The delta-hedge share formula
Hedge Shares = −Delta × Number of Options × 100
Rebalancing the hedge as the stock moves
| Scenario | Market Maker Action | Why |
|---|---|---|
| Stock rises | Buy more shares (delta increased) | Rebalance hedge to stay neutral |
| Stock falls | Sell shares (delta decreased) | Reduce hedge as exposure shrinks |
| High gamma | Frequent rebalancing needed | Delta changes rapidly near expiration |
Why delta hedging never stays put
Delta hedging is not perfect — it’s a continuous process. Gamma means delta changes with every stock move, requiring constant rebalancing. Market makers profit from the bid-ask spread and theta decay, not from stock direction.
Rebalancing a hedge after a price move
If you sold 10 ATM calls (delta 0.50), you’d need to buy 500 shares to hedge. If the stock rises $5 and delta becomes 0.65, you’d need 650 shares — buy 150 more.
How delta hedging drives a gamma squeeze
A market maker sold calls and is delta-hedged with shares. A gamma squeeze starts — the stock rockets higher. What happens?
How hedging flows amplify stock moves
Reaching delta-neutral on a long book
Market maker is long 1000 options contracts (delta 0.50 per). They want market-neutral exposure. What do they do?
Check your understanding
Sit with the ideas.
Options dealers are heavily short gamma on a major stock heading into monthly expiration. The stock starts moving sharply higher. How does dealer hedging affect the stock's momentum?
Why: