Quantitative finance — options pricing, risk, volatility, and market theory.
A deep-dive into the most celebrated formula in quantitative finance. We unpack the five core assumptions, derive the intuition behind d₁ and d₂, and examine where the model breaks down in real markets.
Greeks quantify how an option's price changes with respect to market variables. This guide covers all first- and second-order Greeks — delta, gamma, vega, theta, rho and beyond — with real-world hedging context.
Monte Carlo simulation is the workhorse of exotic option pricing. We walk through the algorithm step-by-step — from GBM path generation to variance reduction techniques — with convergence analysis.
Implied volatility is not flat. The volatility surface — spanning strikes and maturities — encodes the market's probability distribution of future returns. We explain the skew, term structure, and how traders use the surface.