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Featured Papers in Mathematics and Finance
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Featured Papers in Mathematics and Finance

A special issue of Journal of Risk and Financial Management (ISSN 1911-8074). This special issue belongs to the section "Mathematics and Finance".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 27310

Special Issue Editors

Prof. Dr. W. Brent Lindquist

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA
Interests: mathematical and empirical finance; computational applied mathematics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Svetlozar (Zari) Rachev

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
Interests: mathematical and empirical finance; probability metrics; mass transportation problems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the seminal works of Kenneth Arrow, Fischer Black, Harry Markowitz, Robert Merton, Franco Modigliani, Paul Samuelson, Myron Scholes, Richard Thaler, James Tobin, and many others, mathematics, probability theory, and stochastic calculus have become the foundation of finance theories. This Special Issue is dedicated to new ideas in finance that are based on novel mathematical approaches. We welcome mathematical papers in all areas of quantitative finance, including, but not limited to, post-modern portfolio theory, dynamic asset pricing, efficient market hypothesis, behavioral finance, ESG finance, risk management, and financial models for high-frequency trading. We invite papers that challenge the mathematical foundations of finance and seek extensions of dynamic asset pricing beyond semimartingales, as shown in [1]. Additionally, we seek papers that clarify the mathematical correctness of basic finance notions and theories, such as performance measures [2] and no-arbitrage option pricing [3,4]. 

References

[1] Robert A. Jarrow. Philip Protter. Hasanjan Sayit. "No arbitrage without semimartingales." Ann. Appl. Probab. 19 (2) 596–616, April 2009. https://doi.org/10.1214/08-AAP554
[2] Reward–risk ratios Patrick Cheridito and Eduard Kromer, Journal of Investment Strategies, VOLUME 3, NUMBER 1 (DECEMBER 2013) PAGES: 3–18 DOI: 10.21314/JOIS.2013.022
[3] Abootaleb Shirvani, F. Fabozzi, Boryana Racheva-Iotova, S. Rachev, Option Pricing with Greed and Fear Factor: The Rational Finance Approach, The Journal of Derivatives, 2021, 2, 77–119.
[4] Yuan Hu, W. Brent Lindquist, Svetlozar T. Rachev, Abootaleb Shirvani and Frank J. Fabozzi, Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis, Journal of Economic Dynamics and Control, 2022, vol. 137, issue C.

About the Editor:

Dr. W. Brent Lindquist is a professor in the Department of Mathematics and Statistics at Texas Tech University, specializing in computational mathematical finance. He received his PhD in theoretical physics from Cornell, and transitioned to a career in computational mathematics at the Courant Institute for Mathematical Sciences at New York University. Prior to joining Texas Tech, Dr. Lindquist served as professor and chair in the Department of Applied Mathematics and Statistics at Stony Brook University, where he helped lead the transition of that department into one of the top 10 applied math programs in the country.
As a computational mathematician, Brent has developed theory and numerical methods for: portfolio optimization; option pricing; PDEs; flow in porous media; automated 3D image analysis for porous media, neuron, and fiber morphology; Riemann problems in 2D; hierarchy formation in social animal groups; and the numerical solution of Feynman diagrams. He is a co-recipient of the Lee Segal prize from the Society of Mathematical Biology. He was one of the founding developers of the Frontier package used to study reservoir flow at field scales and is the principal architect of the 3DMA-Rock code for studying flow at the pore-scale. Dr. Lindquist has over 100 publications, has presented his research in 25 countries on 5 continents, and participated as PI or co-PI in projects receiving $20M of grant funding. He has supervised 40 PhD students. 

Svetlozar (Zari) Todorov Rachev is a professor at Texas Tech University who specializes in mathematical finance, probability theory, and statistics. He is recognized for his significant contributions to probability metrics, derivative pricing, financial risk modeling, and econometrics. In the field of risk management, he is credited as the originator of the methodology behind FinAnalytica's flagship product which received several awards, including the "Best Market Risk Solution Provider" at the Waters Rankings in 2010, 2012, and 2015, and the "Most Innovative Specialist Vendor" at the Risk Awards in 2014.
Rachev earned an MSc degree from the Faculty of Mathematics at Sofia University in 1974, a PhD degree from Lomonosov Moscow State University in 1979, and a Dr Sci degree from Steklov Mathematical Institute in 1986. Rachev's contributions to mathematical finance include his work on the application of non-Gaussian models for risk assessment, option pricing, and their applications in portfolio theory. He is also known for introducing a new risk-return ratio, the "Rachev Ratio," which measures the reward potential relative to tail risk in a non-Gaussian setting.
In probability theory, Rachev's books on probability metrics and mass-transportation problems are widely cited.
In the 2023 edition of the Research.com Ranking of Top Scientists in the field of Economics and Finance, Rachev was ranked 540 in the world and 364 in the United States. In the same edition, he was also ranked number 386 among the Best Mathematics Scientists in the world.

