Implied Volatility vs Historical: Why the Smile Exists
Historical volatility measures the past; implied volatility prices the future, and the two are routinely confused. This post covers how each is…
Option Greeks Explained: Delta, Gamma, Vega and Theta
Traders do not watch option prices, they watch sensitivities. This post explains delta, gamma, vega, theta and rho in plain language with…
Black-Scholes Explained: What Each of the 5 Inputs Does
The Black-Scholes formula has five inputs and a set of assumptions, and knowing what each does is worth more than reproducing the…
Brownian Motion and Itô’s Lemma Without the Measure Theory
Stochastic calculus is usually taught starting from measure theory, which is not where the intuition lives. This post builds it from coin…
Binomial Tree Option Pricing: Replication in 5 Simple Steps
Replication is the single most important idea in derivatives pricing, and it can be demonstrated exactly with secondary-school arithmetic. This post prices…
Forwards, Futures and Swaps: Derivatives You Can Price With Arithmetic
Forwards, futures and swaps dominate global derivative volume, and all three can be priced with a yield curve and arithmetic. This post…
Yield Curve Explained: How to Read One and Where It Comes From
A yield curve is built, not observed. This post covers what the curve says about the economy, the difference between par yields,…
Present Value: The One Equation All of Finance Rests On
Discounting is the one operation that every valuation in finance reduces to. This post explains present value from first principles, works through…
What Is Quantitative Finance? A Practical Introduction
Quantitative finance applies mathematics, statistics and code to pricing, risk and trading. Here is what quants actually do, the toolkit they rely…