data & mathematics
Showing 31 articles in data & mathematics.
Value at Risk in Python: Rolling Volatility, EWMA, and Breach Testing
Build and backtest historical, rolling-normal, EWMA, and Student-t VaR in Python, then compare breaches, fat-tail failure modes, and Expected Shortfall.
Longstaff-Schwartz: Monte Carlo Meets Optimal Stopping
Learn how least-squares Monte Carlo turns American option pricing into backward regression, with reproducible Python benchmarks and practical caveats.
100 Posts Later: How Sharing My Work Helped Me Find My Momentum Again
My 100th post is a reflection on rebuilding momentum through public learning—and how 165,000 words across AI, enterprise software, mathematics, and finance changed me.
Finite Differences and PSOR: Solving the American Put PDE
The Black-Scholes PDE becomes a linear complementarity problem for American options. Crank-Nicolson discretization plus Projected SOR solves it efficiently — and produces the free boundary as a byproduct.
Binomial Trees for American Puts: CRR, Convergence, and Leisen-Reimer
Price American puts with CRR and Leisen-Reimer trees, understand parity-driven convergence, extract the exercise boundary, and benchmark accuracy in Python.
The American Option Problem: Why Early Exercise Has No Closed Form
American options force a holder to choose between acting now and waiting. That decision creates an optimal stopping problem with no closed-form solution — and a free boundary that is the central unknown of all American option pricing methods.
Monte Carlo Option Pricing: When Closed Forms Stop Helping
When Black-Scholes has no formula, Monte Carlo does the job. A story-driven guide to pricing path-dependent options, variance reduction, and convergence in Python.
The Small-World Revolution: Mapping the Seditious Metadata of 1775 Boston
A network science analysis of the Committees of Correspondence, Sons of Liberty, and Boston Masons to show how Paul Revere functioned as a high-betweenness-centrality node.
TabFM: Google's Zero-Shot Tabular Foundation Model for SPY Volatility
Google's TabFM turns tabular prediction into in-context learning. Here is what matters, why the non-commercial license matters, and how to test it on SPY volatility.
Black-Scholes Without the Magic: Turning Random Paths into a Pricing Equation
A story-driven derivation of Black-Scholes: how GBM, Itô calculus, delta hedging, and no-arbitrage turn a random stock path into an option pricing equation.
The Most Important Lemma of 2026 Was Written by an AI. There's No Way to Cite It.
GPT-5.5 suggested a four-line argument that helped disprove a 50-year-old conjecture. That argument is now un-citable. Here's what that means for the future of knowledge.
Geometric Brownian Motion in Python: The First Model Every Quant Learns
A practical, story-driven introduction to geometric Brownian motion: why quants model log returns, how volatility drag appears, and how to simulate price paths in Python.
From Itô to Black-Scholes: How Randomness Became a Pricing Engine
The bridge from stochastic calculus to quantitative finance: how Bachelier, Wiener, Itô, Black, Scholes, and Merton turned random price paths into a pricing engine.
Why Your LLM is a Stochastic Process (And Why Temperature=0 Doesn't Save You)
A deep dive into why Large Language Models are auto-regressive Markov chains, how GPU floating-point non-associativity and FlashAttention break determinism, and why agent pipelines behave like controlled stochastic systems.
The Quiet Genius Who Made Randomness Calculable
Brownian motion had been observed, priced, explained, and made rigorous. Kiyosi Itô did something stranger: he built a calculus for paths too jagged to differentiate.
The One-Line Change That Beats Brute Force: Antithetic Variates in Monte Carlo Pricing
Monte Carlo option pricing has a brutal tax: to halve your error you need four times the paths. But one almost trivial idea — mirroring every random shock — buys up to 4.7× the accuracy for free. Meet antithetic variates.
The Unstoppable Mind: Norbert Wiener and the Mathematics of Continuous Randomness
A child who graduated university at 14, a PhD at 18, then years of wandering before MIT. Norbert Wiener didn't just tame randomness — he built the mathematical house it lives in, then invented cybernetics and warned the world about machines.
Dolt: What If Your Database Had a Git History?
Dolt is a MySQL-compatible database where every row has lineage, every schema change is a commit, and your entire data history is one SQL query away. Here is why 22,000+ developers are rethinking how they store data.
Bachelier's Revenge: How a Forgotten Thesis Shaped Modern Finance
In 1900, a French orphan wrote a PhD thesis that predated Einstein by 5 years and seeded the Black-Scholes formula. Then the world forgot him. The story of how one equation — setting expectation to zero — became worth trillions.
When Randomness Met Calculus: A Practitioner's Guide to Stochastic Differential Equations
Itô gave randomness a mathematical language. Now let us use it. A hands-on guide to stochastic differential equations — what they mean, where they appear in physics, biology, and finance, and how to simulate them in Python with the Euler-Maruyama method.
From Pollen Grains to Nuclear Bombs: The Astonishing Story of Monte Carlo Methods
How a game of solitaire played by a sick mathematician in 1946 led to one of computing's most powerful techniques — and why randomness became the solution to the world's hardest problems.
From Symbolic Math to Random Sampling: Mastering Integral Calculations with Python
Explore three powerful approaches to solving integrals: analytical methods, Sympy symbolic integration, and Monte Carlo numerical methods. Learn how randomness can solve mathematical problems with stunning accuracy.
SymPy: Bridging the Math Gap in Gen AI Systems
Discover how SymPy transforms LLMs from approximate text predictors into precise mathematical reasoning engines. Learn to build neuro-symbolic AI systems that handle calculus, stochastic differential equations, and complex symbolic math with 100% accuracy.
Chronos-2: The Evolution from Univariate to Universal Time Series Forecasting
Amazon introduces Chronos-2, a foundation model that handles univariate, multivariate, and covariate-informed forecasting in a zero-shot manner using in-context learning.
Bridging Legal Requirements and Technical Implementation: A Practical Guide to AI Governance Frameworks
Explore how modern technology platforms like OpenMetadata, DataHub, and Apache Atlas enable organizations to meet evolving legal requirements from EU AI Act to NIST frameworks while building robust AI governance systems.
Open-Source Data Governance Frameworks: A Strategic Analysis of OpenMetadata, DataHub, Apache Atlas, and Amundsen
Comprehensive comparison of leading open-source data governance platforms - OpenMetadata, DataHub, Apache Atlas, and Amundsen - with practical guidance for strategic selection and implementation.
Data Governance for AI and RAG Systems: A Strategic Imperative
Discover why specialized data governance frameworks are critical for AI and RAG systems, and learn practical strategies to ensure responsible, secure, and effective AI deployment.
Introducing The Data Guy Show: Your New Favorite Podcast on AI, Data, and the Future
Announcing The Data Guy Show — a lively new podcast where Mo and Nazz break down the world of AI, data science, and agentic systems. Meet your hosts and discover what’s in store!
Building Your AI Data Moat: Competitive Advantage Through Proprietary Data
Learn concrete strategies for creating an unassailable competitive advantage through collecting, annotating, and protecting your organization's proprietary data assets in the AI era.
Part 4: Generating Test Data with Ragas
Discover how to generate robust test datasets for evaluating Retrieval-Augmented Generation systems using Ragas, including document-based, domain-specific, and adversarial test generation techniques.
Data is King: Why Your Data Strategy IS Your Business Strategy
Discover why controlling unique, high-quality data is your organization's most valuable competitive advantage in the AI era, and how a strategic approach to data ownership is becoming essential to business success.