Prof. Dr. W. Brent Lindquist
Prof. Dr. Svetlozar (Zari) Rachev
Guest Editors

Manuscript Submission Information

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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. Journal of Risk and Financial Management is an international peer-reviewed open access monthly 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 1400 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

  • mathematics of quantitative finance
  • semimartingales in finance
  • extensions of the fundamental asset pricing theorem beyond semimartingales
  • dynamic asset pricing approaches to behavioral finance
  • mathematical models in high-frequency finance
  • axiomatic approach to ESG finance
  • mathematical models reconciling market microstructure and dynamic asset pricing theory
  • mathematical models in momentum investing theory
  • mathematical models in optimal trade execution
  • mathematical models in technical analysis
  • mathematical models in active management theory
  • mathematical models in financial fundamental analysis

Published Papers (19 papers)

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Research

25 pages, 2381 KiB  
Article
Separating Equilibria with Search and Selection Effort: Evidence from the Auto Insurance Market
by David Rowell and Peter Zweifel
J. Risk Financial Manag. 2024, 17(4), 154; https://doi.org/10.3390/jrfm17040154 - 11 Apr 2024
Viewed by 437
Abstract
The objective of this paper is to assess the behavior of policyholders and insurance companies in the presence of adverse selection by accounting for costly search and selection efforts, respectively. Insurers seek to stave off high-risk types, while consumers are hypothesized to maximize [...] Read more.
The objective of this paper is to assess the behavior of policyholders and insurance companies in the presence of adverse selection by accounting for costly search and selection efforts, respectively. Insurers seek to stave off high-risk types, while consumers are hypothesized to maximize coverage at a given premium. Reaction functions are derived for the two players giving rise to Nash equilibria in efforts space, which are separating almost certainly regardless of the share of low risks in the market. Empirical evidence from the Australian market for automobile insurance is analyzed using Structural Equation Modeling. Convergence has been achieved with both the developmental and test samples. Both consumer search and insurer selection are found to be positively correlated with risk type, providing a good measure of empirical support for the theoretical model. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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17 pages, 568 KiB  
Article
Penalized Bayesian Approach-Based Variable Selection for Economic Forecasting
by Antonio Pacifico and Daniela Pilone
J. Risk Financial Manag. 2024, 17(2), 84; https://doi.org/10.3390/jrfm17020084 - 18 Feb 2024
Viewed by 1167
Abstract
This paper proposes a penalized Bayesian computational algorithm as an improvement to the LASSO approach for economic forecasting in multivariate time series. Methodologically, a weighted variable selection procedure is involved in handling high-dimensional and highly correlated data, reduce the dimensionality of the model [...] Read more.
This paper proposes a penalized Bayesian computational algorithm as an improvement to the LASSO approach for economic forecasting in multivariate time series. Methodologically, a weighted variable selection procedure is involved in handling high-dimensional and highly correlated data, reduce the dimensionality of the model and parameter space, and then select a promising subset of predictors affecting the outcomes. It is weighted because of two auxiliary penalty terms involved in prior specifications and posterior distributions. The empirical example addresses the issue of pandemic disease prediction and the effects on economic development. It builds on a large set of European and non-European regions to also investigate cross-unit heterogeneity and interdependency. According to the estimation results, density forecasts are conducted to highlight how the promising subset of covariates would help to predict potential contagion due to pandemic diseases. Policy issues are also discussed. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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18 pages, 361 KiB  
Article
Almost Perfect Shadow Prices
by Eberhard Mayerhofer
J. Risk Financial Manag. 2024, 17(2), 70; https://doi.org/10.3390/jrfm17020070 - 10 Feb 2024
Cited by 1 | Viewed by 984
Abstract
Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that [...] Read more.
Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
19 pages, 2425 KiB  
Article
Implementing Intraday Model-Free Implied Volatility for Individual Equities to Analyze the Return–Volatility Relationship
by Martin G. Haas and Franziska J. Peter
J. Risk Financial Manag. 2024, 17(1), 39; https://doi.org/10.3390/jrfm17010039 - 18 Jan 2024
Viewed by 1491
Abstract
We implement the VIX methodology on intraday data of a large set of individual equity options. We thereby consider approaches based on monthly option contracts, weekly option contracts, and a cubic spline interpolation approach. Relying on 1 min, 10 min, and 60 min [...] Read more.
We implement the VIX methodology on intraday data of a large set of individual equity options. We thereby consider approaches based on monthly option contracts, weekly option contracts, and a cubic spline interpolation approach. Relying on 1 min, 10 min, and 60 min model-free implied volatility measures, we empirically examine the individual equity return–volatility relationship on the intraday level using quantile regressions. The results confirm a negative contemporaneous link between stock returns and volatility, which is more pronounced in the tails of the distributions. Our findings hint at behavioral biases causing the asymmetric return–volatility link rather than the leverage and volatility-feedback effects. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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16 pages, 883 KiB  
Article
An Investigation into the Spatial Distribution of British Housing Market Activity
by David Paul Gray
J. Risk Financial Manag. 2024, 17(1), 22; https://doi.org/10.3390/jrfm17010022 - 06 Jan 2024
Viewed by 1217
Abstract
This paper sets out to consider how a simple and easy-to-estimate power-law exponent can be used by policymakers to assess changes in economic inequalities, where the data can have a long tail—common in analyses of economic disparities—yet does not necessarily deviate from log-normality. [...] Read more.
This paper sets out to consider how a simple and easy-to-estimate power-law exponent can be used by policymakers to assess changes in economic inequalities, where the data can have a long tail—common in analyses of economic disparities—yet does not necessarily deviate from log-normality. The paper finds that the time paths of the coefficient of variation and the exponents from Lavalette’s function convey similar inferences about inequalities when analysing the value of house purchases over the period 2001–2022 for England and Wales. The house price distribution ‘steepens’ in the central period, mostly covering the post-financial-crisis era. The distribution of districts’ expenditure on house purchases ‘steepens’ more quickly. This, in part, is related to the loose monetary policy associated with QE driving a wedge between London and the rest of the nation. As prices can rise whilst transactions decline, it may be better for policymakers to focus on the value of house purchases rather than house prices when seeking markers of changes in housing market activity. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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7 pages, 245 KiB  
Communication
Information Theory and the Pricing of Contingent Claims: An Alternative Derivation of the Black–Scholes–Merton Formula
by Thomas P. Davis
J. Risk Financial Manag. 2023, 16(12), 501; https://doi.org/10.3390/jrfm16120501 - 05 Dec 2023
Viewed by 1245
Abstract
This paper seeks to determine the best subjective probability to use to carry out expectation values of uncertain future cash flows with the smallest number of assumptions. This results in the unique distribution that guarantees no more information is present other than the [...] Read more.
This paper seeks to determine the best subjective probability to use to carry out expectation values of uncertain future cash flows with the smallest number of assumptions. This results in the unique distribution that guarantees no more information is present other than the stated assumptions. The result is a novel derivation of the well-known Black–Scholes equation without the need to introduce high-level mathematical machinery. This formalism fits nicely into introductory courses of finance, where the value of any financial instrument is given by the present value of uncertain future cash flows. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
22 pages, 707 KiB  
Article
Using the Capital Asset Pricing Model and the Fama–French Three-Factor and Five-Factor Models to Manage Stock and Bond Portfolios: Evidence from Timor-Leste
by Fernando Anuno, Mara Madaleno and Elisabete Vieira
J. Risk Financial Manag. 2023, 16(11), 480; https://doi.org/10.3390/jrfm16110480 - 12 Nov 2023
Cited by 1 | Viewed by 3324
Abstract
Timor-Leste is a new country still in the process of economic development and does not yet have a capital market for stock and bond investments. These two asset classes have been invested in international capital markets such as the US, the UK, Japan, [...] Read more.
Timor-Leste is a new country still in the process of economic development and does not yet have a capital market for stock and bond investments. These two asset classes have been invested in international capital markets such as the US, the UK, Japan, and Europe. We examine the performance of the capital asset pricing model (CAPM) and the Fama–French three-factor and five-factor models on the excess returns of Timor-Leste’s equity and bond investments in the international market over the period 2006 to 2019. Our empirical results show that the market factor (MKT) is positively and significantly associated with the excess returns of the CAPM and the Fama–French three-factor and five-factor models. Moreover, the two variables Small Minus Big (SMB) as a size factor and High Minus Low (HML) as a value factor have a negative and significant effect on the excess returns in the Fama–French three-factor model and five-factor model. Further analysis revealed that the explanatory power of the Fama–French five-factor model is that the Robust Minus Weak (RMW) factor as a profitability factor is positively and significantly associated with excess returns, while the Conservative Minus Aggressive (CMA) factor as an investment factor is insignificant. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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24 pages, 984 KiB  
