Module 6:
Greek Letters and Volatility Smiles
1. Module Overview
This module explains the Greek letters (Greeks) used in options to measure risk and sensitivity. It also introduces the concept of the volatility smile, showing how real market behavior differs from theoretical models.
2. Learning Objectives
By the end of this module, you will be able to:
- Understand the purpose of option Greeks
- Identify and interpret Delta, Gamma, Theta, Vega, and Rho
- Explain how option values change with market conditions
- Understand what a volatility smile is and why it exists
3. What Are Greeks
Greeks measure how sensitive an option’s price is to different factors.
Key idea:
Greeks help traders and risk managers understand and control exposure.
4. The Main Greeks
4.1 Delta (Price Sensitivity)
What it measures:
- Change in option price when the underlying price changes
Underlying price ↑ → Option value changes (Delta)
Key points:
- Call options → positive Delta
- Put options → negative Delta
- Higher Delta = stronger price sensitivity
4.2 Gamma (Change in Delta)
What it measures:
- How quickly Delta changes as price moves
Price moves → Delta changes → Gamma measures the change
Key points:
- High Gamma = more sensitivity
- Important for managing large price movements
4.3 Theta (Time Decay)
What it measures:
- Loss of option value over time
Time passes → Option value decreases
Key points:
- Always negative for option buyers
- Accelerates as expiry approaches
4.4 Vega (Volatility Sensitivity)
What it measures:
- Change in option price due to volatility changes
Volatility ↑ → Option value ↑
Key points:
- Applies to both calls and puts
- Higher uncertainty increases option value
4.5 Rho (Interest Rate Sensitivity)
What it measures:
- Impact of interest rate changes
Interest rates ↑ → Call value ↑ (generally)
Key points:
- Less significant than other Greeks
- More relevant for long-term options
5. Summary Table of Greeks
| Greek | Measures | Key Effect |
|---|---|---|
| Delta | Price sensitivity | Direction |
| Gamma | Change in Delta | Acceleration |
| Theta | Time decay | Loss over time |
| Vega | Volatility sensitivity | Uncertainty impact |
| Rho | Interest rate sensitivity | Rate effect |
6. Volatility Smile
6.1 What Is a Volatility Smile
A volatility smile shows that implied volatility differs across strike prices.
Implied Volatility
^
| *
| * *
| * *
| * *
--------------------> Strike Price
Meaning:
- Options far from the strike (deep in/out of the money) have higher volatility
- Not all options are priced with the same volatility
6.2 Why It Exists
Real markets differ from theory because:
- Extreme price movements occur more often than expected
- Investors demand protection (especially for downside risk)
- Market supply and demand affect pricing