Track 3 of 25

Pricing and the Greeks

Why an option costs anything before expiry, what the five inputs do, and what delta, gamma, theta, vega and rho each measure. Every example computed from one stated base case.

20 lessons

Mark a lesson complete and it is remembered here.

Why an option has a price before expiry at allBefore expiry the outcome is unknown, and an unknown outcome with a favourable floor is worth money.6 min
The intuition behind Black and Scholes, before any formulaThe model prices an option by asking what it would cost to manufacture its payoff with stock and cash.7 min
Input one: the price of the underlyingThe underlying's price moves the option's price, but not one for one, and the ratio itself changes.6 min
Input two: the strikeThe strike is the only input that never changes, and it sets where all the curvature happens.6 min
Input three: time to expiryMore time is worth more money, but the value grows with the square root of time, not with time.6 min
Input four: volatilityVolatility is how far the underlying is expected to wander, and it is the input the price is most sensitive to.7 min
Input five: the risk-free rateThe rate matters because part of the replicating package is financed, and it barely matters on short contracts.6 min
The formula, once, with every term in wordsTwo terms, one for stock and one for cash, each weighted by a probability-like number.8 min
Implied volatility is an output, not an inputThe market gives you a price; implied volatility is what you get by running the formula backwards.7 min
The volatility smile, plainlyThe model assumes one volatility per underlying; the market quotes a different one at every strike.7 min
Delta as a rate of changeDelta is how much the option's price moves for a one-dollar move in the underlying, right now.6 min
Delta as a rough probability, and the caveatDelta is close to the chance of finishing in the money, but it is not that number and the gap is systematic.7 min
Gamma: the rate of change of deltaGamma measures how quickly your exposure changes underneath you, and it explodes near expiry.7 min
Theta: the shape of decayTheta is the value an option loses per day when nothing else changes, and nothing else never happens.6 min
Why decay is not linearDecay follows the square root of time in reverse, so most of it happens at the end.7 min
Vega, and why volatility crush is not a surpriseVega measures sensitivity to implied volatility, and volatility reliably falls once uncertainty resolves.7 min
Rho, and why it rarely matters until rates moveRho measures rate sensitivity, and it is nearly invisible on short contracts and material on long ones.6 min
How the Greeks interact in one positionReal outcomes are the sum of several Greeks acting at once, and they frequently cancel.8 min
Where Black and Scholes is known to be wrongThe model's assumptions are all false in specific, well-documented ways, and the market prices around them.8 min
What a pricing model can and cannot tell youA model converts assumptions into numbers; it cannot tell you whether the assumptions hold.7 min

Educational only. Nothing in this track is investment, legal or tax advice, or a recommendation to enter into any transaction. Completion is stored in this browser and nowhere else.