Mathematical Finance Research Articles

Machine learning methods for financial forecasting and trading profitability: Evidence during the Russia–Ukraine war

PurposeThis study aims to evaluate the effectiveness of machine learning models to yield profitability over the market benchmark, notably in periods of systemic instability, such as the ongoing war between Russia and Ukraine.Design/methodology/approachThis study made computational experiments using support vector machine (SVM) classifiers to predict stock price movements for three financial markets and construct profitable trading strategies to subsidize investors’ decision-making.FindingsOn average, machine learning models outperformed the market benchmarks during the more volatile period of the Russia–Ukraine war, but not during the period before the conflict. Moreover, the hyperparameter combinations for which the profitability is superior were found to be highly sensitive to small variations during the model training process.Practical implicationsInvestors should proceed with caution when applying machine learning models for stock price forecasting and trading recommendations, as their superior performance for volatile periods – in terms of generating abnormal gains over the market – was not observed for a period of relative stability in the economy.Originality/valueThis paper’s approach to search for financial strategies that succeed in outperforming the market provides empirical evidence about the effectiveness of state-of-the-art machine learning techniques before and after the conflict deflagration, which is of potential value for researchers in quantitative finance and market professionals who operate in the financial segment.

A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance

A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance

Deep Time Series Forecasting Models: A Comprehensive Survey

Deep learning, a crucial technique for achieving artificial intelligence (AI), has been successfully applied in many fields. The gradual application of the latest architectures of deep learning in the field of time series forecasting (TSF), such as Transformers, has shown excellent performance and results compared to traditional statistical methods. These applications are widely present in academia and in our daily lives, covering many areas including forecasting electricity consumption in power systems, meteorological rainfall, traffic flow, quantitative trading, risk control in finance, sales operations and price predictions for commercial companies, and pandemic prediction in the medical field. Deep learning-based TSF tasks stand out as one of the most valuable AI scenarios for research, playing an important role in explaining complex real-world phenomena. However, deep learning models still face challenges: they need to deal with the challenge of large-scale data in the information age, achieve longer forecasting ranges, reduce excessively high computational complexity, etc. Therefore, novel methods and more effective solutions are essential. In this paper, we review the latest developments in deep learning for TSF. We begin by introducing the recent development trends in the field of TSF and then propose a new taxonomy from the perspective of deep neural network models, comprehensively covering articles published over the past five years. We also organize commonly used experimental evaluation metrics and datasets. Finally, we point out current issues with the existing solutions and suggest promising future directions in the field of deep learning combined with TSF. This paper is the most comprehensive review related to TSF in recent years and will provide a detailed index for researchers in this field and those who are just starting out.

Quantization of stochastic volatility models: Numerical tests and an open source implementation

The aim of this paper is to discuss the implementation of the recursive marginal quantization algorithm of Fiorin et al. (2018), to several stochastic volatility models. After recalling the theoretical framework and the main features of the method, we evaluate the performance of the algorithm for the pricing of derivatives. We also discuss an open source implementation of the algorithm. For most models we consider, with the exception of the Stein and Stein model, recursive marginal quantization provides a viable alternative to Monte Carlo simulations.

Continuous trading strategy based on deep reinforcement learning

Automatic trading policy has been researched with reinforcement learning (RL). Designing a profitable and applicable policy is of great significance for research in quantitative finance. Incoprating with deep learning, typical deep reinforcement learning (DRL) algorithms such as Proximal Policy Optimization (PPO) have shown their effectiveness. To improve the practical applicability, the manner in which we train our model should better simulate the dynamic of the stock market. A sliding window training strategy is a better solution, which employes training, validation and trading procedures on dataset with a sliding window. However, this empirical strategy can still be further investigated in algorithm evaluation and the experiment designation such as choice of sliding window. In this paper, we further investigated the continuous trading strategy (CTS). We evaluated the performance of a wider range of algorithms, including PPO, Deep Deterministic Policy Gradient (DDPG), Advantage Actor-Critic (A2C), Soft Actor-Critic (SAC). Moreover, we trained our models on a longer term period. We also provide detailed observations and suggestions on experiment settings. These discussions will facilitate researchers in their future work.

