The Greeks: How an Option Price Moves

Course episode nine, Wilmott chapter eight. A price is useful for about one second; then the stock moves, a day passes, volatility shifts. The Greeks are the sensitivities that say how the price responds. The episode opens with the vocabulary of the value sheet: boundary conditions (state the edges first), marching backward from expiry, the diffusion picture in which a sharp payoff corner becomes a smooth curve, partial derivatives (a rate of change in one direction with the others held still), and the fact that the same equation prices a call, a put, or an early-exercise contract with only the edges changed. The slopes of that sheet are the Greeks. Inputs: stock price, strike, volatility, rate, time. Outputs: delta (the share count that hedges the option), gamma (how fast delta changes), theta (the clock), vega (volatility), rho (the interest rate). Run once on a three-month at-the-money call: about eight dollars, delta fifty-four hundredths, gamma two hundredths, theta about four cents a day, vega about twenty cents a point. The one inside idea: every Greek is a local slope, so Greeks change as the market moves, add across a book, and gamma and theta are locked with opposite signs. The takeaway: ask which Greek dominates the risk of a position right now. Ends with a prompt for your own AI model. For educational purposes only; not financial, investment, tax, or legal advice. Nothing here is a recommendation to buy or sell any instrument. Past performance is not indicative of future results. Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.