Net the Book

Question

All options are on one share each. Your book: long 500 calls with Delta = 0.40, Gamma = 0.03; long 800 puts with Delta = -0.25, Gamma = 0.02; short 200 shares. What single stock trade flattens your delta? After it, what is your gamma, and if the stock then jumps 2, roughly what delta are you carrying?

Accepted Answer

Net delta: multiply and add (shares have Delta = 1, Gamma = 0): 500(0.40) + 800(-0.25) + (-200)(1) = 200 - 200 - 200 = -200. Buy 200 shares. That's the whole first-order hedge. Net gamma: same drill, and note both option legs are long, so both gammas are positive (puts have negative delta, positive gamma, the classic sign slip): 500(0.03) + 800(0.02) = 15 + 16 = +31. The stock position contributes nothing, shares are linear. You are delta-flat, long 31 units of gamma. After a 2 jump: delta picks up roughly gamma × move: Delta_textnew approx 0 + 31 times 2 = +62 text share-equivalents, so you'd sell ≈ 62 shares to re-flatten, selling into strength, the long-gamma rhythm. (Second-order caveat: gamma itself changes as spot moves, so 62 is a local estimate, good for small moves relative to the gamma profile's width.) Why interviewers run this drill: the entire risk apparatus of an options desk is built on the fact that Greeks aggregate linearly across arbitrary positions, thousands of strikes and expiries collapse into one delta, one gamma, one vega, one theta per underlying. The classic traps being tested: forgetting the sign on short positions, giving puts negative gamma, letting the

Net the Book

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