📚 Complete Guide to GAMMA in Options Trading
Understanding the Greek that Measures Delta's Rate of Change
• Introduction to Gamma
• What You Will Learn
Gamma is one of the most important Greeks in options trading. This e-book will help you understand:
- How Gamma measures the speed of Delta changes
- Why Gamma is crucial for options traders
- How to use Gamma in your trading strategy
- Real-world examples with Indian Rupee calculations
• The Greeks Family
Gamma is part of the "Greeks" family, which includes:
| Greek | Measures | Symbol |
|---|---|---|
| Delta | Price change sensitivity | Δ |
| Gamma | Delta change rate | Γ |
| Theta | Time decay | Θ |
| Vega | Volatility sensitivity | ν |
| Rho | Interest rate sensitivity | ρ |
• What is Gamma?
• Simple Definition
Gamma measures how much Delta changes when the underlying stock price moves by ₹1.
Think of it this way:
- Delta tells you how much your option price changes
- Gamma tells you how much Delta itself changes
- Gamma is the "acceleration" while Delta is the "speed"
• Key Characteristics
| Characteristic | Description |
|---|---|
| Range | 0 to 1 (maximum at-the-money) |
| Sign | Always positive for long options |
| Peak | Highest when option is at-the-money |
| Time Effect | Increases as expiration approaches |
| Long vs Short | Long = Positive, Short = Negative |
• How to Calculate Gamma
• Basic Formula
Gamma (Γ) = Change in Delta ÷ Change in Stock Price
Γ = ΔΔ ÷ ΔS
• Step-by-Step Calculation
- Find the current Delta of your option
- Note the current stock price
- Calculate Delta if stock moves ₹1 up
- Subtract old Delta from new Delta
- That difference is your Gamma
• Example Calculation
| Parameter | Value |
|---|---|
| Stock Price | ₹1,000 |
| Option Delta (at ₹1,000) | 0.50 |
| Option Delta (at ₹1,001) | 0.52 |
| Change in Delta | 0.52 - 0.50 = 0.02 |
| Gamma | 0.02 |
Interpretation: For every ₹1 move in stock price, Delta changes by 0.02
• Why Gamma Matters
• Critical Reasons to Understand Gamma
- Predicts how quickly your position risk changes
- Helps you manage portfolio hedging requirements
- Shows when options become more or less responsive
- Critical for day traders and scalpers
- Affects profit and loss acceleration
• Real-World Impact
| Scenario | Gamma Impact | Result |
|---|---|---|
| High Gamma + Price moves in your favor | Delta increases quickly | Profits accelerate 🚀 |
| High Gamma + Price moves against you | Delta decreases quickly | Losses accelerate ⚠️ |
| Low Gamma positions | Delta changes slowly | Stable, predictable movement |
| Near expiration | Gamma spikes | High risk and opportunity |
• Understanding Gamma Values
• Gamma by Moneyness
| Option Type | Gamma Level | Explanation |
|---|---|---|
| At-The-Money (ATM) | Highest ⬆️ | Maximum sensitivity to price changes |
| Near-The-Money | High 📈 | Significant Delta changes |
| In-The-Money (ITM) | Moderate 📊 | Delta already high, less room to change |
| Out-of-The-Money (OTM) | Low ⬇️ | Delta already low, minimal changes |
| Deep OTM | Very Low 📉 | Almost no Delta movement |
• Gamma and Time to Expiration
| Time Remaining | ATM Gamma | Trading Implication |
|---|---|---|
| 90+ Days | Low | Stable, slow Delta changes |
| 30-60 Days | Moderate | Noticeable Delta movement |
| 7-30 Days | High | Rapid Delta changes |
| 0-7 Days | Very High | Extreme volatility in Delta |
| Expiration Day | Maximum | Wild swings possible ⚡ |
• Gamma Risk Management
• Understanding Gamma Risk
Gamma risk is the risk that your Delta will change unexpectedly, making your position more profitable or more risky than planned.