Article
Relations among Bitcoin Futures, Bitcoin Spot, Investor Attention, and Sentiment
by Arun Narayanasamy, Humnath Panta and Rohit Agarwal
J. Risk Financial Manag. 2023, 16(11), 474; https://doi.org/10.3390/jrfm16110474 - 03 Nov 2023
Viewed by 1532
Abstract
This research investigates the function of price discovery between the Bitcoin futures and the spot markets while also analyzing the impact of investor sentiment and attention on these markets. This study utilizes various statistical models to examine the short-term and long-term relations between [...] Read more.
This research investigates the function of price discovery between the Bitcoin futures and the spot markets while also analyzing the impact of investor sentiment and attention on these markets. This study utilizes various statistical models to examine the short-term and long-term relations between these variables, including the bivariate Granger causality model, the ARDL and NARDL models, and the Johansen cointegration procedure with a vector error correction mechanism. The results suggest that there is no statistical evidence of price discovery between the Bitcoin spot price and futures, and the term structure of the Bitcoin futures neither enriches nor impairs this lead lag relation. However, the study finds robust evidence of a long-run cointegrating relation between the two markets and the presence of asymmetry in them. Moreover, this research indicates that investor sentiment exhibits a lead lag relation with both the Bitcoin futures and the spot markets, while investor attention only leads to the Bitcoin spot market, without showing any lead lag relation with the Bitcoin futures. These findings highlight the crucial role of investor behavior in affecting both Bitcoin futures and spot prices. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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17 pages, 401 KiB  
Article
Pricing Path-Dependent Options under Stochastic Volatility via Mellin Transform
by Jiling Cao, Xi Li and Wenjun Zhang
J. Risk Financial Manag. 2023, 16(10), 456; https://doi.org/10.3390/jrfm16100456 - 20 Oct 2023
Viewed by 1107
Abstract
In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction [...] Read more.
In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction term, we use Mellin transform. We also conduct a sensitivity analysis on these formulas, and compare the option prices calculated by them with those generated by Monte-Carlo simulation. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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18 pages, 2107 KiB  
Article
Interconnectedness of Cryptocurrency Uncertainty Indices with Returns and Volatility in Financial Assets during COVID-19
by Awad Asiri, Mohammed Alnemer and M. Ishaq Bhatti
J. Risk Financial Manag. 2023, 16(10), 428; https://doi.org/10.3390/jrfm16100428 - 26 Sep 2023
Viewed by 1431
Abstract
This paper investigates the dynamic relationship between cryptocurrency uncertainty indices and the movements in returns and volatility across spectrum of financial assets, comprising cryptocurrencies, precious metals, green bonds, and soft commodities. It employs a Time-Varying Parameter Vector Autoregressive (TVP-VAR) connectedness approach; the analysis [...] Read more.
This paper investigates the dynamic relationship between cryptocurrency uncertainty indices and the movements in returns and volatility across spectrum of financial assets, comprising cryptocurrencies, precious metals, green bonds, and soft commodities. It employs a Time-Varying Parameter Vector Autoregressive (TVP-VAR) connectedness approach; the analysis covers both the entire sample period spanning August 2015 to 31 December 2021 and the distinct phase of COVID-19 pandemic. The findings of the study reveal the interconnectedness of returns within these asset classes during the COVID-19 pandemic. In this context, cryptocurrency uncertainty indices emerge as influential transmitters of shocks to other financial asset categories and it significantly escalates throughout the crisis period. Additionally, the outcomes of the study imply that during times of heightened uncertainty, exemplified by events such as the COVID-19 pandemic, the feasibility of portfolio diversification for investors might be constrained. Consequently, the amplified linkages between financial assets through both forward and backward connections could potentially compromise financial stability. This research sheds light on the impact of cryptocurrency uncertainty on the broader financial market, particularly during periods of crisis. The findings have implications for investors and policymakers, emphasizing the need for a comprehensive understanding of the interconnectedness of financial assets and the potential risks associated with increased interdependence. By recognizing these dynamics, stakeholders can make informed decisions to enhance financial stability and manage portfolio risk effectively. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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15 pages, 363 KiB  
