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’s Relationship With Spot And Strike Price

### Gamma with respect to change in spot price:

The table below shows how Gamma changes with respect to change in SPOT PRICE, given the other factors are constant. Let’s find out the same for a **16500 strike Call and Put option, assuming the volatility to be 17% and days to expiry 17 days.**

**Observations: **

We can clearly observe that as spot price increases from 16100 to 16900, call premium increases and put premium decreases. Gamma is highest at ATM (here 0.0008) and decreases as spot price moves away in either direction. When Nifty slides down to 16100, gamma too goes down to 0.0007. When Nifty goes up to 16900, gamma still goes down to 0.0005.

The Gamma peaks when the option hits ATM status. This implies that the rate of change of Delta is highest when the option is ATM. In other words, ATM options are most sensitive to the changes in the underlying. Also, since ATM options have the highest Gamma – avoid shorting ATM options.

Let us now evaluate how Gamma changes with respect to change in other variables.

### Gamma with respect to change in Strike Price:

**Given the spot 16500, volatility at 17% and days to expiry 17 days.**

We can see that the Gamma is highest (0.0008) at the ATM(13500) and decreases as Nifty moves away on either side. When Nifty comes down to 15500, gamma too slides down to 0.0001 and when Nifty moves up to 17500, gamma still reduces to 0.0002. This explains why **gamma has a bell curve. **

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