Option Greeks

Module Units

- 1. Introduction To Greeks
- 2. Black Scholes Model
- 3. Introduction To Delta
- 4. Delta’s Relationship With Spot And Strike Price
- 5. Delta And Time To Expiry
- 6. Delta And Volatility
- 7. Delta Adds Up
- 8. Delta Hedging
- 9. Introduction To Gamma
- 10. Gamma’s Relationship With Spot And Strike Price
- 11. Gamma And Time To Expiry
- 12. Gamma And Volatility
- 13. Important Properties Of Gamma
- 14. Introduction To Theta
- 15. Theta’s Relationship With Spot And Strike Price
- 16. Theta And Time To Expiry
- 17. Theta And Volatility
- 18. Important Properties Of Theta
- 19. Rho
- 20. Introduction To Vega
- 21. Vega’s Relationship With Strike Price
- 22. Vega And Time To Expiry
- 23. Volatility
- 24. Volatility And Normal Distribution
- 25. Types Of Volatility
- 26. The VIX Index
- 27. Volatility Smile
- 28. Delta Neutral Hedging
- 29. Calendar Spread
- 30. Diagonal Spread With Calls
- 31. Diagonal Spread With Puts
- 32. Gamma Delta Neutral Option Strategy
- 33. Gamma Scalping Strategy
- 34. Put Call Parity
- 35. Options Arbitrage
- 36. Conversion-Reversal Arbitrage
- 37. Box Spread
- 38. Conclusion

# Gamma And Volatility

**Gamma with respect to change in volatility:**

When volatility is low, the Gamma of At-the-money (ATM) options is high, while the Gamma for deep In-the-money(ITM) or Out-of-the-money (OTM) options approaches 0. This phenomenon arises because when volatility is low, the time value of such options is low, but it goes up dramatically as the underlying stock price approaches the strike price.

When volatility is high, Gamma tends to be stable across all strike prices. This is due to the fact that when volatility is high, the time value of deep In or Out-of-the-money options is already quite substantial. Thus, the increase in the time value of these options as they move nearer to At-the money will be less dramatic and hence the low and stable Gamma.

Keeping constant, the strike 16500, spot at 16500 and days to expiry 17, let us calculate how changes in volatility changes the gamma of an option.

As volatility increases, there will be an increase in the price of the options and vice versa. Thereby, we can see that as volatility decreases, call Delta decreases and put Delta increases.

The Gamma too increases. High Gamma values mean that the option tends to experience volatile swings.

**GAMMA WITH RESPECT TO CHANGE IN RATE OF INTEREST RATE**

Strike 16500 spot 16500 days to expiry 17 Volatility 17%

As the interest rate decreases, we can find Gamma increasing for the ATM call and put.

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