Derivative Pricing using Quantum Signal Processing

Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on Quantum Signal Processing (QSP) to encode financial derivative payoffs directly into quantum amplitudes, alleviating the quantum circuits from the burden of costly quantum arithmetic. Compared to current state-of-the-art approaches in the literature, we find that for derivative contracts of practical interest, the application of QSP significantly reduces the required resources across all metrics considered, most notably the total number of T-gates by ∼16x and the number of logical qubits by ∼4x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of ∼5x. Overall, we find that quantum advantage will require 4.7k logical qubits, and quantum devices that can execute 109 T-gates at a rate of 45MHz. While in this work we focus specifically on the payoff component of the derivative pricing process where the method we present is most readily applicable, similar techniques can be employed to further reduce the resources in other applications, such as state preparation.

Can Machine Learning Explain Alpha Generated by ESG Factors?

Can Machine Learning Explain Alpha Generated by ESG Factors?

Hierarchical fuzzy model applied to oil trading

Computer trading is currently relatively limited to quantitative trading in paper markets, such as, futures, swaps, and options, ignoring the large volume of physical commodities trading. Numerical algorithms and mathematical methods are frequently applied in the trading of non-physical commodities and stock markets. However, the physical trade of oil does not have a computer program that represents an unquestionable development that includes more complex and subjective factors that traders take into consideration when entering a transaction. Using fuzzy logic, this work proposes a new approach to base a method that can rank oils and the variables, commonly involved in the trading. It uses fuzzy logic to blend objective and subjective factors and brings in two key hierarchical steps to the process. It is shown that this model can also be useful for apprising a decision-making process, improving internal communication, and for the management of physical commodities trading. Here the options of trading are assessed accordingly to its numerical and linguistic judgments, considering even abrupt outcomes. The wide-ranging options, successive filters, and factors evaluation that mirror the technical and expert trading decision making process make it possible for the future application of artificial intelligence (AI) in physical commodities trading.

Time series analysis and applications in data analysis, forecasting and prediction

Time series analysis is an essential field in data analysis, particularly within forecasting and prediction domains. Researching and building time series models play a crucial role in understanding and predicting the temporal dynamics of various phenomena. In mathematics, time series data is defined as data points indexed in chronological order and have a consistent time interval between consecutive observations. This can include data such as daily stock prices, annual national income, quarterly company revenue, and more. The advantage of time series data is that it can capture the state of a variable over time. In contrast, the world is constantly changing, and phenomena rarely remain static they typically exhibit variations over time. Therefore, time series data has highly practical applications and is used in various fields, including statistics, econometrics, financial mathematics, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, telecommunications, and signal processing. ARIMA, which stands for Auto Regressive Integrated Moving Average, is a widely used time series forecasting method in data science. It is a popular model for analyzing and predicting time-dependent data points. ARIMA combines autoregression, differencing, and moving averages to capture different aspects of time series data. In this paper, we study ARIMA, which is a significant model for analyzing and predicting time series data.

Estimation and Prediction of Commodity Returns Using Long Memory Volatility Models

Modelling the volatility of commodity prices and creating more reliable models for estimating and forecasting commodity price returns are crucial. The body of research on statistical models that can fully reflect the empirical characteristics of commodity price returns is lacking. The main aim of this research was to develop a modelling framework that could be used to accurately estimate and forecast commodity price returns by combining long memory models with heavy-tailed distributions. This study employed dual hybrid long-memory generalised autoregressive conditionally heteroscedasticity (GARCH) models with heavy-tailed innovations, namely, the Student-t distribution (StD), skewed-Student-t distribution (SStD), and the generalised error distribution (GED). Based on the smallest forecasting metrics values for mean absolute error (MAE) and mean squared error (MSE) values, the best performing LM-GARCH-type model for lithium is the ARFIMA (1, o, 1)-FIAPARCH (1, ξ, 1) with normal innovations. For tobacco, the best model is ARFIMA (1, o, 1)-FIGARCH (1, ξ, 1) with SStD innovations. The robust performing model for gold is the ARFIMA (1, o, 1)-FIGARCH (1, ξ, 1)-GED model. The best performing forecasting model for crude oil and cotton returns are the FIAPARCH 1,ξ, 1−SStD model and HYGARCH 1,ξ, 1−StD model, respectively. The results obtained from this study would be beneficial to those concerned with financial market modelling techniques, such as derivative pricing, risk management, asset allocation, and valuation.

