Integrated Quant Capstones

Build and validate a small numerical toolkit - differentiation, integration, linear solves, least squares, decompo

Simulate, estimate, and validate the building blocks of continuous-time finance: distributions, the CLT, and Brownian mo

From Itô’s lemma and GBM to Black–Scholes and risk-neutral pricing - then confirm the closed form with

Measure realized volatility, back out implied volatility, model conditional variance with GARCH, and confront the volati

Build a time-aware backtest with regularization, honest transaction costs, and explicit model risk - and refuse to

Split a large order to balance market impact against timing risk - the Almgren–Chriss trade-off, TWAP/VWAP b

Quote a two-sided market, earn the spread, manage inventory, and confront adverse selection - the Avellaneda&ndash

The full arc: a research question turned into a reproducible, bias-controlled, cost-aware, risk-analyzed study with an h