Mathematical Finance Research Articles

Reinforcement Learning-Based Multimodal Model for the Stock Investment Portfolio Management Task

Machine learning has been applied by more and more scholars in the field of quantitative investment, but traditional machine learning methods cannot provide high returns and strong stability at the same time. In this paper, a multimodal model based on reinforcement learning (RL) is constructed for the stock investment portfolio management task. Most of the previous methods based on RL have chosen the value-based RL methods. Policy gradient-based RL methods have been proven to be superior to value-based RL methods by a growing number of research. Commonly used policy gradient-based reinforcement learning methods are DDPG, TD3, SAC, and PPO. We conducted comparative experiments to select the most suitable method for the dataset in this paper. The final choice was DDPG. Furthermore, there will rarely be a way to refine the raw data before training the agent. The stock market has a large amount of data, and the data are complex. If the raw stock market data are fed directly to the agent, the agent cannot learn the information in the data efficiently and quickly. We use state representation learning (SRL) to process the raw stock data and then feed the processed data to the agent. It is not enough to train the agent using only stock data; we also added comment text data and image data. The comment text data comes from investors’ comments on stock bars. Image data are derived from pictures that can represent the overall direction of the market. We conducted experiments on three datasets and compared our proposed model with 11 other methods. We set up three evaluation indicators in the paper. Taken together, our proposed model works best.

CNN-BiLSTM-Attention Based Stock Price Prediction and Quantitative Investment Strategy

With the rapid development of technology and the increasing maturity of financial markets, stock price prediction has become a hot topic and an important trend in the financial field. However, the stock market has complexity and volatility, in order to reduce the investment risk and ensure the maximization of benefits, selecting the optimal stock to predict the stock price and formulating the quantitative trading strategy are extremely important issues for financial academics and investors. For the research of stock price prediction and quantitative trading, firstly, the quantitative stock selection model combining XGBoost and multi-factor stock selection model is constructed, and four stocks are screened out, and then the CNN-BiLSTM-Attention model is proposed to predict the stock price trend of the selected stocks, and it is found from the prediction results of the four stocks that the prediction accuracies all reach more than 95%, which is higher than that of the single model prediction. accuracy and passed the validity test of the fitted model. Secondly, based on the quantitative investment portfolio given in the above analysis and the quantitative stock trading strategy of MACD, the prediction results are verified, and the total return of most stocks based on the strategy is higher than 40% at the highest, and the loss is controlled within 10%, which indicates that the trading strategy in this paper is effective and feasible. The study concludes that greater returns can be obtained by calculating the total returns of stock portfolios based on different portfolio approaches.

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.

Online Portfolio Based on Trend Trading Strategy Considering Investor Sentiment Using Text Analysis

Intelligent online portfolios have become an important research topic in the field of quantitative finance. This paper proposes an online portfolio based on trend trading strategy using fuzzy logic technology analysis method and considering investor sentiment. Firstly, the paper uses SVM classification algorithm to analyze stock comment text data in online forums and constructs investor sentiment indicators. Secondly, the paper transforms the heuristic algorithm of technical trading into corresponding fuzzy IF-THEN rules and combines them into a fuzzy investment decision system. Thirdly, the paper constructs a new online portfolio based on trend trading strategy. Finally, the paper uses the text data of investor reviews and stock trading data on the internet for empirical analysis to illustrate the effectiveness of the online portfolio strategy constructed. The results indicate that online portfolios constructed based on trend trading strategies can achieve higher performance than benchmark strategies while considering transaction costs.

A Weak MLMC Scheme for Lévy-Copula-Driven SDEs with Applications to the Pricing of Credit, Equity and Interest Rate Derivatives

This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for Lévy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain approximation [Mijatović, Aleksandar, Matija Vidmar, and Saul Jacka. 2012. “Markov Chain Approximations for Transition Densities of Lévy Processes.” Electronic Journal of Probability 19]) of the pure-jump component of the driving Lévy process and is particularly suited if the multidimensional driver is given by a Lévy copula. The multilevel version of the algorithm requires a new coupling of the approximate Lévy drivers in the consecutive levels of the scheme, which is defined via a coupling of the corresponding Poisson point processes. The multilevel scheme is weak in the sense that the bound on the level variances is based on the coupling alone without requiring strong convergence. Moreover, the coupling is natural for the proposed discretization of jumps and is easy to simulate. The approximation scheme and its multilevel analogous are applied to examples taken from mathematical finance, including the pricing of credit, equity and interest rate derivatives.

Big-Data Technology in Finance: Quality of Stock-Trading Information in Vietnamese Stock Market

Quantitative finance is a field of applied research where the data is important information investors’ profitability and financial risk of financial assets in the processes of decision-making. And financial institutions and securities have applied big-data technologies in stock market to exploit useful information for investors using mobile stock-trading apps. The standardization of database from the raw data of companies’ financial statements, statistical reports and stock-trading data support to enhance data mining analysis by predictive patterns with high feasibility for useful information for investors’ decision-making. And quantitative tools of predictive patterns for financial advanced indexes test expected market return and favourable market timing for buying or selling stocks in stages of market cycle and prediction of market risk before market-trend crash. On the development of securities’ mobile stock-trading apps, the addition of new advanced indexes increases the quality of stock-trading information in Vietnamese stock market generally, seeks competitive advantages of market segments for securities particularly when they change big-data technology in mobile stock-trading apps. This contribution has a better using FinTech combined with stock-trading algorithms to provide more useful and confident information of optimal profitability and financial risk management that individual and institutional investors catch up the trend of big-data technology.

Probabilistic simulation of electricity price scenarios using Conditional Generative Adversarial Networks

A novel approach for generative time series simulation of electricity price scenarios is presented. A “Time Series Simulation Conditional Generative Adversarial Network” (TSS-CGAN) generates short-term electricity price scenarios. In particular, the network is capable of generating a 24-dimensional output vector that corresponds to the expected behavior of electricity markets. The model can replace typical approaches from financial mathematics like statistical factor models to model the price distribution around a given forecast. The data cover a 3-year period from 2020 to 2023. Our empirical study is conducted on the EPEX SPOT market in Europe. An electricity price scenario includes the prices of the hourly contracts of a day-ahead auction at the EPEX SPOT power exchange. The model uses multivariate time series as input factors, consisting of point forecasts of electricity prices and fundamental data on generation and load profiles. The architecture of a TSS-CGAN is based on the idea of Conditional Generative Adversarial Networks combined with 1D Convolutional Neural Networks and Bidirectional Long Short-Term Memory. The model is evaluated using qualitative and quantitative criteria. For the evaluation, 10,000 simulations of a test period are carried out. Qualitative criteria are whether the model follows certain electricity market-specific regularities and depicts them adequately. The quantitative analysis includes common error metric, compared to benchmark models, like DeepAR, Prophet and Temporal Fusion Transformer, the examination of the quantile ranges, the error distribution and a sensitivity analysis. The results show that the TSS-CGAN outperforms benchmark models such as DeepAR by reducing the continuous ranked probability score by 50% and considers market-specific circumstances such as the production of fluctuating energies and reacts correctly to changes in the corresponding variables.

Harnessing machine learning for enhanced quantitative financial strategies: Applications and case studies

Machine learning algorithms have long been an essential tool for quantitative finance, as they play an important role in the asset pricing, portfolio optimisation and financial risk management. This work discusses how to apply Random Forest, Support Vector Machine (SVM), and Neural Networks to further develop and enhance the quantitative investment research. With automatic feature selection, reconstruction of high-dimensional data and resist against over-fitting, Random Forest has been an efficient ensemble approach with remarkable prediction performance. For this reason, Random Forest is leveraged for the stock price prediction. SVM, particularly known for its robustness in high-dimensional classification task, has a non-linear optimisation ability that can be employed to capture the inherent non-linear dependencies in options prices. Neural Networks, as a learning approach capable of discovering complex relationships, is employed for the portfolio optimisation, with a promise for further improving the risk-adjusted portfolio return. The work is conducted through practical case studies to simulate how Random Forest, SVM and Neural Networks enable us to further improve the financial performance, and to illustrate its advantage, disadvantage and practical application in quantitative finance.

