CM2 Financial Engineering
Options, binomial trees, Brownian motion and portfolio theory, with the CM2 formula sheet and the CM1 mathematics it builds on.
Interactive tools
Option payoff diagrams
Price calls and puts with Black-Scholes, combine up to four legs plus the underlying, and see breakevens, max profit and max loss instantly. Made for CM2, SP5 and CFA revision, with name-the-position and draw-the-payoff test modes.
Binomial option pricing
The Cox-Ross-Rubinstein tree drawn live: European and American calls and puts, early-exercise nodes highlighted, and convergence to Black-Scholes as the steps multiply. Includes a test-yourself mode with worked solutions.
Brownian motion simulator
A fan of share-price paths animating live, with drift and volatility sliders. The model behind Black-Scholes, and the volatility drag made visible. CM2.
Efficient frontier playground
Three assets with adjustable returns, risks and correlations: the frontier, the minimum-variance and tangency portfolios and the capital market line, drawn live. CM2, SP5 and CFA.
Interest rate models
Vasicek and CIR short-rate fans with mean reversion on sliders: negative-rate counts, the Feller condition, and the pull towards the long-run level made physical. CM2.
Value at Risk & Expected Shortfall
Slide the confidence level and watch VaR and TVaR move on Normal and fat-tailed t distributions, run a historical simulation on a dealt year of daily P&L, and see the two-loans example where VaR fails subadditivity. CS2, CM2 and SP5, with a test-yourself mode and worked solutions.
Reference sheets
CM2 formula cheat sheet
Portfolio theory, CAPM, Brownian motion and Ito, Black-Scholes and the Greeks, the binomial model and risk measures: financial engineering's greatest hits on one page.
CM1 formula cheat sheet
Interest conversions, annuities-certain, the life table, assurance and annuity EPVs, premium conversion, reserves and loan schedules: the CM1 core in proper notation on one page. CM2 builds on it throughout.