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…

First-Order Forward Difference Approximations — Differential equations are great, many first year college math majors have absolutely no idea about the fun that will ensue. Nevertheless, as an (financial) engineer myself, I am biased toward approximation. In this article I will demonstrate the finite difference method as an effective way to approximate differential equations. This…

Probability, Statistics, and Simulation — Its been quite a while since I’ve written an article and I’ve been eager to return but was uncertain how I should make my grand reentrance. Then I decided uncertainty is exactly how — in this article I will be discussing common random variables. Everybody wants to build artificially intelligent…

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

Financial Modeling Prep’s Analyst Recs and Social Sentiment — Does the wisdom of the crowds inform analyst recommendations? In this article, I examine the relationship between analyst recommendations and social sentiment. Should such a relationship exist, there may be several implications in the context of short-term and long-term trading strategies involving social sentiment. That is, if social sentiment is…

Financial Modeling Prep’s Historic Social Sentiment — Often retail investors, even algorithmic retail investors, disregard the effort required to build a trading strategy. Some use technical indicators, moon phases, and the likes — others use scientific research. This article serves as a guide to the process of researching trading signals, particularly in the context of social sentiment. …

This is not the correct interpretation. Formally, if we constructed 100 confidence intervals from arbitrary samples we would expect roughly 95 of them to contain the parameter where roughly 5 will not within these intervals. There is nothing special about the range of numbers in a given sample's confidence interval, but rather that the range may contain the parameter with a certain degree of confidence.

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 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…