Greeks & Hedging
Options Pricing handed you the Greeks. This course makes you trade with them — neutralise delta, breathe with gamma, pay rent to theta, ride the volatility surface with vega, and explain every dollar of a day's P&L.
Managing a live options book — delta, gamma, theta, vega and rho in depth, delta-neutral hedging, the discrete-rebalancing tradeoff, gamma scalping, the volatility surface, vega risk, and daily P&L attribution.
Pricing a single option is a one-time calculation. Running a book of them is a job — continuous, twitchy, P&L-bleeding — and it’s run almost entirely through the Greeks. Options Pricing told you where delta, gamma, theta, vega and rho come from; this course is about living off them, hour by hour.
Here’s what you’ll learn to do with each Greek:
- Delta & gamma — keep your stock exposure pinned to zero, and understand why gamma (how fast delta moves) never lets it stay pinned.
- Theta & rho — the clock Greeks: the rent you pay for holding optionality, and the quiet pull of interest rates.
- The gamma–theta tradeoff — two sides of one coin: no convexity without paying decay, no decay without being short convexity.
- Vega & the volatility surface — implied vol is a landscape, bending across strike (skew and smile) and maturity (term structure); your book is long or short vega at every point.
- Delta-neutral hedging — why and how often you re-hedge, and the brutal tradeoff between hedging error and transaction costs.
- Gamma scalping — the trade that makes long-gamma desks money, where it all comes down to one question: did realized vol beat the implied vol you paid?
- P&L attribution — split a day’s change into delta, gamma, theta, vega and rho pieces until every dollar is explained.
This is the most hands-on quant course on the ladder — every Greek earns its keep with an analogy, a worked number, and a chart you can poke. Bring Options Pricing; you’ll use all of it.
In this topic
- 1 Delta & Gamma Up Close Delta as hedge ratio and rough probability, position/dollar delta, then gamma — the curvature that makes delta move, dollar gamma, why long gamma is convexity you pay for, and how gamma explodes near expiry. 10 min
- 2 Theta, Rho & the Clock Theta — the rent you pay (or collect) for optionality, why it accelerates near expiry, and its sign by position; rho and interest-rate sensitivity; and the deep gamma–theta tradeoff that defines every options position. 9 min
- 3 Vega & the Volatility Surface Vega — sensitivity to implied volatility, why it peaks at the money and grows with maturity; vega risk in a book; and the volatility surface that bends across strike (skew/smile) and maturity (term structure), plus vanna and volga at a glance. 10 min
- 4 Delta-Neutral Hedging Dynamic hedging in practice — why a delta hedge won't stay put (gamma), continuous vs discrete rebalancing, hedging error proportional to gamma, and the U-shaped tradeoff where rebalancing more often shrinks error but runs up transaction costs. 10 min
- 5 Gamma Scalping & P&L Attribution How a long-gamma, delta-hedged book makes money — the hedge forces you to buy low and sell high, scalp P&L ≈ ½Γ(ΔS)², and the net comes down to realized vs implied volatility. Then P&L attribution: decompose a day's profit into delta, gamma, theta, vega and rho. 10 min
- 6 Final Exam: Running the Book A graded, locked capstone across the whole Greeks & Hedging course — delta and gamma, theta and rho, vega and the volatility surface, delta-neutral hedging, gamma scalping, and P&L attribution. 15 min
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