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Quantitative Methods for Financial Derivatives and Markets
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Quantitative Methods for Financial Derivatives and Markets

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 5262

Special Issue Editor

Dr. Michael J. Tomas

E-Mail Website
Guest Editor
Grossman School of Business, University of Vermont, Burlington, VT 05405, USA
Interests: derivative security pricing; commodity exchanges; fixed income markets

Special Issue Information

Dear Colleagues,

This Special Issue intends to address a range of topics related to derivative securities and their markets, including but not limited to new derivative pricing models, enhancements and/or novel applications of numerical techniques to existing derivative models, volatility studies, market frictions and microstructure, fixed-income models, and studies on risk and credit. We welcome articles that employ methods such as diffusion processes (Brownian motion, Fractional Brownian motion, jump diffusion models, etc…), traditional numerical techniques (binomial/trinomial models, finite difference, finite element, Monte-Carlo etc…), and/or appropriate statistical models for empirical studies using market data.

Dr. Michael J. Tomas
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 250 words) can be sent to the Editorial Office for assessment.

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 1600 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

  • derivative securities
  • derivative pricing models
  • derivative markets
  • volatility
  • microstructure

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Published Papers (2 papers)

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Research

20 pages, 723 KB  
Article
Optimal Investment and Consumption Problem with Stochastic Environments and Delay
by Stanley Jere, Danny Mukonda, Edwin Moyo and Samuel Asante Gyamerah
J. Risk Financial Manag. 2026, 19(1), 62; https://doi.org/10.3390/jrfm19010062 - 13 Jan 2026
Viewed by 604
Abstract
This paper examines an optimal investment–consumption problem in a setting where the financial environment is influenced by both stochastic factors and delayed effects. The investor, endowed with Constant Relative Risk Aversion (CRRA) preferences, allocates wealth between a risk-free asset and a single risky [...] Read more.
This paper examines an optimal investment–consumption problem in a setting where the financial environment is influenced by both stochastic factors and delayed effects. The investor, endowed with Constant Relative Risk Aversion (CRRA) preferences, allocates wealth between a risk-free asset and a single risky asset. The short rate follows a Vasiˇček-type term structure model, while the risky asset price dynamics are driven by a delayed Heston specification whose variance process evolves according to a Cox–Ingersoll–Ross (CIR) diffusion. Delayed dependence in the wealth dynamics is incorporated through two auxiliary variables that summarize past wealth trajectories, enabling us to recast the naturally infinite-dimensional delay problem into a finite-dimensional Markovian framework. Using Bellman’s dynamic programming principle, we derive the associated Hamilton–Jacobi–Bellman (HJB) partial differential equation and demonstrate that it generalizes the classical Merton formulation to simultaneously accommodate delay, stochastic interest rates, stochastic volatility, and consumption. Under CRRA utility, we obtain closed-form expressions for the value function and the optimal feedback controls. Numerical illustrations highlight how delay and market parameters impact optimal portfolio allocation and consumption policies. Full article
(This article belongs to the Special Issue Quantitative Methods for Financial Derivatives and Markets)
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38 pages, 4339 KB  
Article
Deep Learning and Transformer Architectures for Volatility Forecasting: Evidence from U.S. Equity Indices
by Gergana Taneva-Angelova and Dimitar Granchev
J. Risk Financial Manag. 2025, 18(12), 685; https://doi.org/10.3390/jrfm18120685 - 2 Dec 2025
Cited by 1 | Viewed by 4098
Abstract
Volatility forecasting plays a crucial role in financial markets, portfolio management, and risk control. Classical econometric models such as GARCH, ARIMA, and HAR-RV are widely used but face limitations in capturing the nonlinear and regime-dependent dynamics of financial volatility. This study compares traditional [...] Read more.
Volatility forecasting plays a crucial role in financial markets, portfolio management, and risk control. Classical econometric models such as GARCH, ARIMA, and HAR-RV are widely used but face limitations in capturing the nonlinear and regime-dependent dynamics of financial volatility. This study compares traditional econometric models (HAR-RV, ARIMA, GARCH) with deep learning (DL) architectures (LSTM, CNN-LSTM, PatchTST-lite, and Vanilla Transformer) in forecasting realized variance (RV) for major U.S. equity indices (S&P 500, NASDAQ 100, and the Dow Jones Industrial Average) over the period 2000–2025. RV is used as the dependent variable because it is a standard model-free proxy for market volatility. Forecast accuracy is evaluated across forecast horizons of h = 1, 5, 22 days using QLIKE, RMSE, and MAE, along with Diebold–Mariano (DM) significance tests and overfitting diagnostics. Results show that Transformer-based models achieve the lowest errors and strongest generalization, particularly at short horizons and during volatile periods. Overall, the findings highlight the growing advantage of AI-driven models in delivering stable and economically meaningful volatility forecasts, supporting more effective portfolio allocation and risk management—especially in environments marked by rapid market shifts and structural breaks. Full article
(This article belongs to the Special Issue Quantitative Methods for Financial Derivatives and Markets)
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