This is where you take the chair. Five lessons handed you the full risk dashboard — how delta and gamma steer your directional exposure, how theta and rho tick the clock and the curve, how vega and the volatility surface price your fear, how a delta-neutral hedge is rebalanced into existence, and how gamma scalping turns a hedge into a strategy whose P&L you can decompose to the penny. Now you run the book without a net. No formula sheet, no hints, no second guesses: every answer locks the instant you submit it, and every wrong option is a misconception that has cost a real trainee real money. Read all four choices, twice, before you commit.
How this exam works
This is a graded exam. Questions arrive one at a time. Once you submit an answer it is final — there is no going back, no second try, and a wrong answer simply fails that question. Your score stays hidden until the very end, where you need 70% to pass. Slow down and read every option before you commit.
You are long 40 call contracts (each on 100 shares) with a per-share delta of 0.35. What is your position delta in shares, and what does it mean?
Select an answer to continue.
Whatever the score reads, the dashboard you just stress-tested — delta and gamma steering direction and convexity, theta and rho ticking time and rates, vega and the surface pricing fear, the delta-neutral hedge you rebalance into shape, and the gamma scalp whose P&L you can attribute term by term — is exactly what an options market-maker watches every minute the book is open. Here is the whole course in one glance.
Big picture
Running the Greeks Book
- Greeks & Hedging
- Delta & gamma up close
- Delta = N(d1) = hedge ratio; position delta = contracts × 100 × delta
- Gamma = rate of change of delta; peaks ATM near expiry
- Dollar gamma = delta change per 1% move
- Sign table: long option = +gamma; short put = +delta, −gamma
- Theta, rho & the clock
- Theta negative for long options; accelerates near expiry
- Gamma–theta duality: rent convexity by paying decay
- Rho: call positive, put negative; small at short tenors
- Theta is a per-day rate: weekly bleed ≈ 5 × daily theta
- Vega & the volatility surface
- Vega = S·φ(d1)·√T; price per 1 vol point
- Peaks ATM, grows with √T
- Short end = big gamma; long end = big vega
- Smile (symmetric) vs equity skew; term structure axis
- Delta-neutral hedging
- Rehedge because gamma keeps moving delta
- Hedging error proportional to gamma
- Error standard deviation shrinks like 1/√N
- Transaction-cost U-curve; delta-neutral is NOT riskless
- Gamma scalping & P&L attribution
- Long gamma: buy low / sell high as you rehedge
- Scalp per move ≈ 1/2 × gamma × (dS)^2
- Profit when realized vol > implied vol (minus theta)
- Attribution: delta·dS + ½gamma·(dS)² + vega·dσ + theta·dt
- Delta & gamma up close