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Mathematics
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Mathematical Aspects of Trading and Valuating Financial Assets
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Mathematical Aspects of Trading and Valuating Financial Assets

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: 20 June 2025 | Viewed by 43069

Special Issue Editors

Prof. Dr. Gil Cohen

E-Mail Website
Guest Editor
Department of Management, Western Galilee Academic College, P.O. Box 2125, Acre 2412101, Israel
Interests: investment; financial markets; corporate finance
Special Issues, Collections and Topics in MDPI journals
Dr. Mahmoud Qadan

E-Mail Website
Guest Editor
School of Business, Faculty of Social Sciences, University of Haifa, Haifa 3498838, Israel
Interests: finance; asset pricing; capital markets; financial econometrics

Special Issue Information

Dear Colleagues,

The financial markets have become more and more complex in recent years since a high portion of trades is performed by computerized systems. Those system tries to make sense of the chaotic nature of financial assets prices. The advance in this field enables researchers and practitioners to design trading systems that are based on complex computations derived from years of manual trading experience. Algorithmic trading systems integrate information in a short period of time and translate that information into trading decisions. This special issue of Mathematics will concentrate on this process of high-frequency trading of various financial assets such as commodities, cryptocurrencies, stocks, and ETFs. Authors should present the mathematical concepts behind their trading systems and perform a simulation that implements those concepts. These trading systems can use daily data or intraday data from various sources of information to reach their long/short decisions. We also welcome paper that uses advanced computational methods such as neuron network and fuzzy systems to identify efficient portfolios and access returns. In addition, this special issue welcomes financial assets valuations that are based on innovative mathematics and can contribute to the literature in that field. For example, methods of stocks valuation with uncertain income distribution.

Prof. Dr. Gil Cohen
Dr. Mahmoud Qadan
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

  • trading systems
  • high frequency
  • stocks valuation
  • cryptocurrencies
  • complex systems
  • simulations

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Published Papers (6 papers)