Article
Does Fiscal Consolidation Affect Non-Performing Loans? Global Evidence from Heavily Indebted Countries (HICs)
by Habib Ur Rahman, Adam Arian and John Sands
J. Risk Financial Manag. 2023, 16(9), 417; https://doi.org/10.3390/jrfm16090417 - 19 Sep 2023
Cited by 2 | Viewed by 1164
Abstract
This study explores fiscal consolidations’ impact on non-performing loans (NPLs) in highly indebted countries (HICs) following the global financial crisis (GFC) and subsequent sovereign debt crisis. A dynamic panel data estimator was applied to obtain the unbiased estimator due to NPLs’ time persistence. [...] Read more.
This study explores fiscal consolidations’ impact on non-performing loans (NPLs) in highly indebted countries (HICs) following the global financial crisis (GFC) and subsequent sovereign debt crisis. A dynamic panel data estimator was applied to obtain the unbiased estimator due to NPLs’ time persistence. The findings reveal that fiscal consolidation measures increase NPLs since they limit the household and business loan-serving capacity. Extended analysis categorises fiscal consolidation episodes into (1) the fiscal consolidation weak form (FCWE) and (2) the fiscal consolidation strong form (FCSE). The extended analysis results reveal that the FCWE and FCSE improve NPLs by 1.55% and 31.10%, respectively. The weak-to-strong form transition of the fiscal consolidation analysis resulted in improving NPLs by 28.55 percentage points. NPL definition challenges, the potential influence of loan restructuring and regulatory restrictions, and implications for policymakers and financial institutions in managing NPLs in highly indebted economies were explored. Investigating the potentially different effects of both forms of fiscal consolidation (FCWE and FCSE) on NPLs in countries with different definitions of NPLs, including a comparison study between different definitions, was identified as an implication for future research. Finally, future studies should examine how restrictions on IFRS 9 may affect the FCWE and NPL as well as FCSE and NPL associations. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
23 pages, 1540 KiB  
Article
Spatial Multivariate GARCH Models and Financial Spillovers
by Rosella Giacometti, Gabriele Torri, Kamonchai Rujirarangsan and Michela Cameletti
J. Risk Financial Manag. 2023, 16(9), 397; https://doi.org/10.3390/jrfm16090397 - 06 Sep 2023
Cited by 2 | Viewed by 1535
Abstract
We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows the conditional variance of log-returns of each bank to depend on past [...] Read more.
We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows the conditional variance of log-returns of each bank to depend on past volatility shocks to other banks and their past squared returns in a parsimonious way. The backtesting of the resulting risk measures provides evidence that (i) the multivariate GARCH model with Student’s t distribution is more accurate than both the standard multivariate Gaussian model and the Filtered Historical Simulation (FHS), and (ii) the introduction of a spatial component improves the assessment of risk profiles and the market risk spillovers. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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13 pages, 2245 KiB  
Article
Properties of VaR and CVaR Risk Measures in High-Frequency Domain: Long–Short Asymmetry and Significance of the Power-Law Tail
by Tetsuya Takaishi
J. Risk Financial Manag. 2023, 16(9), 391; https://doi.org/10.3390/jrfm16090391 - 01 Sep 2023
Viewed by 837
Abstract
This study investigates the properties of risk measure, value at risk (VaR) and conditional VaR (CVaR), using high-frequency Bitcoin data. These data allow us to conduct a high statistical analysis. Our findings reveal a disparity in VaR and CVaR values between the left [...] Read more.
This study investigates the properties of risk measure, value at risk (VaR) and conditional VaR (CVaR), using high-frequency Bitcoin data. These data allow us to conduct a high statistical analysis. Our findings reveal a disparity in VaR and CVaR values between the left and right tails of the return probability distributions. We refer to this disparity as “long–short asymmetry”. In the high-frequency domain, the tail distribution can be accurately described by a power-law function. Moreover, the ratio of CVaR to VaR is expected to be determined solely by the power-law exponent. Through empirical analysis, we confirm that this ratio property holds true for high confidence levels. Furthermore, we investigate the relationship between risk measures (VaR and CVaR) and realized volatility. We observe that they trace a trajectory in a two-dimensional plane. This trajectory changes gradually, indicating periods of both high and low risk. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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25 pages, 405 KiB  
