Your book is short 2,000 shares of gamma per point with the underlying at 100, all from short at-the-money straddles expiring in a month. Overnight the stock gaps to 92. Estimate the loss from the gamma term, say whether the quadratic estimate is high or low here, and say what you do at the open.

Your book is short 2,000 shares of gamma per point with the underlying at 100, all from short at-the-money straddles expiring in a month. Overnight the stock gaps to 92. Estimate the loss from the gamma term, say whether the quadratic estimate is high or low here, and say what you do at the open.

Approach: Apply the second-order estimate for the move, then ask how gamma itself behaves across an 8-point move on a short straddle before deciding how much of the estimate to trust.

Roughly $64,000 of gamma loss, and the quadratic estimate is an overstatement here. The second-order term is 0.5*Gamma*(dS)^2 = 0.5*2000*64 = $64,000, but gamma on a short at-the-money straddle is largest at the strike and falls away quickly, so an 8-point move on a one-month option leaves the position with far less gamma at 92 than at 100 and the true loss lands below the estimate. Working against that, implied volatility almost always rises on an 8% gap down, so the short vega leg adds a second loss that the gamma calculation ignores entirely. At the open the correct action is to reduce the position rather than to chase the delta, because rehedging a short gamma book with stock locks in every subsequent oscillation while leaving the exposure that caused the loss fully in place. Buying back the nearest strikes costs the most on the day it is most needed, and that is the structural cost of carrying gap risk in a short gamma book.

Follow-up: How would a long out-of-the-money put wing, bought a month earlier at a 6 volatility point premium to the at-the-money, have changed both the gamma and the vega outcome?

Key concepts: short gamma, gap risk, quadratic estimate, vega, delta hedging.