A dynamic pythagorean exponent: Applications to baseball and structural modeling in risk management

AbstractThe famous Pythagorean theorem relating a team's winning percentage over a season to it's total runs scored and surrendered has been the subject of much attention, in both popular culture and academia. In academia, a main focus has been to find the optimal value for the exponent in the formula, originally taken to be 2 in Bill James' work. The optimal value has been obtained in many published works via regression or other statistical estimation techniques, and calibrated to various sports to reflect the type of play in each sport. In this short article, we borrow from ideas in quantitative finance and risk management to estimate the distribution of these Pythagorean exponents, viewing them as random variables that can evolve over time. We carry out our analysis in a manner similar to that of implied volatility from the Black‐Scholes formula. We present the result of our analysis of 150 years of team data via the Lahman package in R, and also provide dynamic models for an evolving measure of the Pythagorean exponent. This includes suggestions for modeling credit default as well as contract valuation in sports via macro variables in connection with historically implied parameters.

Research on Problems and Solutions of Quantitative Investment in the Chinese Market

Quantitative investment has gradually become increasingly important in the Chinese finance market in recent decades. It improves the efficiency of investment, reduces the risk of investment, enhances the liquidity of some market assets and provides new opportunities to accumulate wealth for investors. As a new investment method, it raises some problems which lead to the turmoil of the market when it keeps developing and gaining traction. This paper will review the current situation of quantitative investment in the Chinese market from its development history and the sizes of funds. This study shows that there are mainly four problems existing in the application of quantitative investment in China. Listed below are problems. The evident government intervention in the market has a negative impact on the fitting effectiveness of quantitative models. Some kinds of assets and commodities face poor liquidity and for them, quantitative investment strategies can hardly be conducted accurately. The accuracy of quantitative analysis can be unreliable for the financial data is sometimes incomplete and unreliable in the Chinese market. The high-frequency trading affects the stability of the whole market because of lack of market supervision. This paper also puts forward relevant countermeasures and suggestions according to these problems. This study has great significance to the healthy development of quantitative investment in the Chinese market.

Theory and Practice of Quantitative Investment Strategies

This paper provides an overview of the theory and practice of quantitative investment strategies, beginning with the definition of quantitative investment, its history of development, and its importance in financial markets. It then delves into the theoretical foundations of quantitative investment, including financial market theory, the application of mathematical and statistical methods, and the theory of risk management and portfolio optimisation. Common quantitative investment strategies, such as spread trading, momentum strategy, mean reversion strategy, etc., are then detailed, as well as the design, implementation process and practical application of these strategies. Examples of successful and failed strategies are further analysed, as well as the challenges and problems faced, such as data quality, model overfitting, and market changes. Finally, future trends in quantitative investing are looked at, including the application of artificial intelligence and big data, advances in algorithmic trading, changes in the regulatory environment, and the impact of sustainable investing and ESG factors. This paper aims to provide investors, researchers and market regulators with a comprehensive understanding and outlook of quantitative investing.

Preface: 3rd International Conference on Financial Technology and Market Management (FTMM 2024)

The 2024 3rd International Conference on Financial Technology and Market Management (FTMM 2024) have been conducted during July 27-28, 2024, in San Francisco, USA. This conference aims to bring together leading academic scientists, researchers, and scholars to exchange and share their experiences and research results on all aspects of economics, business, and marketing management. It also provides a premier interdisciplinary platform for researchers, practitioners, and educators to present and discuss the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of economics, business, and marketing management. More than 180 participants from China, Japan, Malaysia, France, and some other countries attended FTMM 2024. About 36 presentations including 6 plenary talks were presented. The presentations are grouped into 9 areas of particular interest: (1): Economic and monetary crisis, (2): Taxes and regulation, (3): Emerging markets issues, (4): Corporate finance and governance, (5): Asset pricing, investment, and portfolio management, (6): Financial markets, (7): Risk management and quantitative finance, (8) Econometric modeling and empirical issues, (9): Mathematical Finance. With best regards, Conference Organizing Chair San Francisco, USA

Research on the Development of Investment Portfolio Theory

This paper provides a comprehensive analysis of portfolio theory evolution and its practical applications, tracing its development since Harry Markowitz introduced Modern Portfolio Theory (MPT) in 1952. The urgency to enhance capital market efficiency, optimize asset portfolios, and effectively measure and manage risks has intensified due to the rapid transmission of risk across global financial markets. This study reviews historical advancements and recent achievements in portfolio theory and practice. Furthermore, it constructs a theoretical research framework to guide the future development of quantitative investment strategies, focusing on active portfolio management. This framework also delineates several prospective research avenues. The advent of artificial intelligence and big data has transformed portfolio theory into a multidisciplinary nexus involving mathematical statistics, machine learning, and behavioral finance. This integration is crucial for refining asset portfolio optimization and understanding the dynamics of risk spillover and its determinants. The findings and theoretical advancements discussed herein are vitally important for fostering the sustainable development of capital markets and ensuring economic and financial stability. This study not only revisits foundational theories but also sets the stage for pioneering future research in financial analysis and portfolio management.

Special issue of Quantitative Finance in honor of Michael Dempster's 85th birthday

Special issue of Quantitative Finance in honor of Michael Dempster's 85th birthday

Framework for multivariate carbon price forecasting: A novel hybrid model

The complex characteristics of volatility and non-linearity of carbon price pose a serious challenge to accurately predict carbon price. Therefore, this study proposes a new hybrid model for multivariate carbon price forecasting, including feature selection, deep learning, intelligent optimization algorithms, model combination and evaluation indicators. First, this study collects and organizes the historical carbon price series of Hubei and Shanghai as well as the influencing factors in five dimensions including structured and unstructured data, totaling twenty variables. Second, data dimensionality reduction is performed and input variables are obtained using the least absolute shrinkage and selection operator, followed by the introduction of nine advanced deep learning models to predict carbon price and compare the prediction effects. Then, through the combination of models, three models with the best performance are combined with Pelican optimization algorithm to construct a hybrid forecasting model. Finally, the experimental results show that the developed forecasting model outperforms other comparation models in terms of prediction accuracy, stability and statistical hypothesis testing, and exhibits excellent prediction performance. Furthermore, this study also applies the developed model to European carbon market price prediction and uses the Hubei carbon market as an example for quantitative trading simulation, and the empirical results further verify its robust prediction performance and investment application value. In conclusion, the proposed hybrid prediction model can not only provide high-precision carbon market price prediction for the government and corporate decision makers, but also help investors optimize their trading strategies and improve their returns.

Analytically pricing volatility options and capped/floored volatility swaps with nonlinear payoffs in discrete observation case under the Merton jump-diffusion model driven by a nonhomogeneous Poisson process

In this paper, we introduce novel analytical solutions for valuating volatility derivatives, including volatility options and capped/floored volatility swaps, employing discrete sampling within the framework of the Merton jump-diffusion model, which is driven by a nonhomogeneous Poisson process. The absence of a comprehensive understanding of the probability distribution characterizing the realized variance has historically impeded the development of a robust analytical valuation approach for such instruments. Through the application of the cumulative distribution function of the realized variance conditional on Poisson jumps, we have derived explicit expectations for the derivative payoffs articulated as functions of the extremum values of the square root of the realized variance. We delineate precise pricing structures for an array of instruments, encompassing variance and volatility swaps, variance and volatility options, and their respective capped and floored variations, alongside establishing put-call parity and relationships for capped and floored positions. Complementing the theoretical advancements, we substantiate the practical efficacy and precision of our solutions via Monte Carlo simulations, articulated through multiple numerical examples. Conclusively, our analysis extends to the quantification of jump impacts on the fair strike prices of volatility derivatives with nonlinear payoffs, facilitated by our analytic pricing expressions.

