Financial Engineering Research Articles

Numerical solutions of PDEs for corporate bond pricing: A computational finance approach

Abstract. In this paper, we will see how one can use numerical algorithms to solve PDEs, containing partial derivative terms, for corporate bond pricing. We utilise the Black-Scholes framework which involves adding stochastic interest rates and credit risk into a PDE model. Then, we will take a quick look at some different numerical methods to solve the PDE model, like finite difference methods (FDM), finite element methods (FEM) as well as standard Monte Carlo (MC) simulations. Above all, we provide some simulations to show how well they work for PDEs, and how much time it takes. We would like to highlight that numerical methods lead to more accurate and efficient bond pricing with these methods, and also that we can analyse together how well each method works under different market scenarios. The paper will end with future directions for numerical methods, which should allow including more sophisticated algorithms and machine-learning techniques that improve scalability and can be used in a real-time manner in financial markets.

A note on the numerical approximation of Greeks for American-style options

In this note, we consider the approximation of the Greeks Delta and Gamma of American-style options through the numerical solution of time-dependent partial differential complementarity problems (PDCPs). This approach is very attractive as it can yield accurate approximations to these Greeks at essentially no additional computational cost during the numerical solution of the PDCP for the pertinent option value function. For the temporal discretization, the Crank–Nicolson method is arguably the most popular method in computational finance. It is well-known, however, that this method can have an undesirable convergence behaviour in the approximation of the Greeks Delta and Gamma for American-style options, even when backward Euler damping (Rannacher smoothing) is employed.In this note, for the temporal discretization of the PDCP, we study an interesting family of diagonally implicit Runge–Kutta (DIRK) methods together with the two-stage Lobatto IIIC method. Through ample numerical experiments for one- and two-asset American-style options, it is shown that these methods can yield a regular second-order convergence behaviour for the option value as well as for the Greeks Delta and Gamma. A mutual comparison reveals that the DIRK method with suitably chosen parameter θ is preferable.

Numerical Methods and Computation in Financial Mathematics: Solving PDEs, Monte Carlo Simulations, and Machine Learning Applications

Abstract. This paper delves into three fundamental numerical methods and computational techniques in financial mathematics: Finite Difference Methods (FDM), Monte Carlo Simulations (MCS), and Machine Learning (ML) applications. Finite Difference Methods are widely utilized for solving partial differential equations (PDEs) in option pricing, with various schemes offering different stability and convergence properties. Monte Carlo Simulations provide a powerful approach for pricing complex derivatives and risk management, addressing the challenges of high-dimensionality and computational complexity. Machine Learning has revolutionized predictive modeling in finance, enabling sophisticated analysis of large datasets to uncover hidden patterns and enhance trading strategies. Through a detailed examination of these methods, including specific examples and data, this paper highlights their theoretical foundations, practical implementations, and the advancements they bring to computational finance. By bridging theoretical approaches with practical applications, we aim to offer insights into the future directions and challenges in financial mathematics.

Bagehot’s giant bubble failure

Modern economic history literature has extensive coverage of the Overend, Gurney crash of 1866 and the associated Lender of Last Resort operations of the Bank of England. But it basically ignores the giant British investment mania of the 1860s that led to that crisis and to the crisis of 1867 that followed. Yet that mania has many other interesting features that are relevant for dealing with bubbles. In particular, that historical episode shows that high interest rates may not suffice to deflate a bubble. It also demonstrates the dangers of “financial innovation,” which flowered in that period and enabled promoters to mislead and ruin investors in novel ways, while producing a rapid expansion of the railway system that escaped public notice. Even some of the most sophisticated contemporary observers, such as Walter Bagehot, who were bothered by the market anomalies they saw, were deceived by that pioneering “financial engineering” which has strong similarities to the one that led to the Global Financial Crisis of 2008. This paper points out some of the many neglected aspects of that mania. Those include an illustration of the evolution of economic thought towards ignoring underlying causes of financial crises and concentrating just on the panics in which they culminate.

How can AI-integrated applications affect the financial engineers’ psychological safety and work-life balance: Chinese and Iranian financial engineers and administrators’ perspectives

