Numerical example

Let's work through a complete numerical example for each Greek (Delta, Theta, Gamma, Vega, and Rho) for both a stock option (no dividend) and a currency option using the formulas.

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Scenario:

Stock Option (No Dividend):

• Stock Price (S) = ₹100
• Strike Price (K) = ₹105
• Time to Expiration (T) = 1 year
• Volatility (σ) = 20% (0.20)
• Risk-Free Interest Rate (r) = 5% (0.05)
• Dividend Yield (q) = 0%

Currency Option:

• Spot Price (S) = ₹75 (foreign currency per 1 unit)
• Strike Price (K) = ₹80
• Time to Expiration (T) = 0.5 years
• Volatility (σ) = 15% (0.15)
• Risk-Free Interest Rate (r) = 4% (0.04)
• Foreign Interest Rate (r_f) = 2% (0.02)

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1. Delta (Δ)

Stock Option (No Dividend):

Currency Option:

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2. Theta (Θ)

Stock Option (No Dividend):

Currency Option:

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3. Gamma (Γ)

Stock Option (No Dividend):

Currency Option:

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4. Vega (ν)

Stock Option (No Dividend):

Currency Option:

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5. Rho (ρ)

Stock Option (No Dividend):

Currency Option:

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Summary Table of Results:

Greek	Stock Option (No Dividend)	Currency Option
Delta	0.5418	0.367
Theta	-5.594	-2.637
Gamma	0.0198	0.0671
Vega	39.65	20.721
Rho	45.41	13.13

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This is how you calculate each of the Greeks for both a stock option (no dividend) and a currency option.