Article
Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets
by Pierpaolo Angelini and Fabrizio Maturo
J. Risk Financial Manag. 2023, 16(8), 369; https://doi.org/10.3390/jrfm16080369 - 11 Aug 2023
Cited by 2 | Viewed by 1083
Abstract
Bound choices such as portfolio choices are studied in an aggregate fashion using an extension of the notion of barycenter of masses. This paper answers the question of whether such an extension is a natural fashion of studying bound choices or not. Given [...] Read more.
Bound choices such as portfolio choices are studied in an aggregate fashion using an extension of the notion of barycenter of masses. This paper answers the question of whether such an extension is a natural fashion of studying bound choices or not. Given n risky assets, the question of why it is appropriate to treat only two risky assets at a time inside the budget set of the decision-maker is handled in this paper. Two risky assets are two goods. They are two marginal goods. The question of why they always give rise to a joint good inside the budget set of the decision-maker is addressed by this research work. A single risky asset is viewed as a double one using four nonparametric joint distributions of probability. The variability of a joint distribution of probability always depends on the state of information and knowledge associated with a given decision-maker. For this reason, two variability tensors are defined to identify the riskiness of the same risky asset. A multilinear version of the Sharpe ratio is shown. It is based on tensors. After computing the expected return on an n-risky asset portfolio, its riskiness is obtained using mean quadratic differences developed through tensors. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
16 pages, 851 KiB  
Article
Multicriteria Portfolio Choice and Downside Risk
by Anna Rutkowska-Ziarko and Pawel Kliber
J. Risk Financial Manag. 2023, 16(8), 367; https://doi.org/10.3390/jrfm16080367 - 10 Aug 2023
Viewed by 814
Abstract
In this study, we investigated some extensions of the classical portfolio theory and try to evaluate them in a situation of crisis. We studied some additional criteria for portfolio selection, based on market multiples representing the overall situation of companies. Additionally, we investigated [...] Read more.
In this study, we investigated some extensions of the classical portfolio theory and try to evaluate them in a situation of crisis. We studied some additional criteria for portfolio selection, based on market multiples representing the overall situation of companies. Additionally, we investigated semi-variance as an alternative measure of risk. We developed a range of portfolios that were built using different criteria for risk and the fundamental values of companies from the Polish stock market. Then, we compared their returns during the crisis that occurred after the outbreak of the COVID-19 pandemic. The results of empirical research on the major companies traded on the Warsaw Stock Exchange reveal that investors can achieve better investment results by augmenting the standard Markowitz model with an additional criterion connected with the fundamental standing of companies, such as book-to-market or earnings-to-market ratios. The second result is that using nonclassical risk measures such as semi-variance instead of variance provides better results, and this method of measuring risk is especially essential in periods characterized by the collapse of the capital market. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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15 pages, 6635 KiB  
Article
The Six Decades of the Capital Asset Pricing Model: A Research Agenda
by Santosh Kumar, Ankit Kumar, Kamred Udham Singh and Sujit Kumar Patra
J. Risk Financial Manag. 2023, 16(8), 356; https://doi.org/10.3390/jrfm16080356 - 28 Jul 2023
Cited by 1 | Viewed by 2567
Abstract
This paper re-examines the presence of the Sharpe–Treynor–Lintner–Mossin capital asset pricing model (CAPM) in the finance literature and is accompanied by a bibliometric summary analysis. The popular model is in its sixth decade; we summarized the relevance of the CAPM using publication and [...] Read more.
This paper re-examines the presence of the Sharpe–Treynor–Lintner–Mossin capital asset pricing model (CAPM) in the finance literature and is accompanied by a bibliometric summary analysis. The popular model is in its sixth decade; we summarized the relevance of the CAPM using publication and citation trends, as well as identifying its most prolific and impactful contributors. This paper is based on a systematic review of the literature and was completed with the help of various bibliometric techniques. During the study process, we presented a map of various themes and areas of the CAPM and its evolution. Our findings indicate that the extant literature on this topic (the cost of capital, asset pricing, portfolio, risk management, beta, systematic risk, and value premium) is based on the principles and assumptions of the CAPM. We are considering suggestions on the future use, trend, and direction of the CAPM, based on our summary of thematically developed clusters. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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8 pages, 1445 KiB  