BackgroundThe integration of AI in finance has significantly reshaped the role of financial engineers, improving efficiency and decision-making. However, it also affects psychological safety and work-life balance. Financial engineers face increased pressure to keep up with evolving technologies, fear of job displacement due to automation, and blurred boundaries between work and personal life. Exploring the link between AI applications, psychological well-being, and work-life balance is crucial for optimizing individual performance and organizational success, ensuring a sustainable and supportive work environment.ObjectivesThis qualitative study investigates how AI-integrated finance applications influence financial engineers’ psychological safety and work-life balance. By exploring financial engineers’ lived experiences and perceptions, the study seeks to provide insights into the human implications of AI adoption in finance.Methodology: The study utilized qualitative research methods, specifically thematic analysis, to examine data from 20 informants selected through theoretical sampling. Thematic analysis techniques were employed to identify recurring patterns, themes, and meanings within the data, allowing for a rich exploration of the research questions.Findings: Data analysis revealed several themes related to the impact of AI-integrated applications on financial engineers’ psychological safety and work-life balance. These themes include the perception of job security, the role of automation in workload management, and the implications of AI for professional identity and job satisfaction.ConclusionsThis study’s findings highlight the multifaceted effects of AI integration in finance, shedding light on the opportunities and challenges it presents for financial engineers. While AI offers potential benefits such as increased efficiency and productivity, it raises concerns about job security and work-related stress. Overall, the study underscores the importance of considering the human implications of AI adoption in finance and calls for proactive measures to support the well-being of financial professionals in an AI-driven environment.

Application and Empirical Analysis of Random Volatility Model in Financial Markets

The Stochastic Volatility Model (SVM), as a key innovation in modern financial engineering, has profoundly changed our understanding of the volatility characteristics of financial markets. This model not only considers the volatility of asset prices as a time-varying random variable, but also simulates this uncertainty by introducing stochastic processes such as Brownian motion or more complex stochastic differential equations, thereby achieving a precise characterization of the dynamic characteristics of volatility. Compared to traditional fixed or historical average volatility assumptions, SVM can capture sudden changes in market sentiment, the impact of news events, and the influence of macroeconomic factors on volatility, providing investors with a more realistic perspective on the market. This article not only deeply analyzes the theoretical basis and construction methods of SVM, but also verifies its effectiveness and applicability in different financial market environments through empirical analysis and actual market data, providing valuable references and insights for financial practitioners, scholars, and policy makers.

An adapted Black Widow Optimization Algorithm for Financial Portfolio Optimization Problem with cardinalty and budget constraints

Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz’s 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential.

Antithetic multilevel Monte Carlo method for approximations of SDEs with non-globally Lipschitz continuous coefficients

In the field of computational finance, one is commonly interested in the expected value of a financial derivative whose payoff depends on the solution of stochastic differential equations (SDEs). For multi-dimensional SDEs with non-commutative diffusion coefficients in the globally Lipschitz setting, a kind of one-half order truncated Milstein-type scheme without Lévy areas was recently introduced by Giles and Szpruch (2014), which combined with the antithetic multilevel Monte Carlo (MLMC) gives the optimal overall computational cost O(ϵ−2) for the required target accuracy ϵ. Nevertheless, many nonlinear SDEs in applications have non-globally Lipschitz continuous coefficients and the corresponding theoretical guarantees for antithetic MLMC are absent in the literature. In the present work, we aim to fill the gap and analyze antithetic MLMC in a non-globally Lipschitz setting. First, we propose a family of modified Milstein-type schemes without Lévy areas to approximate SDEs with non-globally Lipschitz continuous coefficients. The expected one-half order of strong convergence is recovered in a non-globally Lipschitz setting, where even the diffusion coefficients are allowed to grow superlinearly. This then helps us to analyze the relevant variance of the multilevel estimator and the optimal computational cost is finally achieved for the antithetic MLMC. Since getting rid of the Lévy areas destroys the martingale properties of the scheme, the analysis of both the convergence rate and the desired variance becomes highly non-trivial in the non-globally Lipschitz setting. By introducing an auxiliary approximation process, we develop non-standard arguments to overcome the essential difficulties. Numerical experiments are provided to confirm the theoretical findings.

Comparative Analysis of Portfolio Management Models: Markowitz, CAPM, and Multi-Factor Models

This paper presents a comparative analysis of three foundational portfolio management models: the Markowitz Efficient Frontier, the Capital Asset Pricing Model (CAPM), and Multi-Factor Models. It aims to explore their theoretical foundations, empirical applicability, and practical usage to assess their strengths and limitations in financial portfolio management. The Markowitz model is appreciated for its detailed risk-return optimization framework but criticized for its reliance on historical data and computational demands. The CAPM simplifies risk assessment through market beta, yet its assumptions of market efficiency and a risk-free rate are viewed as impractical under current market conditions. Multi-Factor Models address some limitations of the CAPM by incorporating various risk factors, offering enhanced explanatory power but also adding complexity in factor selection.The study concludes that while no single model is universally superior, the choice of model should depend on the specific needs of the portfolio manager, including risk-return objectives and market environment. The paper suggests a blended or adaptive approach to model selection, highlighting the need for flexibility in response to evolving market dynamics and advances in computational finance.

Portfolio Optimization Strategies: New Approaches Based on Machine Learning Forecasting

This study provides an in-depth discussion and comprehensive review of the latest applications of machine learning techniques in the field of portfolio optimization. The article begins with an overview of traditional portfolio optimization theory and its limitations, and then focuses on how machine learning predictive models, which have flourished in recent years, can provide new perspectives and tools for solving the problems of non-linearity, dynamics and uncertainty in investment decision-making. This paper provides a detailed overview of the application practices of various machine learning algorithms (e.g., deep learning, reinforcement learning, integrated learning, etc.) in the areas of asset return prediction, risk assessment, and optimal weight allocation, and analyses their advantages and challenges compared to traditional methods. The analysis of relevant research cases reveals the significant effect of machine learning predictions in increasing expected portfolio returns, reducing risk exposure, and achieving effective diversification. The study also explores possible future trends and potential research directions for machine learning in portfolio optimization, highlighting the importance of combining domain knowledge with big data-driven intelligent investment decisions. This review aims to provide financial scholars and practitioners with a new way of thinking about portfolio optimization, and to promote the combination of theoretical research and practical operation in the fields of financial engineering and investment management, so as to achieve more accurate and efficient investment decisions.

Reforms of the Financial System in the European Union –Towards a New Legal-Institutional Order

The combination of the legal documents including the 2021-2027 EU long-term budget, NextGenerationEU, andthe Own Resources Decision (3) (Decision of 14 December 2020 on the system of own resources of the EuropeanUnion, repealing Council Decision 2014/335/EU, Euratom of 26 May 2014 on the system of own resources of theEuropean Union) has been praised as a groundbreaking achievement and political success of the EU authorities,one whose importance is no lesser than that of the establishment of the EU’s common market. The package hasmarked a powerful turn in EU’s politics, in that it helps move the debts of the countries receiving funds fromNextGenerationEU as well as within National Recovery and Resilience Plans (NRRPs) outside their national budgetarysystems. As is emphasised in a number of EU documents, the increases in EU Member States’ deficits anddebts have been due to the financial and health crisis. However, how or in what ways the new own resources andnew outside-Treaty financial engineering might contribute to the funding and eventual repayment of NextGenerationEUdebt, has not been explained.In parallel, the aforementioned success has given the basis for further action in view of in-EU integration, as expressedin the project to amend EU Treaties. Work on the amendment will continue during the present EuropeanParliament’s term. Analysis of the directions of change in the Treaty provisions covering EU fiscal and monetarypolicies and the gradually remoulded model of EU funding form t he core of this present paper.

Factors affecting financial engineering and product development in Islamic Financial Institutions

Purpose This study aims to analyze Islamic financial institutions’ (IFIs) current financial engineering and product development procedures. Design/methodology/approach The paper is quantitative in nature and the survey questionnaire were collected from managers and IF experts working for Islamic Banks, Takaful and other IFIs in Turkey, Malaysia and UAE. Two-stage structural equation modeling was used to test the hypothesis. Findings The findings highlighted that the Shari’ah Supervisory Board, Strategy and Planning of IFIs, Legal and Regulatory framework, pricing of a new product and financial performance positively impact the new product development (NPD) process. At the same time, Islamic values have no significant positive impact. Research limitations/implications When generalizing the research results, data collection from the right departments was the main limitation of the current study. Future research may opt to collect data only from Product Development Departments. Practical implications The findings of this study will allow IFIs to reflect on their present methods, procedures and Shari’ah compliance framework for the NPD process. Originality/value Factors affecting the product development and financial engineering process are discussed in the literature. The findings of this study can be regarded as building blocks for future academic research on product development and financial engineering in Islamic finance.

Dimension reduction for Quasi-Monte Carlo methods via quadratic regression

Quasi-Monte Carlo (QMC) methods have been gaining popularity in computational finance as they are competitive alternatives to Monte Carlo methods that can accelerate numerical accuracy. This paper develops a new approach for reducing the effective dimension combined with a randomized QMC method. A distinctive feature of the proposed approach is its sample-based transformation that enables us to choose a flexible manipulation via regression. In the proposed approach, the first step is to perform a regression using the samples to estimate the parameters of the regression model. An optimal transformation is proposed based on the regression result to minimize the effective dimension. An advantage of this approach is that adopting a statistical approach allows greater flexibility in selecting the regression model. In addition to a linear model, this paper proposes a dimension reduction method based on a linear-quadratic model for regression. In numerical experiments, we focus on pricing different types of exotic options to test the effectiveness of the proposed approach. The numerical results show that different regression models are chosen depending on the underlying risk process and the type of derivative securities. In particular, we show several examples where the proposed method works while existing dimension reductions are ineffective.

