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Mathematics
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Quantitative Finance and Stochastic Volatility with Their Numerical Models
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Quantitative Finance and Stochastic Volatility with Their Numerical Models

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 2019

Special Issue Editor

Prof. Dr. Cristina Raluca Gh. Popescu

E-Mail Website
Guest Editor
1. Department of Business Administration, Faculty of Business and Administration, University of Bucharest, 030018 Bucharest, Romania
2. Department of Economics and Economic Policy, Economy I Doctoral School, Faculty of Theoretical and Applied Economics, The Bucharest University of Economic Studies, 010374 Bucharest, Romania
Interests: economics; management; finance; auditing; accounting; mathematics; econometrics; statistics; quantitative finance; stochastic volatility; numerical models; business counseling; financial analysis; control and evaluation; intellectual capital; corporate governance; sustainability; sustainable development; business environment; business process management; quality management; human resources management
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue focuses on the broad topic of “Quantitative Finance and Stochastic Volatility with Their Numerical Models” and includes novel research on the emerging challenges that are specific to quantitative finance and stochastic volatility with their numerical models. The papers should be original and reflect the current international context, especially as a result of the pandemic context, in terms of inclusive, resilient, and innovative businesses and industry, with a particular emphasis on quantitative finance and stochastic volatility with their numerical models. Furthermore, the papers should be focused on quantitative finance and stochastic volatility with their numerical models while addressing the challenges and changes that have recently occurred in economic and financial areas as a result of the struggle to support the inclusion and the use of sustainability assessment instruments and methods meant to ensure performance and excellence at a global level.

Theoretical and empirical articles on the topic of quantitative finance and stochastic volatility with their numerical models, with a particular emphasis on sustainability assessment instruments and methods, are welcome.

Contributions focusing on, but not limited to, the implications of quantitative finance and stochastic volatility with their numerical models, recent advances in business and industry, sustainability assessment instruments and methods, inclusive and innovative businesses, sustainability and sustainable economic development and growth, new trends in challenging times (today’s pandemic context) and the path to performance and excellence, entrepreneurship, small and medium-sized enterprises, successful business process management, and quality management are encouraged.

We are interested in conceptual, theoretical, methodological, empirical, and systematic review studies.

Prof. Dr. Cristina Raluca Gh. Popescu
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

  • quantitative finance
  • stochastic volatility
  • numerical models
  • sustainability assessment instruments and methods
  • mathematical analysis and numerical techniques
  • mathematical modeling
  • probabilistic techniques
  • multidisciplinary mathematical and statistical models and applications
  • dynamical systems
  • differential equations
  • partial differential equations
  • practical statistics
  • combinatorics and number theory
  • probability theory
  • multivariate calculus
  • time series analysis
  • differential equations
  • statistical data mining
  • financial mathematics
  • group theory and applications
  • actuarial statistics

Published Papers (1 paper)

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Research

22 pages, 5759 KiB  
Article
On the Class of Risk Neutral Densities under Heston’s Stochastic Volatility Model for Option Valuation
by Benzion Boukai
Mathematics 2023, 11(9), 2124; https://doi.org/10.3390/math11092124 - 30 Apr 2023
Viewed by 1114
Abstract
The celebrated Heston’s stochastic volatility (SV) model for the valuation of European options provides closed form solutions that are given in terms of characteristic functions. However, the numerical calibration of this five-parameter model, which is based on market option data, often remains a [...] Read more.
The celebrated Heston’s stochastic volatility (SV) model for the valuation of European options provides closed form solutions that are given in terms of characteristic functions. However, the numerical calibration of this five-parameter model, which is based on market option data, often remains a daunting task. In this paper, we provide a theoretical solution to the long-standing ‘open problem’ of characterizing the class of risk neutral distributions (RNDs), if any, that satisfy Heston’s SV for option valuation. We prove that the class of scale parameter distributions with mean being the forward spot price satisfies Heston’s solution. Thus, we show that any member of this class could be used for the direct risk neutral valuation of option prices under Heston’s stochastic volatility model. In fact, we also show that any RND with mean being the forward spot price that satisfies Heston’s option valuation solution must also be a member of the scale family of distributions in that mean. As particular examples, we show that under a certain re-parametrization, the one-parameter versions of the log-normal (i.e., Black–Scholes), gamma, and Weibull distributions, along with their respective inverses, are all members of this class and thus, provide explicit RNDs for direct option pricing under Heston’s SV model. We demonstrate the applicability and suitability of these explicit RNDs via exact calculations and Monte Carlo simulations, using already published index data and a calibrated Heston’s model (S&P500, ODAX), as well as an illustration based on recent option market data (AMD). Full article
(This article belongs to the Special Issue Quantitative Finance and Stochastic Volatility with Their Numerical Models)
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