Interactive models

Explore what changes when an assumption changes

Each model connects an input to an output and states what the result can—and cannot—support. Use the linked research question when empirical validation is available.

Choose a model

Five questions that can be explored directly

Interactive5–10 minutes

What drives an option’s value?

The option-pricing model runs Black–Scholes–Merton and a Cox–Ross–Rubinstein tree side by side. Change spot, strike, maturity, rate, dividend yield, and volatility; observe price and Greek sensitivity.

Use it to: Inspect no-arbitrage pricing, sensitivity, and numerical convergence
Do not use it to: Represent every exercise feature or observed market dynamic

Use the pricer

Interactive5–10 minutes

How sensitive is an allocation to its inputs?

The efficient-frontier model samples twenty thousand long-only portfolios over six illustrative asset classes and compares minimum-variance, maximum-Sharpe, and equal-weight answers.

Use it to: Inspect risk–return geometry, constraints, and assumption sensitivity
Do not use it to: Treat illustrative moments as forecasts or recommendations

Explore the frontier

Empirical10–15 minutes

Does a risk model survive backtesting?

The market-risk study provides a cost-aware, leak-free portfolio path, block-bootstrap intervals, formal VaR coverage tests, and dated stress windows.

Use it to: Inspect risk-model validation, calibration, and stress design
Do not use it to: Treat one frozen history as a bound on future losses

Inspect the backtest

Empirical10–15 minutes

What exposure is a factor fund actually delivering?

The factor study compares six-factor ETF regressions, HAC intervals, rolling exposure, chronological holdouts, and false-discovery corrections.

Use it to: Inspect attribution, product-label verification, and statistical governance
Do not use it to: Interpret alpha independently of the selected factor model

Inspect factor evidence

Interactive5–10 minutes

What market behavior can a process represent?

The stochastic-process model simulates GBM, Ornstein–Uhlenbeck, Merton jumps, Heston stochastic volatility, and a regime-switching process with a seeded generator.

Use it to: Inspect path behavior, distribution shape, and model differences
Do not use it to: Treat a simulated process as a market forecast

Simulate a process

Interpretation

Review assumptions and error estimates before interpreting output.

Each linked question connects the model to empirical evidence, uncertainty, limitations, and a reproducible implementation.

Start with a question Review the method