Computational Efficiency

Fast Learning in Quantitative Finance with Extreme Learning Machine ArXiv ID: 2505.09551 “View on arXiv” Authors: Liexin Cheng, Xue Cheng, Shuaiqiang Liu Abstract A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously addressed using deep neural networks, can be efficiently solved using single-layer neural networks without iterative gradient-based training. This is achieved through the extreme learning machine (ELM) framework. ELM utilizes a single-layer network with randomly initialized hidden nodes and output weights obtained via convex optimization, enabling rapid training and inference. We present various applications in both supervised and unsupervised learning settings, including option pricing, intraday return prediction, volatility surface fitting, and numerical solution of partial differential equations. Across these examples, ELM demonstrates notable improvements in computational efficiency while maintaining comparable accuracy and generalization compared to deep neural networks and classical machine learning methods. We also briefly discuss theoretical aspects of ELM implementation and its generalization capabilities. ...

Assets Forecasting with Feature Engineering and Transformation Methods for LightGBM ArXiv ID: 2501.07580 “View on arXiv” Authors: Unknown Abstract Fluctuations in the stock market rapidly shape the economic world and consumer markets, impacting millions of individuals. Hence, accurately forecasting it is essential for mitigating risks, including those associated with inactivity. Although research shows that hybrid models of Deep Learning (DL) and Machine Learning (ML) yield promising results, their computational requirements often exceed the capabilities of average personal computers, rendering them inaccessible to many. In order to address this challenge in this paper we optimize LightGBM (an efficient implementation of gradient-boosted decision trees (GBDT)) for maximum performance, while maintaining low computational requirements. We introduce novel feature engineering techniques including indicator-price slope ratios and differences of close and open prices divided by the corresponding 14-period Exponential Moving Average (EMA), designed to capture market dynamics and enhance predictive accuracy. Additionally, we test seven different feature and target variable transformation methods, including returns, logarithmic returns, EMA ratios and their standardized counterparts as well as EMA difference ratios, so as to identify the most effective ones weighing in both efficiency and accuracy. The results demonstrate Log Returns, Returns and EMA Difference Ratio constitute the best target variable transformation methods, with EMA ratios having a lower percentage of correct directional forecasts, and standardized versions of target variable transformations requiring significantly more training time. Moreover, the introduced features demonstrate high feature importance in predictive performance across all target variable transformation methods. This study highlights an accessible, computationally efficient approach to stock market forecasting using LightGBM, making advanced forecasting techniques more widely attainable. ...

Isogeometric Analysis for the Pricing of Financial Derivatives with Nonlinear Models: Convertible Bonds and Options ArXiv ID: 2412.08987 “View on arXiv” Authors: Unknown Abstract Computational efficiency is essential for enhancing the accuracy and practicality of pricing complex financial derivatives. In this paper, we discuss Isogeometric Analysis (IGA) for valuing financial derivatives, modeled by two nonlinear Black-Scholes PDEs: the Leland model for European call with transaction costs and the AFV model for convertible bonds with default options. We compare the solutions of IGA with finite difference methods (FDM) and finite element methods (FEM). In particular, very accurate solutions can be numerically calculated on far less mesh (knots) than FDM or FEM, by using non-uniform knots and weighted cubic NURBS, which in turn reduces the computational time significantly. ...