Formula
Hedge Shares = −Delta × Number of Options × 100
Compare
| 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 |
Key point
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.
Try it
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.
Check-in
A market maker sold calls and is delta-hedged with shares. A gamma squeeze starts — the stock rockets higher. What happens?
Key insight
Check-in
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: