Quantitative Markets Research Lab

What This Is#

An open-source research platform on the mathematical structure of financial markets — built as a personal research institution, not a personal portfolio. The intellectual through-line is stated everywhere deliberately: markets are complex adaptive systems, and models clarify uncertainty; they do not eliminate it. The method is a discipline: state a model's assumptions precisely, implement it faithfully, confront it with data, and record where it breaks.

Everything is public: the research site runs interactive pricers and simulators in the browser, and the repository carries the full Python library, notebooks, and tests.

The Research Site#

Nine pages, each a self-contained piece of the argument — the interactive tools implement the same mathematics discussed in the prose:

• Home — the program, the central thesis, and the map of the modules.
• Interactive Asset Pricing — a Black–Scholes–Merton pricer with live Greeks against a Cox–Ross–Rubinstein binomial tree: two routes to the same no-arbitrage price, and where they part ways.
• Interactive Portfolio Optimization — an efficient-frontier explorer over six asset classes; sample twenty thousand portfolios and watch assumptions do the work.
• Risk Analytics — drawdowns, rolling volatility, VaR and Expected Shortfall, with an honest account of what tail estimates cannot say.
• Stochastic Simulation — five canonical processes simulated live (GBM, Ornstein–Uhlenbeck, Merton jumps, Heston, regime switching), each with its SDE and its blind spots.
• Factor Research — market, size, value, momentum, quality, and low volatility as organizing dimensions of return.
• Mathematical Notes — Itô's lemma, risk-neutral pricing, Feynman–Kac and the Black–Scholes PDE, Monte Carlo error scaling, and why fat tails break Gaussian VaR.
• From Black-Scholes to Stochastic Volatility — the flagship study: the volatility smile as empirical refutation, and Heston dynamics as a disciplined response.
• About the Lab — the project, its author, and its credo.

The Library#

A Python research library in seven subpackages, every public signature implemented against a written API contract:

• Models — vectorized Black–Scholes with Greeks and implied volatility, CRR binomial, Heston (the Albrecher "little trap" characteristic function with Gauss–Legendre quadrature, plus full-truncation Euler simulation), Merton jump-diffusion, Hagan SABR, and OLS factor models.
• Portfolio — mean–variance and the efficient frontier, Black–Litterman with Idzorek's omega, equal-risk-contribution risk parity solved by damped Newton to ~1e-14, Lopez de Prado's hierarchical risk parity, and robust and resampled variants.
• Risk — four VaR estimators, Expected Shortfall, drawdown analytics, scenario and correlation stress testing.
• Backtesting — an engine with a test that proves no look-ahead, with proportional costs and slippage.
• Math — Monte Carlo for GBM/OU/CIR/regime-switching processes, a Crank–Nicolson PDE solver with Rannacher start-up and PSOR for American options, Higham PSD repair, and Ledoit–Wolf shrinkage.
• Data — cache-first loaders over committed real snapshots: fifteen ETFs daily from 2015 through mid-2026, plus the Fama–French five factors and momentum.

Verification#

Claims are only as good as their checks. The suite runs 201 tests in about four seconds, anchored to theory rather than fixtures: put–call parity to 1e-10, binomial and PDE convergence to Black–Scholes, Merton at zero jump intensity reducing exactly to Black–Scholes, Heston Monte Carlo agreeing with the semi-analytic price, and Expected Shortfall never below VaR. Continuous integration runs the suite on Python 3.10 through 3.12.

Findings Worth Defending#

• Maximum-Sharpe mean–variance optimization earned a 1.12 Sharpe in-sample and decayed to 0.44 out-of-sample (2022–26), while risk-based allocations roughly halved out-of-sample volatility — the estimation-error tax, measured.
• "Robust" box-uncertainty optimization concentrated harder than plain MVO, because the uncertainty set haircuts the level of expected returns without changing their ranking.
• SPY exhibited a 27× range in realized volatility and a worst day near ten sigmas under a Gaussian lens — the fat-tail argument, from data.
• The SPY–TLT correlation flipped from −0.35 to +0.37 across the 2022 regime break: the diversification everyone priced in was itself regime-dependent.

What I Learned#

The platform is the proof that the four pillars compose: pricing theory, portfolio mathematics, risk measurement, and software engineering discipline in one verifiable system. The deeper lesson is epistemic — the failures are the research product as much as the successes. A model that misprices the wings of the volatility surface is telling you something true about markets, if you are prepared to listen.