Scenario Description Consider a financial asset whose price, Xt​, follows a mean-reverting stochastic process. A common model for mean reversion is the Ornstein-Uhlenbeck (OU) process, defined by the stochastic differential equation (SDE): Objective The trader aims to maximize the expected cumulative profit from trading this asset over a finite horizon, subject to transaction costs. The trader’s control is the rate of buying or selling the asset, denoted by ut​, at time t. Hamilton-Jacobi-Bellman (HJB) Equation To find the optimal trading strategy, we frame this as a stochastic control problem ..read more

Introduction: Financial modeling has long sought to develop frameworks that accurately capture the complex dynamics of asset prices. Traditional models often focus on either momentum or mean reversion effects, struggling to incorporate both simultaneously. In this blog post, we introduce a two-factor model that aims to address this issue by integrating both momentum and mean reversion effects within the stochastic processes governing stock prices. The Motivation Behind the Two-Factor Model: The development of the two-factor model is motivated by the empirical observation that financial market ..read more

Intelligent-Technologies-1 The post Intelligent Technologies appeared first on QUANTITATIVE RESEARCH AND TRADING ..read more

High-frequency statistical arbitrage leverages sophisticated quantitative models and cutting-edge technology to exploit fleeting inefficiencies in global markets. Pioneered by hedge funds and proprietary trading firms over the last decade, the strategy identifies and capitalizes on sub-second price discrepancies across assets ranging from public equities to foreign exchange. At its core, statistical arbitrage aims to predict short-term price movements based on probability theory and historical relationships. When implemented at high frequencies—microseconds or milliseconds—the quantitative mod ..read more

In a previous article I made a detailed comparison of Mathematica and Python and tried to identify areas where the former excels. Despite the many advantages of the Python technology stack, I was able to pinpoint a few areas in which I think Mathematica holds the upper hand. Whether those are sufficient to warrant the investment of time and money required to master the Wolfram Language is another matter, which the user must decide for himself. In this comparison between Matlab and Python I won’t reiterate the strengths of the Python that make it the programming language of choice for so many d ..read more

Python vs. Wolfram Language As an avid user of both Python and Wolfram Language for technical computing, I’m often asked how they compare. Python’s strengths as an open-source language are clear: Ubiquity – With millions of users, Python has become ubiquitous across fields like data science, ML engineering, web development, and scientific research. This massive adoption fuels continuous enhancement of its tools. Comprehensive capabilities – Python’s expansive ecosystem of 200,000+ libraries spans everything from numerical computing to web frameworks to industrial automation. It is a versatile ..read more

Momentum-Mean-Reversion The post Momentum & Mean Reversion in Discrete and Continuous Time Processes appeared first on QUANTITATIVE RESEARCH AND TRADING ..read more

I’m delighted to introduce my new series of custom-designed AI tools powered by cutting-edge generative technology. With just a click, you can now access a range of intelligent assistants tailored for different tasks. These AI helpers are the product of fine-tuning powerful models called Generative Pre-trained Transformers (GPTs). I’ve carefully adjusted them to excel at everything from writing to math to coding and beyond. To try one out, simply click the icon below for the assistant you need. A new world of AI support is now at your fingertips. As a subscriber to ChatGPT, you can use these G ..read more

Recent-Advances-in-Equity-Analytics-and-the-Equities-Entity-Store-1 The post Recent Advances in Equity Analytics and the Equities Entity Store: Fractional Integration appeared first on QUANTITATIVE RESEARCH AND TRADING ..read more

Pricing-Options-Using-Machine-Learning-AlgorithmsDownload The post Pricing Options Using Machine Learning Algorithms appeared first on QUANTITATIVE RESEARCH AND TRADING ..read more