Option Greeks Lecture Notes

Importance of Option Greeks

• Essential for options trading beginners.
• Inform about the risks your option positions are exposed to.

Delta

• Definition: Predicts an option's price change relative to a $1 shift in the stock price.
  • Sensitivity of option price to stock price changes.
  • Visualizing Delta: Use an options pricing calculator.
• Call Options:
  • Positive deltas: Price moves in the same direction as stock price.
  • Example: Call option delta of +0.5 means a $1 increase in stock price results in a $0.50 option price increase.
• Put Options:
  • Negative deltas: Price moves in the opposite direction of the stock price.
• Delta Range:
  • Call option deltas: 0 to +1.
  • Put option deltas: 0 to -1.
• Example: Apple call option with an initial delta of 0.47. Stock price increase from $132 to $136 led to a call price increase from $7 to $9.
• Probability Interpretation: Delta as the probability of an option expiring in the money.

Gamma

• Definition: Estimates how an option's delta will change given a $1 shift in the stock price.
• Example: Call with a delta of 0.5 and gamma of 0.05 implies a delta increase to 0.55 with a $1 stock price increase.
• Impact on Sensitivity:
  • Call options: Sensitivity increases with stock price rise.
  • Put options: Sensitivity increases as stock price falls.

Theta

• Definition: Predicts the expected decrease in an option's price over time, assuming no stock price or volatility change.
• Time Decay: Option prices typically fall as expiration approaches due to reduced probability of large stock price movements.

Vega

• Definition: Indicates the expected changes in an option's price corresponding to a 1% shift in implied volatility.
• Impact of Volatility:
  • Increase in volatility inflates option prices due to larger anticipated stock price movements.
  • Decrease in volatility deflates option prices.

Practical Examples

• Tesla call option with a vega of 0.31: A 1% increase in implied volatility raises option price by 31 cents, and vice versa.

Position Level Greeks

• Example Position:
  • Delta of +175: Potential $175 gain/loss with a $1 stock price change.
  • Gamma of +7: Delta will increase by 7 points with a $1 stock price increase.
  • Theta of -2.8: $2.80 loss with the passage of one day if stock price and volatility remain constant.
  • Vega of +81: $81 gain/loss with 1% volatility change.

Contract Multiplier

• Options have a multiplier of 100 shares, affecting calculations such as delta.
• Example: $2.50 option price means $250 purchase, and a delta change reflects a $50 profit/loss.

Intrinsic vs. Extrinsic Value

• Theta and Vega:
  • Affect only extrinsic value, not intrinsic value.
  • Intrinsic value: Remains constant regardless of time passage or volatility changes.

Conclusion

• Understanding option Greeks is vital for managing risk and making informed trading decisions.
• Options Greeks tutorial by Chris from Project Finance.