, with which we conclude that the sentiment index analyzed reflects a sectorial effect more than individual one. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

9 pages, 1543 KiB

Open AccessArticle

The Lie Algebraic Approach for Determining Pricing for Trade Account Options

by Shih-Hsien Tseng, Tien Son Nguyen and Ruei-Ci Wang

Mathematics 2021, 9(3), 279; https://0-doi-org.brum.beds.ac.uk/10.3390/math9030279 - 30 Jan 2021

Cited by 1 | Viewed by 1922

Abstract

In recent years, many advanced techniques have been applied to financial problems; however, very few scholars have used the Lie theory. The purpose of this study was to examine the options for a trade account through Lie symmetry analysis. According to our results, it is effective for determining analytical solutions for pricing issues and solving other partial differential equations. The proposed solution can be used by further researchers or practitioners in option pricing problems for better performance compared with the classical Black–Scholes model. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)

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