Gamma Scalping and Volatility Trading
Gamma Scalping and Volatility Trading
Gamma scalping is a trading strategy that profits from realized volatility by systematically rebalancing a delta-hedged options position. When realized volatility exceeds implied volatility, the rebalancing gains outweigh theta decay. This strategy is the core of options market-making and volatility arbitrage.
Definition and Key Concepts
The Gamma Scalping Mechanism
Basic concept:
- Long options = Long gamma
- Delta-hedge the position to be direction-neutral
- As the stock moves, delta changes
- Rebalance by buying low (after drops) and selling high (after rises)
- Collect small profits on each rebalance
Why it works: Gamma causes the position to become naturally "wrong" after moves. Rebalancing locks in gains from the moves themselves.
Key Relationships
| Variable | Long Gamma Effect |
|---|---|
| Stock rises | Delta increases; sell stock to rebalance |
| Stock falls | Delta decreases; buy stock to rebalance |
| Theta | Decay works against you (cost) |
| Vega | Profit if IV rises; loss if IV falls |
P/L equation: Daily P/L ≈ ½ × Gamma × (ΔS)² - Theta
If ½ × Gamma × (ΔS)² > Theta, the strategy profits.
Realized vs. Implied Volatility
The key decision variable:
| Condition | Action | Expected P/L |
|---|---|---|
| Realized > Implied | Buy options (long gamma) | Positive |
| Realized < Implied | Sell options (short gamma) | Positive |
| Realized = Implied | Either side | Break-even |
How It Works in Practice
Position Setup
Typical gamma scalping portfolio:
| Component | Position | Purpose |
|---|---|---|
| Long straddle | Long 100 ATM calls + 100 ATM puts | Long gamma, long vega |
| Stock hedge | Variable | Neutralize delta |
| Funding | Cash or borrowed | Finance positions |
Initial metrics:
- Premium paid: $500,000
- Gamma: 500 deltas per $1 move
- Theta: -$5,000 per day
- Vega: +$50,000 per 1% IV move
Rebalancing Logic
Threshold-based approach:
| Delta Change | Action |
|---|---|
| Delta increases by +500 | Sell 500 shares |
| Delta decreases by -500 | Buy 500 shares |
| Delta within ±500 | No action |
Time-based approach: Rebalance at fixed intervals (hourly, daily) regardless of delta change.
Daily Routine
| Time | Activity |
|---|---|
| Market open | Calculate overnight P/L, verify positions |
| Throughout day | Monitor delta, rebalance as needed |
| Market close | Calculate realized vol, review theta decay |
| End of day | Assess overall P/L and position Greeks |
Worked Example
Trade setup:
- Position: Long 100 ATM straddles (calls + puts)
- Stock price: $100
- Days to expiration: 30
- Implied volatility: 25%
- Total premium: $1,200,000
- Position gamma: 800 deltas per $1
- Daily theta: -$8,000
- Hedge ratio: 0.52 (initial call delta)
Day 1: Stock moves $100 → $102 → $99
Morning move ($100 → $102):
- Delta change: 800 × $2 = 1,600 shares
- Sell 1,600 shares at $102
Afternoon move ($102 → $99):
- Delta change: 800 × $3 = 2,400 shares
- Buy 2,400 shares at $99
Rebalancing P/L:
- Sold 1,600 at $102 = $163,200
- Bought 2,400 at $99 = $237,600
- Net stock P/L: $163,200 - (partial of the $237,600 rebalance)
- Scalping gain: approximately $2,400
Day 1 total:
| Component | P/L |
|---|---|
| Gamma scalping | +$2,400 |
| Theta decay | -$8,000 |
| Net P/L | -$5,600 |
The stock moved, but not enough to cover theta.
Day 2: Stock moves $99 → $95 → $103
Morning move ($99 → $95):
- Gamma gain: ½ × 800 × (4)² = $6,400
Afternoon move ($95 → $103):
- Gamma gain: ½ × 800 × (8)² = $25,600
Day 2 total:
| Component | P/L |
|---|---|
| Gamma scalping | +$32,000 |
| Theta decay | -$8,000 |
| Net P/L | +$24,000 |
Big moves generate profits exceeding theta.
Break-Even Volatility
Daily theta: $8,000 Position gamma: 800
Break-even move: ½ × 800 × (ΔS)² = $8,000 ΔS = √(16,000 / 800) = $4.47
The stock must move $4.47 daily to break even, implying: Daily vol = 4.47 / 100 = 4.47% Annualized = 4.47% × √252 ≈ 71%
This seems high because we have a large theta relative to gamma. In practice, positions are sized so break-even is closer to implied vol (25% in this case).
Risks, Limitations, and Tradeoffs
Theta Drag
Daily cost of carrying long gamma:
| Implied Vol | 30-Day ATM Straddle | Daily Theta (approx) |
|---|---|---|
| 20% | 4.5% of stock | 0.15% of notional |
| 30% | 6.8% of stock | 0.23% of notional |
| 40% | 9.0% of stock | 0.30% of notional |
Higher IV means higher theta cost.
Execution Risk
| Risk | Description |
|---|---|
| Slippage | Unable to rebalance at theoretical price |
| Gaps | Overnight/weekend moves before rebalancing |
| Liquidity | Wide spreads during volatility |
| Timing | Delays reduce scalping efficiency |
Vega Risk
Long gamma positions are typically long vega:
| IV Move | Vega P/L | Net Effect |
|---|---|---|
| IV rises 5% | +$250,000 | Windfall gain |
| IV falls 5% | -$250,000 | Unexpected loss |
Vega can dominate gamma scalping P/L.
VaR Considerations
Gamma scalping VaR (95%, 1-day): Primary risks:
- Vega: $50,000 × 2% IV move × 1.65 = $165,000
- Gamma gap: ½ × 800 × (5)² = $10,000 (adverse)
- Total VaR: ~$175,000
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Over-trading | Too frequent rebalancing | Set threshold bands |
| Ignoring vega | Focusing only on gamma | Hedge or monitor vega |
| Wrong break-even | Miscalculating required vol | Verify math carefully |
| Position sizing | Too large relative to capital | Risk-based sizing |
Checklist and Next Steps
Strategy setup checklist:
- Calculate break-even volatility
- Compare to realized volatility forecast
- Size position for acceptable theta drag
- Set rebalancing thresholds
- Establish vega limits or hedges
- Plan for overnight gap risk
- Document P/L attribution methodology
Daily operations checklist:
- Record opening Greeks
- Execute rebalancing trades
- Track cumulative transaction costs
- Calculate realized volatility
- Compare to implied volatility
- Review P/L attribution
- Adjust position if needed
Related articles:
- For delta hedging fundamentals, see Delta Hedging Basics
- For volatility surface hedging, see Vega Hedging for Volatility Surfaces