Mathematical Finance Research Articles

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.

Dependence on Tail Copula

In real-world scenarios, we encounter non-exchangeable dependence structures. Our primary focus is on identifying and quantifying non-exchangeability in the tails of joint distributions. The findings and methodologies presented in this study are particularly valuable for modeling bivariate dependence, especially in fields where understanding dependence patterns in the tails is crucial, such as quantitative finance, quantitative risk management, and econometrics. To grasp the intricate relationship between the strength of dependence and various types of margins, we explore three fundamental tail behavior patterns for univariate margins. Capitalizing on the probabilistic features of tail non-exchangeability structures, we introduce graphical techniques and statistical tests designed for analyzing data that may manifest non-exchangeability in the joint tail. The effectiveness of the proposed approaches is illustrated through a simulation study and a practical example.

Accelerated numerical solutions for discretized Black–Scholes equations

Abstract Accepted by: Aris Syntetos This study thoroughly investigates the efficiency of advanced numerical extrapolation methods aimed at enhancing the convergence of vector sequences in the realm of mathematical finance. Our focus lies in the application of polynomial extrapolation techniques to calculate finite difference solutions for the Black–Scholes (BS) equation—an indispensable model in options pricing. The performance of our algorithms undergoes rigorous evaluation through a comprehensive analysis involving both simulated and real-world data. Notably, our experiments uncover that a stochastic scheme, incorporating two extrapolation strategies and a random relaxation parameter, outperforms other proposed methods, excelling in both convergence and stability metrics. Our findings underscore the potential of this numerical extrapolation method to enhance the efficiency of financial calculations, particularly in the realm of option pricing. This innovation holds promise for refining financial models and addressing specific challenges within the field of mathematical programming, providing effective solutions to the primary computational bottlenecks commonly encountered in financial decision-making.

Stochastic Mean-Reverting Trend (SMART) Model in Quantitative Finance

Stochastic Mean-Reverting Trend (SMART) Model in Quantitative Finance

Reflections on the Practice and Future Prospects of Quantitative Trading in China

Based on experiences both in China and internationally, quantitative trading has shown certain positive effects in enhancing trading efficiency and market liquidity. However, it also poses risks of increasing market volatility under specific market conditions, necessitating guided and regulated development. This paper briefly introduces the characteristics of quantitative trading, reviews its development within China, analyzes its advantages and disadvantages, summarizes recent regulatory requirements, and reflects on its future prospects in China. Suggestions for the next steps in the regulated development of quantitative trading are also proposed.

The Term Structure of Covered Interest Rate Parity Violations

ABSTRACTWe quantify the impact of risk‐based and nonrisk‐based intermediary constraints (IC) on the term structure of covered interest rate parity (CIP) violations. Using a stochastic discount factor (SDF) inferred from interest rate swaps, we value currency derivatives. The wedge between model‐implied and observed derivative prices reflects the impact of nonrisk‐based IC because our SDF incorporates risk‐based IC. There is no wedge at short horizons, while the wedge accounts for 40% of long‐term CIP violations. Consistent with IC theory, the wedge correlates with the shadow cost of intermediary capital, and the SDF‐implied interest rate is a weighted average of collateralized and uncollateralized interest rates.

Research on Multi Factor Quantitative Investment Strategies Based on Machine Learning

Training models using machine learning algorithms have shown strong capabilities in classification prediction, thus employing machine learning algorithms in quantitative research can significantly enhance the accuracy of investment decisions. Utilizing a combination of multifactor models and machine learning algorithms for quantifying investment strategies holds considerable theoretical and practical research value. The IC analysis method and the random forest algorithm are employed to select factors, which serve as input variables (explanatory variables) for linear regression models. Future 30-day returns are used as the input variable (dependent variable) for regression calculations, establishing linear regression models to identify the relationship between them. Subsequently, this linear relationship is utilized for predicting future stock returns, thereby constructing a stock investment portfolio. The research findings indicate that both sets of strategy combinations exhibit some similarities and have achieved favorable strategy returns. Additionally, they demonstrate strong performance in terms of volatility and risk control, albeit with a deficiency in success rate.

Design of Neuro-Stochastic Bayesian Networks for Nonlinear Chaotic Differential Systems in Financial Mathematics

Design of Neuro-Stochastic Bayesian Networks for Nonlinear Chaotic Differential Systems in Financial Mathematics

Developing Financial Intelligence With Financial Mathematics

Financial intelligence is an individual's ability to understand, manage, and optimize the management of personal finances. Financial mathematics is becoming an important tool in developing financial intelligence. In this research using literature study method this method involves the search and collection of information from related literature sources. Through financial mathematics, one can calculate the future value of an investment, estimate the return on an investment, calculate annuity payments, understand the concept of time value of money, and analyze investment risk. The application of financial mathematics in financial intelligence provides an advantage in taking better financial decisions and managing finances effectively. By utilizing financial mathematics, one can improve their understanding of Finance, make effective financial planning, and take better financial decisions.