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Research

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22 pages, 388 KiB  
Article
Valuation of a Mixture of GMIB and GMDB Variable Annuity
by Yichen Han, Dongchen Li, Kun Fan, Jiaxin Wan and Luyan Li
Mathematics 2024, 12(3), 441; https://doi.org/10.3390/math12030441 - 30 Jan 2024
Viewed by 1665
Abstract
The Guaranteed Minimum Income Benefit (GMIB) and Guaranteed Minimum Death Benefit (GMDB) are options that may be included at the inception of a variable annuity (VA) contract. In exchange for small fees charged by the insurer, they give the policyholder a right to [...] Read more.
The Guaranteed Minimum Income Benefit (GMIB) and Guaranteed Minimum Death Benefit (GMDB) are options that may be included at the inception of a variable annuity (VA) contract. In exchange for small fees charged by the insurer, they give the policyholder a right to receive a guaranteed minimum level of annuity payment (GMIB) and a guaranteed minimum level of payment when the policyholder dies (GMDB), respectively. A combination of these two options may be attractive since it protects the policyholder’s investment from potential poor market behavior as well as mortality risk during the accumulation phase. This study examined the pricing of a composite variable annuity incorporating both the GMIB and GMDB options (a Guaranteed Minimum Income–Death Benefit, notated GMIDB). We used a non-arbitrage valuation method, decomposed the GMIDB value into two parts, and derived an analytical pricing formula based on a constant fee structure. The formula can be used to determine the fair fee to be charged. We conducted comprehensive sensitivity analyses on critical parameters to determine what drives the value of a GMIDB option. Our approach offers a simple and deterministic way to price a VA embedded with the GMIDB option. Our numerical findings suggested that the annuity conversion rate, age of the policyholder, and volatility of risky investments are significant in the valuation of a GMIDB option. Full article
(This article belongs to the Special Issue Mathematical Aspects of Trading and Valuating Financial Assets)
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22 pages, 849 KiB  
Article
Effects of Diesel Price on Changes in Agricultural Commodity Prices in Bulgaria
by Miroslava Ivanova and Lilko Dospatliev
Mathematics 2023, 11(3), 559; https://doi.org/10.3390/math11030559 - 20 Jan 2023
Cited by 2 | Viewed by 3250
Abstract
The aim of this article is to supply the first empirical research inspecting how changes in diesel prices influence the prices of four agricultural commodities in Bulgaria. For this purpose, using a VECM and monthly agricultural commodity prices between January 2011 and July [...] Read more.
The aim of this article is to supply the first empirical research inspecting how changes in diesel prices influence the prices of four agricultural commodities in Bulgaria. For this purpose, using a VECM and monthly agricultural commodity prices between January 2011 and July 2022, we estimated short-run and long-run changes in producer and retail prices of cow’s milk, chicken eggs, greenhouse tomatoes and cucumbers due to the change in average monthly diesel prices. The Granger causality test indicates that diesel prices cannot be used to forecast the behavior of producer and retail prices in the four markets considered. Diesel prices can be used to forecast the behavior of producer prices in only the cow’s milk market, and the diesel price predicts retail prices in the chicken egg and greenhouse cucumber markets. The results of the response of the researched prices of agricultural commodities to diesel price shocks indicate a positive response of both upstream and downstream prices of cow’s milk and chicken egg markets and upstream prices of the greenhouse tomato market despite the initial negative shock. Full article
(This article belongs to the Special Issue Mathematical Aspects of Trading and Valuating Financial Assets)
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21 pages, 826 KiB  
Article
Short-Sale Constraints and Stock Prices: Evidence from Implementation of Securities Refinancing Mechanism in Chinese Stock Markets
by Larry Su, Elmina Homapour and Francisco Chiclana
Mathematics 2022, 10(17), 3141; https://doi.org/10.3390/math10173141 - 1 Sep 2022
Viewed by 2101
Abstract
Qualified Securities for Short-sale Refinancing (QSSR) is a unique trading mechanism that has exogenously increased the supply of loanable securities in Chinese stock markets. Using difference-in-differences (DID) methodology, this paper is the first to investigate whether and to what extent additions to the [...] Read more.
Qualified Securities for Short-sale Refinancing (QSSR) is a unique trading mechanism that has exogenously increased the supply of loanable securities in Chinese stock markets. Using difference-in-differences (DID) methodology, this paper is the first to investigate whether and to what extent additions to the QSSR eligibility list affect short selling activities and stock price behaviors. The paper finds that stocks added to the QSSR list exhibit better liquidity and less negative skewness in returns than non-QSSR stocks. However, QSSR stocks are more volatile and display a higher frequency of extreme negative returns. In addition, on average, QSSR stocks experience larger negative abnormal returns (ARs) and cumulative abnormal returns (CARs) relative to non-QSSR stocks, and the difference in CARs is positively related to investor heterogeneity. The results indicate that short selling has mixed effects on stock prices. Removing short-sale constraints can improve liquidity and reduce price bubbles, but can also increase return volatility and amplify market crashes. Full article
(This article belongs to the Special Issue Mathematical Aspects of Trading and Valuating Financial Assets)
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11 pages, 994 KiB  
Article
The Complexity of Cryptocurrencies Algorithmic Trading
by Gil Cohen and Mahmoud Qadan
Mathematics 2022, 10(12), 2037; https://doi.org/10.3390/math10122037 - 12 Jun 2022
Cited by 9 | Viewed by 3831
Abstract
In this research, we provided an answer to a very important trading question, what is the optimal number of technical tools in order to achieve the best trading results for both swing trade that uses daily bars and intraday trade that uses minutes [...] Read more.
In this research, we provided an answer to a very important trading question, what is the optimal number of technical tools in order to achieve the best trading results for both swing trade that uses daily bars and intraday trade that uses minutes bars? We designed Machine Learning (ML) systems that can trade four major cryptocurrencies: Bitcoin, Ethereum, BNB, and Solana. We found that more indicators do not necessarily mean better trading performance. Swing traders that use daily bars should trade Bitcoin and Solana using Ichimoku Cloud (IC) plus Moving Average Convergence Divergence (MACD), Ethereum with IC plus Chaikin Money Flow (CMF), and BNB with IC alone. With regard to intraday trading, we documented that different cryptocurrencies should be trading using different time frames. These results emphasize that the optimal number of indicators that are used to trade daily bars is one or, at maximum, two. The Multi-Layer (MUL) system that consists of all three examined technical indicators failed to improve the trading results for both days (swing) and intraday trades. The main implication of this study for traders is that more indicators does not necessarily improve trades performances. Full article
(This article belongs to the Special Issue Mathematical Aspects of Trading and Valuating Financial Assets)
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22 pages, 823 KiB  
Article
Tell Me Why I Do Not Like Mondays
by Yasmeen Idilbi-Bayaa and Mahmoud Qadan
Mathematics 2022, 10(11), 1850; https://doi.org/10.3390/math10111850 - 27 May 2022
Cited by 4 | Viewed by 2313
Abstract
We conduct a strict and broad analysis of the 30-day expected volatility (VIX) of five very active individual US stocks, three US domestic indices, and that of 10-year US Treasury notes. We find prominent non-random movement patterns mainly on Mondays and Fridays. Furthermore, [...] Read more.
We conduct a strict and broad analysis of the 30-day expected volatility (VIX) of five very active individual US stocks, three US domestic indices, and that of 10-year US Treasury notes. We find prominent non-random movement patterns mainly on Mondays and Fridays. Furthermore, significant leaps in expected volatility on Monday occur primarily in the first two and the fifth Mondays of the month. We also document that higher values for the 30-day expected volatility on Mondays are more likely when there was a negative change in the volatility on the preceding Fridays. This pattern does not occur on other subsequent days of the week. The results are robust through time and different subsamples and are not triggered by outliers or the week during which the options on the underlying assets expire. Rational and irrational drivers are suggested to explain the findings. Given that, to date, no one has conducted such an examination, our findings are important for investors interested in buying or selling volatility instruments. Full article
(This article belongs to the Special Issue Mathematical Aspects of Trading and Valuating Financial Assets)
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Review

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13 pages, 529 KiB  
Review
Algorithmic Trading and Financial Forecasting Using Advanced Artificial Intelligence Methodologies
by Gil Cohen
Mathematics 2022, 10(18), 3302; https://doi.org/10.3390/math10183302 - 12 Sep 2022
Cited by 37 | Viewed by 28031
Abstract
Artificial Intelligence (AI) has been recently recognized as an essential aid for human traders. The advantages of the AI systems over human traders are that they can analyze an extensive data set from different sources in a fraction of a second and perform [...] Read more.
Artificial Intelligence (AI) has been recently recognized as an essential aid for human traders. The advantages of the AI systems over human traders are that they can analyze an extensive data set from different sources in a fraction of a second and perform actual high-frequency trading (HFT) that can take advantage of market anomalies and price differences. This paper reviews the most important papers published in recent years that use the most advanced techniques to forecast financial asset trends and answer the question of whether those techniques can be used to successfully trade the complex financial markets. All systems use deep learning (DL) and machine learning (ML) protocols to explore nonobvious correlations and phenomena that influence the probability of trading success. Their predictions are based on linear or nonlinear models often combined with social media investors’ sentiment derivations or pattern recognitions. Most of the reviewed papers have proven the successful ability of their developed system to trade the financial markets. Full article
(This article belongs to the Special Issue Mathematical Aspects of Trading and Valuating Financial Assets)
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