• Position Types
| Position | Gamma | Risk Profile | Management Strategy |
|---|---|---|---|
| Long Options | Positive (+) | Limited risk, unlimited potential | Let winners run |
| Short Options | Negative (-) | Limited profit, unlimited risk | Close or hedge quickly |
| Gamma Scalping | Positive (+) | Profit from volatility | Hedge with underlying |
| Iron Condor | Negative (-) | Profit from stability | Monitor breakeven points |
• Risk Management Guidelines
- Monitor Gamma exposure daily for short option positions
- Be extra cautious within 7 days of expiration
- Use stop losses when Gamma is high
- Consider closing positions when Gamma spikes unexpectedly
- Hedge by buying or selling the underlying asset
• Gamma Trading Strategies
• Strategy 1: Gamma Scalping
What it is: Buying options and hedging with the underlying stock to profit from volatility
How it works:
- Buy ATM options (positive Gamma)
- Hedge by shorting equivalent Delta in stock
- As stock moves up: Delta increases, sell stock to rehedge
- As stock moves down: Delta decreases, buy stock to rehedge
- Profit from the rehedging process
Best when: High volatility expected
• Strategy 2: Long Straddle (Positive Gamma)
What it is: Buying both Call and Put at same strike
Benefits:
- Double positive Gamma exposure
- Profits from large moves in either direction
- Delta accelerates as price moves
Risk: Time decay (Theta) if stock doesn't move
• Strategy 3: Short Iron Condor (Negative Gamma)
What it is: Selling OTM Call spread and OTM Put spread
Characteristics:
- Negative Gamma position
- Profits from stable, range-bound markets
- Risk increases if price breaks range
Management: Close early if Gamma risk becomes too high
• Strategy Comparison Table
| Strategy | Gamma Type | Market View | Max Profit | Max Risk |
|---|---|---|---|---|
| Long Call/Put | Positive | Directional | Unlimited | Premium paid |
| Short Call/Put | Negative | Stable/Opposite | Premium received | Unlimited |
| Long Straddle | High Positive | High volatility | Unlimited | Both premiums |
| Short Straddle | High Negative | Low volatility | Both premiums | Unlimited |
| Iron Condor | Negative | Range-bound | Net premium | Spread width |
• Practical Examples
• Example 1: Nifty Call Option
| Parameter | Value |
|---|---|
| Underlying | Nifty 50 Index |
| Current Price | ₹19,500 |
| Strike Price | ₹19,500 (ATM) |
| Option Type | Call Option |
| Premium | ₹150 |
| Delta | 0.50 |
| Gamma | 0.03 |
| Days to Expiration | 15 days |
• Scenario Analysis:
| Nifty Price | New Delta | Option Premium | P&L per Lot |
|---|---|---|---|
| ₹19,400 | 0.47 (0.50 - 0.03) | ₹103 | -₹2,350 |
| ₹19,450 | 0.485 | ₹126 | -₹1,200 |
| ₹19,500 | 0.50 | ₹150 | ₹0 |
| ₹19,550 | 0.515 | ₹175 | +₹1,250 |
| ₹19,600 | 0.53 (0.50 + 0.03) | ₹203 | +₹2,650 |
Note: 1 Nifty lot = 50 units. Calculations are approximate.
• Example 2: Bank Nifty Put Option
| Parameter | Value |
|---|---|
| Underlying | Bank Nifty Index |
| Current Price | ₹44,000 |
| Strike Price | ₹44,000 (ATM) |
| Option Type | Put Option |
| Premium | ₹300 |
| Delta | -0.50 |
| Gamma | 0.025 |
| Days to Expiration | 7 days |
Key Observation: Higher Gamma (0.025) due to closer expiration means Delta will change more rapidly!
• Gamma Decision Flowchart
(Positive Gamma)
• Watch for quick Delta changes
• Set tight stops
• Profits can accelerate
• Stable position
• Hold for direction
• Less rehedging needed
(Negative Gamma)
⚠️ HIGH RISK
• Close position
• Or hedge immediately
• Gamma explosion risk
• Monitor daily
• Keep within risk limits
• Plan exit strategy
• Positive Gamma = Good (profit from moves)
• Negative Gamma = Dangerous (losses accelerate)
• Consider Gamma scalping
• Positive Gamma = Less valuable
• Negative Gamma = Safer
• Theta decay is main factor
• Practice Questions
• Question 1:
You buy a Nifty Call option at ₹19,500 strike. The option has a Delta of 0.48 and Gamma of 0.04. If Nifty rises by ₹50, what will be the approximate new Delta?
• Question 2:
You have sold 10 lots of Bank Nifty Put options (strike ₹44,000) with Gamma of -0.03 per lot. Bank Nifty drops ₹100. How much does your total position Delta change?
• Question 3:
Why is Gamma highest for At-The-Money (ATM) options?
• Question 4:
What happens to Gamma as an option approaches expiration?
• Question 5:
You are long a Straddle (bought both Call and Put at ₹50 strike) on a stock trading at ₹50. Each option has Gamma of 0.05. The stock suddenly jumps to ₹52. Should you be happy or worried? Explain using Gamma.