Designing Efficient Pair-Trading Strategies for the Technology Stock Market

Pairs trading is a quantitative trading approach that exploits instances of financial markets exhibiting disequilibrium. Through the identification of a pair of stocks with a his-torical pattern of correlated movement, and under the assumption that their price differentials will return to a central tendency, an investor can seek to gain from this mean-reversion by establishing a long position in the designated pair. Throughout the years, numerous trading frameworks and methodologies have been devised to enhance the efficacy of this strategy. This paper proposes an approach based on cointegration and correlation, but ultimately utilizes cointegration to identify the pair trading investment strategy that can be applied to technology sector stocks and metal futures in China over the last five years. The top five ranked portfo-lios are then evaluated. The results indicate that the pairs with Silver and Copper exhibited positive returns, while the pair with Palladium yielded negative returns.

A Girsanov transformed Clark-Ocone-Haussmann type formula for $$L^1$$-pure jump additive processes and its application to portfolio optimization

AbstractWe derive a Clark-Ocone-Haussmann (COH) type formula under a change of measure for $$ L^1 $$ L 1 -canonical additive processes, providing a tool for representing financial derivatives under a risk-neutral probability measure. COH formulas are fundamental in stochastic analysis, providing explicit martingale representations of random variables in terms of their Malliavin derivatives. In mathematical finance, the COH formula under a change of measure is crucial for representing financial derivatives under a risk-neutral probability measure. To prove our main results, we use the Malliavin-Skorohod calculus in $$ L^0 $$ L 0 and $$ L^1 $$ L 1 for additive processes, as developed by Di Nunno and Vives (2017). An application of our results is solving the local risk minimization (LRM) problem in financial markets driven by pure jump additive processes. LRM, a prominent hedging approach in incomplete markets, seeks strategies that minimize the conditional variance of the hedging error. By applying our COH formula, we obtain explicit expressions for locally risk-minimizing hedging strategies in terms of Malliavin derivatives under the market model underlying the additive process. These formulas provide practical tools for managing risks in financial market price fluctuations with $$L^1$$ L 1 -additive processes.

Quantitative Strategies Based on FinGPTs Analysis of the Federal Reserves Attitude

This paper explores the impact of the Federal Reserve (Fed) on financial markets, specifically through the sentiment scoring of Fed meeting minutes by the AI analysis model FinGPT and its correlation with market performance. The article first introduces the method of sentiment analysis using FinGPT and conducts an in-depth analysis of the meeting minutes from 1990 to 2020 using this method. Furthermore, key market data, such as the S&P 500 Index, real estate, and financial sector indices, are used to assess the actual impact of the Feds attitude on market dynamics. Through quantitative trading and backtesting analysis, this study verifies the performance and effectiveness of a single-factor strategy in different markets. The results show that while the Feds sentiment scores have high predictive validity and market adaptability in the financial sector, their performance in the real estate market and the broader stock market index is relatively weaker. The findings indicate that the market applicability of the strategy is significantly influenced by market type and economic environment. Future strategy optimization needs to consider these factors to enhance adaptability and efficiency across different markets.

Random Processes and Their Applications in Financial Mathematics

Random processes are fundamental tools in modern financial mathematics, widely applied in fields such as financial derivatives pricing, risk management, and interest rate models. This paper systematically introduces the basic theory of random processes, including definitions and classifications, Brownian motion and geometric Brownian motion, and stochastic differential equations. Furthermore, the paper explores specific applications of random processes in financial mathematics, focusing on financial derivatives pricing, risk management and portfolio optimization, and applications in interest rate models and credit risk. Through theoretical and empirical research, this paper reveals the significant role and development prospects of random processes in financial mathematics, providing new ideas and methods for risk management and pricing models in financial markets.