Adjusting a delta hedge after a sharp drop
Question
You own a call and have hedged it by shorting delta shares. Bad news hits and the stock falls $10 overnight. Do you buy or sell stock to restore the hedge?
Short answer
Buy shares back. The call's delta falls when the stock drops (positive gamma), so you are now short more shares than the hedge needs and must cover some. Being long gamma means you rebalance by buying after falls and selling after rises.
Adapted from Crack, Heard on the Street, Q2.7, p.24; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- The One-Period Binomial Model: Replication, Delta Hedging, and Risk-Neutral Pricing
- Derivation — From Binomial Trees to Black-Scholes in the Continuous Limit
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