Communication
Exploring Implied Certainty Equivalent Rates in Financial Markets: Empirical Analysis and Application to the Electric Vehicle Industry
by Yifan He and Svetlozar Rachev
J. Risk Financial Manag. 2023, 16(7), 344; https://doi.org/10.3390/jrfm16070344 - 24 Jul 2023
Viewed by 948
Abstract
In this paper, we mainly study the impact of the implied certainty equivalent rate on investment in financial markets. First, we derived the mathematical expression of the implied certainty equivalent rate by using put-call parity, and then we selected some company stocks and [...] Read more.
In this paper, we mainly study the impact of the implied certainty equivalent rate on investment in financial markets. First, we derived the mathematical expression of the implied certainty equivalent rate by using put-call parity, and then we selected some company stocks and options; we considered the best-performing and worst-performing company stocks and options from the beginning of 2023 to the present for empirical research. By visualizing the relationship between the time to maturity, moneyness, and implied certainty equivalent rate of these options, we have obtained a universal conclusion—a positive implied certainty equivalent rate is more suitable for investment than a negative implied certainty equivalent rate, but for a positive implied certainty equivalent rate, a larger value also means a higher investment risk. Next, we applied these results to the electric vehicle industry, and by comparing several well-known US electric vehicle production companies, we further strengthened our conclusions. Finally, we give a warning concerning risk, that is, investment in the financial market should not focus solely on the implied certainty equivalent rate, because investment is not an easy task, and many factors need to be considered, including some factors that are difficult to predict with models. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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17 pages, 3696 KiB  
Article
A New Entropic Measure for the Causality of the Financial Time Series
by Peter B. Lerner
J. Risk Financial Manag. 2023, 16(7), 338; https://doi.org/10.3390/jrfm16070338 - 17 Jul 2023
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Abstract
A new econometric methodology based on deep learning is proposed for determining the causality of the financial time series. This method is applied to the imbalances in daily transactions in individual stocks and also in exchange-traded funds (ETFs) with a nanosecond time stamp. [...] Read more.
A new econometric methodology based on deep learning is proposed for determining the causality of the financial time series. This method is applied to the imbalances in daily transactions in individual stocks and also in exchange-traded funds (ETFs) with a nanosecond time stamp. Based on our method, we conclude that transaction imbalances of ETFs alone are more informative than transaction imbalances in the entire market despite the domination of single-issue stocks in imbalance messages. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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24 pages, 849 KiB  
Article
The Effects of Option Trading Behavior on Option Prices
by Han-Sheng Chen and Sanjiv Sabherwal
J. Risk Financial Manag. 2023, 16(7), 337; https://doi.org/10.3390/jrfm16070337 - 16 Jul 2023
Viewed by 1908
Abstract
This paper investigates the relationship between option trading behavior and option pricing patterns. We argue that greater active trading in the options market due to investor overconfidence leads to higher volatility and larger discrepancies in option pricing, which may be captured by implied [...] Read more.
This paper investigates the relationship between option trading behavior and option pricing patterns. We argue that greater active trading in the options market due to investor overconfidence leads to higher volatility and larger discrepancies in option pricing, which may be captured by implied volatility spread and implied volatility skewness. Using two different measures of excess option trading, we find that trading activities are correlated in different ways with volatility, volatility spread, and volatility skewness. We also find that these relationships exist both over time and cross-sectionally. We suggest that options investors tend to chase “hot” stocks, as we find evidence of a positive relationship between option trading activities and past underlying equity returns. Heavier trading in the options market also tends to make out-of-the-money call options more (less) expensive than the at-the-money counterparts over time (cross-sectionally). Because trading activities do not predict future equity returns, investor overconfidence, and not informed trading, seems to be a more plausible explanation for our findings. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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