*** NOTES REGARDING USAGE OF PROEJCT***

1) Option application only works for Large-Cap Stocks

2) Inputted stock ticker must be a optional stock, meaning option must be offered for ticker symbol.

3) It is recommended to use "Barcharts Option Calculator" WITH the 3D visual Tool to assist in finding current volatility, risk-free rate, option contract expiry date & dividend yield (if applicable) for selected stock ticker. --> https://www.barchart.com/options/options-calculator

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What are the Option Greeks?

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FIRST ORDER (Mathematical Derivative)

• Delta (∂V/∂S): Sensitivity of the option price to changes in the underlying asset's price.
  • 📈 Buyer prefers: Higher (to benefit from price movements)
  • 📉 Seller prefers: Lower (to reduce directional risk)

• Gamma (∂²V/∂S²): Rate of change of Delta with respect to the underlying price (measures convexity).
  • 📈 Buyer prefers: Higher (for greater responsiveness to price changes)
  • 📉 Seller prefers: Lower (to minimize exposure to sharp movements)

• Vega (∂V/∂σ): Sensitivity to changes in implied volatility.
  • 📈 Buyer prefers: Higher (benefits from rising volatility)
  • 📉 Seller prefers: Lower (to avoid increased option value and risk)

• Theta (∂V/∂t): Rate of time decay (loss in value as expiration approaches).
  • 📈 Buyer prefers: Lower (to minimize time decay losses)
  • 📉 Seller prefers: Higher (to benefit from option decay)

• Rho (∂V/∂r): Sensitivity to changes in interest rates.
  • 📈 Buyer prefers: Higher for calls, lower for puts (call values rise with interest rates)
  • 📉 Seller prefers: Lower for calls, higher for puts (to reduce adverse impact)

SECOND ORDER

• Vanna (∂²V/∂S∂σ): Sensitivity of Delta to changes in implied volatility or Vega to changes in the underlying price.
  • 📈 Buyer prefers: Higher (for more favorable hedging adjustments)
  • 📉 Seller prefers: Lower (to maintain stable Delta)

• Charm (∂²V/∂S∂t): Delta's sensitivity to the passage of time (theta per delta).
  • 📈 Buyer prefers: Lower (to avoid excessive Delta erosion)
  • 📉 Seller prefers: Higher (to gain from Delta reduction over time)

• Vomma/Volga (∂²V/∂σ²): Vega's sensitivity to changes in volatility (second-order volatility effect).
  • 📈 Buyer prefers: Higher (for increased responsiveness to volatility shifts)
  • 📉 Seller prefers: Lower (to minimize sudden Vega expansion)

• Veta (∂²V/∂σ∂t): Vega's sensitivity to the passage of time.
  • 📈 Buyer prefers: Higher (to maintain Vega exposure longer)
  • 📉 Seller prefers: Lower (to let volatility exposure decay faster)

THRID ORDER

• Speed (∂³V/∂S³): Gamma's sensitivity to changes in the underlying price (third-order derivative).
  • 📈 Buyer prefers: Higher (for sharper Gamma effects when in-the-money)
  • 📉 Seller prefers: Lower (to reduce extreme Delta shifts)

• Zomma (∂³V/∂S²∂σ): Gamma's sensitivity to changes in volatility.
  • 📈 Buyer prefers: Higher (to benefit from volatility-driven Gamma expansion)
  • 📉 Seller prefers: Lower (to avoid increased risk from Gamma shifts)

• Color (∂³V/∂S²∂t): Gamma's sensitivity to the passage of time.
  • 📈 Buyer prefers: Lower (to keep Gamma exposure stable)
  • 📉 Seller prefers: Higher (to gain from Gamma reduction over time)

• Ultima (∂³V/∂σ³): Third-order sensitivity of Vomma to volatility changes (volatility convexity).
  • 📈 Buyer prefers: Higher (to profit from sharp volatility swings)
  • 📉 Seller prefers: Lower (to reduce exposure to sudden volatility shifts)