Estimation of realized volatility of cryptocurrencies using CEEMDAN-RF-LSTM

Predicting cryptocurrency volatility is crucial for investors, traders, and decision-makers but is complicated by the market’s high non-linearity, volatility, and noise. This paper presents a novel approach, the CEEMDAN-RF-LSTM hybrid model, which is the first to combine the strengths of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Random Forest (RF), and Long Short-Term Memory Network (LSTM) to predict the Realized Volatility (RV) of mainstream cryptocurrencies. The model exploits CEEMDAN’s proficiency in processing non-linear and non-stationary signals, RF’s exceptional feature selection capabilities, and LSTM’s distinctive advantages in dealing with time-series problems. Applied to actual transaction data for Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB), empirical results show the superior performance of our model in predicting actual cryptocurrency volatility. These findings contribute to the academic understanding of cryptocurrency volatility and provide practical guidance for quantitative trading strategy development, offering fresh insights and methodologies for related research fields.

Applying Theorem of Ross to Transition Probability Matrix in Energy Options Pricing after Political Tensions and Russia-Ukraine Conflict

Probability Matrix, it is necessary to obtain energy options pricing. The paper found the true probabilities of transition from the current state of the market to other states. The energy options pricing including effects of Political tensions is proposed. The methods are based on true probabilities of transition to the next state of the energy market. It can be used to predict the movement of the underlying asset of energy options (oil and gas derivatives pricing). For example, one strategy might be to compare the energy sources at the beginning 2022 (before 24.02.2024) with the current state of the market. The results show that this matrix can be implemented in energy options pricing, which represents the true probabilities of transition from the current state of the market to modern state. Practical implementation is an investment strategy in oil and gas futures that should include the median of a given distribution with the current state of the market after beginning of Russia-Ukraine conflict. The absence of arbitrage opportunities is a fundamental principle underlying modern financial pricing theory. This concept is peculiar to the statement of the fundamental theorem of asset pricing. The results prove idea that at a fixed point in time is the information about some market quotations of American Call options can be determined. The results have a set of quotes that are available in both directions: both for strikes and for periods to maturity.

An automated quantitative investment model of stock selection and market timing based on industry information

As a growth asset, many listed companies have distinct characteristics of their respective industries. The listed companies in the same industry have a link effect, which can provide a wealth of information for stock operations. In this paper, a complete automated quantitative investment model is developed based on statistical models that use industry information to select stocks and time the market, thereby bringing out the synergistic effect of the system and ensuring maximum returns on investment. Risk control is taken into consideration in our model, a risk control factor is designed by measuring volatility of stock prices to determine the buying volume and the timing of stop loss, effectively safeguarding capital security. The latest industry classification results published by the China Securities Regulatory Commission are used as the basis for the industry classification. After data preprocessing, there are 70 sub-categories in 18 major categories of industry. We take the stock price of the 70 sub-categories from January 1, 2012 to January 1, 2022 as our research data. The back testing results show that positive returns are obtained in all industries except for six in our model. The average annualized rate of return is 11.10 %, which is higher than the stock indexes of the same period and far higher than the investment model of bank savings. Additionally, in accordance with a real trading system, the experiment simulates the inclusion of all transaction fees in the trading process, demonstrating the practical application value of our expert system.

A Review on the History and Development Direction of Quantitative Finance

A Review on the History and Development Direction of Quantitative Finance

Influence and Promotion of Financial Mathematics on China's Contemporary Financial Market

Influence and Promotion of Financial Mathematics on China's Contemporary Financial Market

A narrative review on quantum finance theory

This paper systematically reviews the historical development trajectory and current situation of quantum financial theory research through an in-depth review of relevant literature. This paper summarizes the history of the concept of quantum finance, elaborates on the development stages of quantum finance, and explains the contributions of representative work in different periods in various aspects, such as theoretical frameworks, mathematical models, and algorithmic tools, which is of great significance to the research path of quantum finance. In addition, the paper introduces in detail the research progress of domestic and foreign body problems, such as quantum algorithm optimization of investment portfolios, quantitative pricing of derivatives, quantum neural networks, etc., laying a good foundation for future in-depth study of this interdisciplinary subject. Overall, this paper systematically reviews the development history of quantum finance research, provides readers with a macro understanding framework by sorting out the progress in different research fields, and has significant reference value for interdisciplinary exchanges.

Quantum Computing Approach to Realistic ESG-Friendly Stock Portfolios

Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in fractional increments, practical implementations often resort to approximations, as fractional stocks are typically not tradeable. While these approximations are effective for large investment budgets, they deteriorate as budgets decrease. To alleviate this issue, a discrete Markowitz portfolio theory (DMPT) with finite budgets and integer stock weights can be formulated, but results in a non-polynomial (NP)-hard problem. Recent progress in quantum processing units (QPUs), including quantum annealers, makes solving DMPT problems feasible. Our study explores portfolio optimization on quantum annealers, establishing a mapping between continuous and discrete Markowitz portfolio theories. We find that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. Our DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods, even for moderate budgets. Responding to the demand for environmentally and socially responsible investments, we enhance our discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks. We introduce a utility function incorporating ESG ratings to balance risk, return and ESG friendliness, and discuss implications for ESG-aware investors.

An approach to duality via image space analysis and applications to linear vector optimization problems

In Yao et al. [Yao CL, Wang SQ, Tammer C. Construction of vector-valued weak separation functions with applications to conjugate duality in vector optimization; 2024. Submitted.], based on the idea of image space analysis and abstract convexity, we proposed a uniform framework of conjugate duality for the constrained vector optimization problems. This paper aims to apply this framework to linear vector optimizations. With the aid of a special collection of separation functions, a set-valued dual problem, which was also derived by Heyde, Löhne, Tammer in [Heyde F, Löhne A, Tammer C. The attainment of the solution of the dual program in vertices for vectorial linear programs. In: Barichard V, Ehrgott M, Gandibleux X, T'Kindt V, editors. Multiobjective programming and goal programming. 2009. p. 13–24. (Lecture Notes in Economics and Mathematical Systems; 618).; Heyde F, Löhne A, Tammer C. Set-valued duality theory for multiple objective linear programs and application to mathematical finance. Math Meth Oper Res. 2009;69:159–179.], is obtained by this approach. Within the uniform framework, we provide a new way to construct this dual model, and to investigate the duality theory of it. In this method, the strong duality is established by the separation of sets in the image space and the generalized saddle points.

News-driven stock market index prediction based on trellis network and sentiment attention mechanism

Applying deep learning, especially time series neural network, to stock market prediction, has become one of the important applications in the quantitative finance field. However, due to the multi-correlation and volatility of the stock market, how to timely and accurately predict it has become a challenging issue. In order to cope with this challenge, a news-driven stock market index prediction model based on TrellisNet and a sentiment attention mechanism (SA-TrellisNet) is proposed. A sentiment analysis model based on CNN and LSTM is presented to obtain the sentiment index of massive news crawled from authoritative financial websites. Furthermore, a sentiment attention mechanism is designed for data fusion of stock data and news sentiment index as the input of the simple and efficient TrellisNet network for model training and prediction. The performance of our model is systematically evaluated using seven major international stock market indices including S&P500, NYSE, DJI, NASDAQ, FTSE 100, Nikkei 225 and SSE, and comparative experiments demonstrate that SA-TrellisNet is competitive to the other state-of-the-art methods in predicting stock market indices.

Research on Machine Learning-based Prediction of Coffee Futures Prices

Coffee is one of the major agricultural commodities in world trade, and its futures are vital tools in the global capital market. The continued vitality of the coffee market and substantial price fluctuations have increased hedging demands among market participants. Consequently, predicting future price trends of coffee futures to yield excess returns has become a focal point in the field of quantitative investment. Machine learning methods are increasingly being applied in the field of quantitative investment due to their performance advantages in complex data classification and regression. This paper analyzes the current state of the coffee futures market and the factors influencing its prices. In this study, five market indicators and one technical indicator, the bias rate, were selected as inputs. The closing price for the subsequent day, along with short-term (50 days) and long-term (200 days) price trends, were forecasted using two machine learning techniques: the linear regression model and the random forest model. The results demonstrated that, of the two predictive models utilized in this study, the random forest model performed better concerning regression prediction evaluation indices. When predicting short-term (50-day) price trends, the linear regression model exhibited superior performance. However, both models revealed significant errors in predicting long-term (200-day) price trends.