What’s new · 3 Aug 2026
Illustrations replaced by falsifiable estimates
The factor and risk modules now publish frozen datasets, confidence intervals, holdout results, multiplicity corrections, and coverage tests.
Read the revision record →An open research program
The mathematical structure of financial markets, examined in public.
Quantitative Markets Research Lab is a quantitative finance research project exploring the mathematical structure of financial markets through asset pricing, portfolio optimization, derivatives modeling, risk analytics, and stochastic simulation. The project combines applied quantitative finance, advanced mathematics, and software engineering to examine how models can clarify uncertainty without pretending to eliminate it.
Active research
Can filtered risk forecasts repair breach clustering?
The 500-day historical VaR baseline fails coverage and independence. The next test is specified before a replacement model is compared.
Inspect the rejection →Recently revised
ETF factor exposures
QQQ’s raw alpha appears significant alone, but does not survive Benjamini–Hochberg correction across six simultaneous tests.
See the evidence →Central thesis
Markets are complex adaptive systems — populations of interacting agents whose collective behavior generates fat tails, volatility clustering, and regime shifts that no closed-form model fully contains. The working position of this lab is therefore modest and demanding at once: models clarify; they do not prophesy.
Every module below is a self-contained piece of that argument. The interactive tools run entirely in your browser — the same mathematics discussed in the prose, implemented in plain JavaScript you can inspect. The heavier empirical work lives in the open-source repository, where the Python research library and notebooks carry the full analysis.
Research modules
01 · Interactive
Asset Pricing
A full Black-Scholes-Merton pricer with live Greeks, set against a Cox-Ross-Rubinstein binomial tree — two routes to the same no-arbitrage price, and where they part ways.
02 · InteractivePortfolio Optimization
An efficient-frontier explorer over six asset classes. Sample twenty thousand portfolios, find minimum variance and maximum Sharpe, and watch assumptions do the work.
03 · EmpiricalRisk Analytics
A cost-aware multi-asset backtest with VaR/ES uncertainty, forecast-coverage tests, and dated historical stress windows.
04 · InteractiveStochastic Simulation
Five canonical processes — GBM, Ornstein-Uhlenbeck, Merton jumps, Heston, regime switching — simulated live, each with its SDE and its blind spots.
05 · EmpiricalFactor Research
ETF exposures estimated from documented factor data, with HAC intervals, rolling betas, chronological holdouts, and multiple-testing correction.
06 · NotesMathematical Notes
Itô's lemma, the GBM solution, risk-neutral pricing, Feynman-Kac and the Black-Scholes PDE, Monte Carlo error scaling, and why fat tails break Gaussian VaR.
07 · Flagship studyFrom Black-Scholes to Stochastic Volatility
Why market reality requires better models: the volatility smile as empirical refutation, and Heston dynamics as a disciplined response.
08 · The labAbout
The project, its author, and its credo: models clarify uncertainty — they do not eliminate it.
09 · Public recordResearch Log
The lab's questions, testable claims, assumptions, evidence, uncertainty, failures, and version-pinned reproduction artifacts — recorded in public.
Method
The lab works in a deliberate sequence: state a model's assumptions precisely, implement it faithfully, confront it with data or simulation, and record where it breaks. The failures are the research product as much as the successes — a pricing model that misprices the wings of the volatility surface is telling you something true about markets, if you are prepared to listen.
Everything here is educational. Empirical modules publish their data vintage and reproduction path; synthetic demonstrations are labeled as such. Nothing on this site is investment advice.