Research on finance Credit Risk Quantification Model Based on Machine Learning Algorithm

Machine learning is a branch of artificial intelligence (AI) technology that enables systems to learn and make predictions and decisions without the need for explicit programming. Machine learning algorithms learn patterns and relationships from data and are able to gradually improve their accuracy.This paper mainly introduces the application of deep learning in financial academia and the financial industry, with a particular focus on the application of machine learning and deep learning in financial quantitative trading. The paper mentions the complexity and challenges of financial markets and the difficulties machine learning faces in processing financial time series data, such as overfitting, non-stationarity, heteroscedasticity and autocorrelation. To overcome these challenges, the paper explores machine learning model design in financial quantitative trading and risk prediction, including data transformation and model construction. In the related work part, it introduces the history and development of quantitative investment, as well as the application of quantitative investment, such as high-frequency trading, arbitrage strategy and commodity trading advisory strategy. It then focuses on the application of machine learning in financial quantification, including the use of supervised and unsupervised learning in stock price forecasting and trading strategy generation. The paper also compares traditional quantitative strategies with machine learning strategies and discusses the advantages of machine learning in solving high-dimensional and non-linear problems. The methodology section introduces the application of the random forest model in financial quantification, including the model principle, feature importance calculation and experimental design. Through the pre-processing, feature selection and model construction of the credit risk prediction dataset, the construction and evaluation process of the random forest model is demonstrated. Finally, the performance of the random forest model is evaluated and compared with other models to demonstrate its advantages and applicability in financial quantification.

ECHO-GL: Earnings Calls-Driven Heterogeneous Graph Learning for Stock Movement Prediction

Stock movement prediction serves an important role in quantitative trading. Despite advances in existing models that enhance stock movement prediction by incorporating stock relations, these prediction models face two limitations, i.e., constructing either insufficient or static stock relations, which fail to effectively capture the complex dynamic stock relations because such complex dynamic stock relations are influenced by various factors in the ever-changing financial market. To tackle the above limitations, we propose a novel stock movement prediction model ECHO-GL based on stock relations derived from earnings calls. ECHO-GL not only constructs comprehensive stock relations by exploiting the rich semantic information in the earnings calls but also captures the movement signals between related stocks based on multimodal and heterogeneous graph learning. Moreover, ECHO-GL customizes learnable stock stochastic processes based on the post earnings announcement drift (PEAD) phenomenon to generate the temporal stock price trajectory, which can be easily plugged into any investment strategy with different time horizons to meet investment demands. Extensive experiments on two financial datasets demonstrate the effectiveness of ECHO-GL on stock price movement prediction tasks together with high prediction accuracy and trading profitability.

StockMixer: A Simple Yet Strong MLP-Based Architecture for Stock Price Forecasting

Stock price forecasting is a fundamental yet challenging task in quantitative investment. Various researchers have developed a combination of neural network models (e.g., RNNs, GNNs, Transformers) for capturing complex indicator, temporal and stock correlations of the stock data.While complex architectures are highly expressive, they are often difficult to optimize and the performances are often compromised by the limited stock data. In this paper, we propose a simple MLP-based architecture named StockMixer which is easy to optimize and enjoys strong predictive performance. StockMixer performs indicator mixing, followed by time mixing, and finally stock mixing. Unlike the standard MLP-based mixing, we devise the time mixing to exchange multi-scale time patch information and realize the stock mixing by exploiting stock-to-market and market-to-stock influences explicitly. Extensive experiments on real stock benchmarks demonstrate our proposed StockMixer outperforms various state-of-the-art forecasting methods with a notable margin while reducing memory usage and runtime cost.Code is available at https://github.com/SJTU-Quant/StockMixer.

EarnHFT: Efficient Hierarchical Reinforcement Learning for High Frequency Trading

High-frequency trading (HFT) is using computer algorithms to make trading decisions in short time scales (e.g., second-level), which is widely used in the Cryptocurrency (Crypto) market, (e.g., Bitcoin). Reinforcement learning (RL) in financial research has shown stellar performance on many quantitative trading tasks. However, most methods focus on low-frequency trading, e.g., day-level, which cannot be directly applied to HFT because of two challenges. First, RL for HFT involves dealing with extremely long trajectories (e.g., 2.4 million steps per month), which is hard to optimize and evaluate. Second, the dramatic price fluctuations and market trend changes of Crypto make existing algorithms fail to maintain satisfactory performances. To tackle these challenges, we propose an Efficient hieArchical Reinforcement learNing method for High Frequency Trading (EarnHFT), a novel three-stage hierarchical RL framework for HFT. In stage I, we compute a Q-teacher, i.e., the optimal action value based on dynamic programming, for enhancing the performance and training efficiency of second level RL agents. In stage II, we construct a pool of diverse RL agents for different market trends, distinguished by return rates, where hundreds of RL agents are trained with different preferences of return rates and only a tiny fraction of them will be selected into the pool based on their profitability. In stage III, we train a minute-level router which dynamically picks a second-level agent from the pool to achieve stable performance across different markets. Through extensive experiments in various market trends on Crypto markets in a high-fidelity simulation trading environment, we demonstrate that EarnHFT significantly outperforms 6 state-of-art baselines in 6 popular financial criteria, exceeding the runner-up by 30% in profitability.

15 years of Adjoint Algorithmic Differentiation (AAD) in finance

Following the seminal ‘Smoking Adjoint’ paper by Giles and Glasserman [Smoking adjoints: Fast monte carlo greeks. Risk, 2006, 19, 88–92], the development of Adjoint Algorithmic Differentiation (AAD) has revolutionized the way risk is computed in the financial industry. In this paper, we provide a tutorial of this technique, illustrate how it is immediately applicable for Monte Carlo and Partial Differential Equations applications, the two main numerical techniques used for option pricing, and review the most significant literature in quantitative finance of the past fifteen years.