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Mathematics
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Financial Mathematics and Applications
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Financial Mathematics and Applications

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

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 5737

Special Issue Editors

Dr. Steven P. Clark

E-Mail Website
Guest Editor
Department of Finance, University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 28223, USA
Interests: mathematical finance; derivatives; corporate finance; stochastic modeling
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Alberto Bueno-Guerrero

E-Mail Website
Guest Editor
Department of Economics, IES Francisco Ayala, 18014 Granada, Spain
Interests: financial risk management; valuation; quantitative finance; risk management; financial modelling
Dr. Jaya Bishwal

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of North Carolina at Charlotte, 376 Fretwell Bldg., 9201 University City Blvd., Charlotte, NC 28223-0001, USA
Interests: stochastic differential inference; mathematical finance and financial econometrics; stochastic analysis and probability

Special Issue Information

Dear Colleagues,

In an essay titled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" published in 1960, physicist Eugene Wigner expressed a sense of wonder that mathematics is such an effective system, which not only allows us to understand the laws of physics, but also enables us to make predictions about the inanimate universe with stunning precision. Inevitably, the mathematical tools that unveiled the inner workings of nature began showing up in the work of social scientists. Yet, human behavior proved to be far less tractable than the orbits of planets. While collective human activity exhibits some degree of statistical regularity, individual behavior remains as enigmatic as ever. Fortunately for financial economists, the principle of no arbitrage has proven to be the bedrock upon which a remarkably useful edifice could be constructed. Indeed, the absence of arbitrage plays the role of a fundamental law of nature for asset pricing and validates the application of rigorous mathematical reasoning in models of financial markets.

For this Special Issue, we invite the submission of manuscripts that, with a nod to Wigner, illustrate the unreasonable effectiveness of mathematics in financial economics. Manuscripts should be written in a rigorous mathematical style and must establish new results, introduce new methods, or provide novel insights into existing methods. While submissions on any topic in Financial Mathematics are welcomed, papers on topics from the list below (see Keywords) are especially encouraged.

Dr. Steven P. Clark
Prof. Dr. Alberto Bueno-Guerrero
Dr. Jaya Bishwal
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

  • transform methods in derivatives pricing
  • Lévy processes
  • volatility modeling
  • random fields and stochastic strings
  • term-structure models
  • Malliavin calculus
  • state-space models
  • applications of techniques from financial mathematics to other fields (e.g., epidemiology, mathematical biology, or physics)

Published Papers (3 papers)

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Research

12 pages, 536 KiB  
Article
A Divestment Model: Migration to Green Energy Investment Portfolio Concept
by Gaoganwe Sophie Moagi, Obonye Doctor and Edward Lungu
Mathematics 2024, 12(6), 915; https://doi.org/10.3390/math12060915 - 20 Mar 2024
Viewed by 430
Abstract
In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased down, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the [...] Read more.
In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased down, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the phase-down rate of the risky asset, c(t), the variable proportion, π(t), in a risky asset and the interest rate, r, of the bond. To guide the growth of the total wealth in this study, we compared it to the Øksendal and Sulem (Backward Stochastic Differential Equations and Risk Measures (2019)) total wealth for which c(t)=0, and π(t) is a constant. We employed the Fokker–Planck equation to find the variable moment, π(t), and the associated variance. We proved the existence and uniqueness of the first moment by Feller’s criteria. We have found a pair (c*(t),r*) for each π(t), which guarantees a growing total wealth. We have addressed the question whether this pair can reasonably be achieved to ensure an acceptable phase-down rate at a financially achievable interest rate, r*. Full article
(This article belongs to the Special Issue Financial Mathematics and Applications)
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39 pages, 1044 KiB  
Article
Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps
by Alberto Bueno-Guerrero and Steven P. Clark
Mathematics 2024, 12(1), 82; https://doi.org/10.3390/math12010082 - 26 Dec 2023
Viewed by 1937
Abstract
We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to [...] Read more.
We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes. Full article
(This article belongs to the Special Issue Financial Mathematics and Applications)
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14 pages, 1936 KiB  
Article
Pricing of Arithmetic Average Asian Option by Combining Variance Reduction and Quasi-Monte Carlo Method
by Lingling Xu, Hongjie Zhang and Fu Lee Wang
Mathematics 2023, 11(3), 594; https://doi.org/10.3390/math11030594 - 23 Jan 2023
Viewed by 2741
Abstract
Financial derivatives have developed rapidly over the past few decades due to their risk-averse nature, with options being the preferred financial derivatives due to their flexible contractual mechanisms, particularly Asian options. The Black–Scholes stock option pricing model is often used in conjunction with [...] Read more.
Financial derivatives have developed rapidly over the past few decades due to their risk-averse nature, with options being the preferred financial derivatives due to their flexible contractual mechanisms, particularly Asian options. The Black–Scholes stock option pricing model is often used in conjunction with Monte Carlo simulations for option pricing. However, the Black–Scholes model assumes that the volatility of asset returns is constant, which does not square with practical financial markets. Additionally, Monte Carlo simulation suffers from slow error convergence. To address these issues, we first correct the asset volatility in the Black–Scholes model using a GARCH model. Then, the low error convergence rate of the Monte Carlo method is improved using variance reduction techniques. Meanwhile, the quasi-Monte Carlo approach based on low discrepancy sequences is used to refine the error convergence rate. We also provide a simulation experiment and result analysis to validate the effectiveness of our proposed method. Full article
(This article belongs to the Special Issue Financial Mathematics and Applications)
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