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Greeks

Delta, gamma, theta, vega, and rho. How an option price responds to every input, one dimension at a time.

01 What the Greeks are, and why Five letters that measure how an option price responds to its five inputs. Position management is multi-dimensional; the Greeks are the dashboard. 8 min
02 Delta in detail Direction sensitivity, probability proxy, hedge ratio. Three jobs in one number, with the same range across every chain. 9 min
03 Gamma in detail The curvature of delta. Highest where it matters most: at the money, near expiration. Where short premium positions go wrong. 9 min
04 Theta in detail Time decay, day by day. Not linear, not symmetric across strikes. The Greek that quietly funds the short premium business. 9 min
05 Vega in detail Volatility sensitivity. Scales with time. The only Greek that lets you bet on the market's nervousness without betting on direction. 9 min
06 Rho in detail Interest rate sensitivity. Small for short-dated options. Real for LEAPS. The Greek that resurfaced in the 2022 rate cycle and surprised a generation of traders. 7 min
07 Delta, gamma, theta, vega: how they act together The Greeks do not work in isolation. The same position has all five active, and managing one without watching the others is how positions blow up. 10 min
08 How IV is back-solved from premium IV is not observed directly. It is the volatility that makes the pricing model match the observed premium. The algorithm is iterative; the catch is that it gets fragile at the edges. 7 min
09 How each Greek evolves over an option's life Greeks are not constants. Each one changes shape as expiration approaches, and the changes interact. Sense for the dynamics beats memorising a single snapshot. 8 min
10 IV skew and term structure Implied volatility is not a single number across a chain. It has a smile across strikes and a curve across expirations. Both shapes carry information. 9 min
11 The volatility risk premium Implied volatility usually overstates realised volatility. The gap is the income source of the entire short premium industry. 8 min
12 Hedging with Greeks How dealers stay direction-neutral while collecting spread. The same mechanics produce gamma squeezes when retail piles in. 9 min
13 Pin risk and expiration day On expiration day, ATM options have an ambiguous outcome. Some longs exercise, some do not; some shorts get assigned, some do not. The uncertainty is a real risk. 7 min
14 Synthetic positions and put-call parity Every option position has a synthetic equivalent built from other instruments. The relationship is enforced by arbitrage and gives the trader options on how to express the same view. 9 min
15 Black-Scholes intuition, without the math The first closed-form option pricing formula, in plain English. What it assumes, why it works, and where it breaks. 9 min