Quantum computational finance for martingale asset pricing in incomplete markets

A derivative is a financial asset whose future payoff is a function of underlying assets. Pricing a financial derivative involves setting up a market model, finding a martingale (“fair game”) probability measure for the model from the existing asset prices, and using that probability measure to price the derivative. When the number of underlying assets and/or the number of market outcomes in the model is large, pricing can be computationally demanding. In this work, we first formulate the pricing problem in a linear algebra setting, including the realistic setting of incomplete markets where derivatives do not have a unique price. We show that the problem can be solved with a variety of quantum techniques such as quantum linear programming and the quantum linear systems algorithm. While in previous works the martingale measure is assumed to be given, here it is extracted from market variables akin to bootstrapping, a common practice among financial institutions. We discuss the quantum zero-sum game algorithm and the quantum simplex algorithm as viable subroutines. For quantum linear systems solvers, we formalize a new market assumption milder than market completeness, which allows the potential for large speedups. Towards prototype use cases, we conduct numerical experiments motivated by the Black–Scholes–Merton model.

Quantum Computational Finance: Quantum Algorithm for Portfolio Optimization

Quantum Computational Finance: Quantum Algorithm for Portfolio Optimization

An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis

Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering. It has now become obvious, even to casual observers, that the classical BS models derived under the EMH framework fail to account for a number of realistic price evolutions in real-time market data. An alternative approach to the EMH framework is the Fractal Market Hypothesis (FMH), which proposes better and clearer explanations of market behaviours during unfavourable market conditions. The FMH involves non-local derivatives and integral operators, as well as fractional stochastic processes, which provide better tools for explaining the dynamics of evolving market anomalies, something that classical BS models may fail to explain. In this work, using the FMH, we derive a time-fractional Black–Scholes partial differential equation (tfBS-PDE) and then transform it into a heat equation, which allows for ease of implementing a high-order numerical scheme for solving it. Furthermore, the stability and convergence properties of the numerical scheme are discussed, and overall techniques are applied to pricing European put option problems.

A comprehensive analysis of LSTM techniques for predicting financial market

The “Financial Engineering” has revolutionized the financial industry by integrating mathematics, finance, economics, statistics, and computational tools to solve complex problems like risk management and portfolio optimization. This interdisciplinary approach has given rise to “AI in Finance”, merging the quantitative techniques of financial engineering with AI’s data-driven capabilities. In this survey, we explore concrete examples of their real-world impact. One such example involves a leading investment firm using machine learning algorithms to analyze market sentiments for informed trading decisions, resulting in significant returns. Additionally, AI-driven credit scoring models are expanding financial access by accurately assessing creditworthiness, especially for underserved populations. Natural language processing algorithms are also employed to parse financial news and social media data, providing investors with timely insights to navigate volatile markets effectively. These advancements highlight the transformative potential of financial engineering and AI in finance. By optimizing investment strategies and mitigating risks, they drive innovation and resilience in today’s dynamic financial landscape. From algorithmic trading to credit risk assessment and market sentiment analysis, the fusion of these disciplines is reshaping traditional paradigms and shaping the future of finance.

Perceptions of Stakeholders on the Financial and Economic Crisis in Lebanon: An In-depth Analysis

Abstract This study examines Lebanon’s enduring financial and economic crisis, exacerbated by economic challenges, the COVID-19 pandemic, and the Port of Beirut explosion. With over 80 % currency devaluation due to sovereign debt default, the crisis has intensified poverty and unemployment, compounded by political turmoil. Using survey data from 178 stakeholders, experts, and academics, this research explores the intricate drivers of Lebanon’s crisis and offers insights for policymakers. Employing quantitative methods, it uncovers the intertwined role of financial mismanagement, government failures, mounting public debt, financial engineering techniques, and political instability in driving the crisis. Recommendations emphasize prudent financial practices, sound governance, and policy interventions. This study sheds light on Lebanon’s complex financial and economic challenges with data-backed perspectives from diverse stakeholders, providing valuable insights for management practitioners and scholars navigating crises in tumultuous environments. It aims to contribute to the management discourse, equipping stakeholders with actionable strategies for addressing and preventing similar crises. It also explores the interplay between stakeholder perspectives and the determinants of the financial crisis in Lebanon. It delves into the interconnected nature of the crisis and demonstrates how stakeholders from various sectors and backgrounds mirror the factors identified in the literature.

Application and Optimization Strategy of Financial Engineering in Risk Management

Financial engineering, as a collection of mathematics, statistics, engineering, computer science and other multidisciplinary fields, provides strong technical support for risk management. Through the technology and methods of financial engineering, risks can be quantitatively analyzed, predicted and controlled, so as to help enterprises and financial institutions better cope with risks and ensure their stable operation. Through the study of risk management practice, we can constantly improve the theoretical system of financial engineering and make it more realistic.

Uncovering the Dynamics in the Application of Machine learning in Computational Finance: A Bibliometric and Social Network Analysis

Uncovering the Dynamics in the Application of Machine learning in Computational Finance: A Bibliometric and Social Network Analysis