A framework for modeling text data using Google Colab — This article is meant to serve as a framework to solve natural language processing (NLP) problems using Python, neural networks, and GPU. Though a high level of math is required to understand everything herein, I wrote this article with the intent that an absolute beginner or seasoned veteran would get…

A Working Library for Securities Pricing — Quantitative Finance In the past, I have written extensively on the topic of securities pricing… Black-Scholes Algorithmic Delta Hedging What Is Implied Volatility? Martingales and Markov Processes Stochastic Integrals Deriving the Black-Scholes Model Python for Pricing Exotics Volatility Trading 101 Risk-Neutral Portfolio Management Black-Scholes Option Pricing is Wrong

Increasing the Efficiency of Matrix Decompositions — As previously exhibited in our article on simulating correlated Brownian motions, the Cholesky decomposition is a very useful matrix decomposition. In practice we usually intend to impose correlation and covariance structures on large spaces, generating a common computational problem: time complexity. Generally speaking, the time complexity of the Cholesky decomposition…

A Guide to Generating Correlated Sample Paths — There are several reasons why one may wish to simulate multiple Brownian motions with an underlying correlation structure. Take for example a stylized fact of the market: the leverage effect…

Implications of Black-Scholes Pricing — Implied volatility can be a tricky topic. This article aims to provide an intuitive and clear understanding of what implied volatility is and how to compute it numerically using Python. First, let’s consider the problem space… Suppose we are trading an option contract on an underlying equity with a European…

Explanation, Derivation and Applications in Python — Introduction The linear algebra essential to data science, machine learning, and artificial intelligence is often overlooked as most introductory courses fail to display the big picture. Concepts such as eigendecomposition and singular value decomposition (SVD) are incredibly important from a practitioner's standpoint; they are the core of dimensionality reduction techniques including…

A Curated Selection of Books by Topic — This list comprises books that I have found helpful on my journey in quantitative finance. This list is by no means exhaustive, but I can personally vouch for the usefulness of each of these books as I have read them myself. Note: I am in no way affiliated with the…

A Quickstart Guide to Generative Machine Learning with Code — Introduction Generative machine learning can be helpful in a variety of contexts. One, for example, is when some closed-form or quasi-closed-form solution is available but computationally expensive. In this case, a neural network may provide a timely solution with an acceptable degree of accuracy. Nevertheless, to train such a network, data…

With Real Strategies Developed by Quantitative Research — Quantitative Research Backtesting quantitative research prior to implementation in a live trading environment (see Algorithmic Trading with Python or Dynamic Algorithmic Trading Systems) is as essential as it is the fruit of a quantitative researcher’s labor. It’s critical to note that the outcome of a backtest is directly related to the quality…