Options Greeks Formulas in Excel

Options Greeks provide important insights into the risks associated with options trading. Below are Excel formulas to calculate common Greeks: Delta, Gamma, Theta, Vega, and Rho.

Key Definitions of Options Greeks

• Delta (Δ): Measures the sensitivity of an option's price to a change in the price of the underlying asset.
• Gamma (Γ): Measures the rate of change of delta over time, reflecting the curvature of the option’s pricing.
• Theta (Θ): Measures the sensitivity of the option's price to the passage of time, representing time decay.
• Vega (ν): Measures the sensitivity of the option’s price to changes in the volatility of the underlying asset.
• Rho (ρ): Measures the sensitivity of the option's price to changes in interest rates.

Required Parameters

To compute the Greeks, the following parameters are generally necessary:

• S: Current price of the underlying asset
• K: Strike price of the option
• T: Time until expiration (in years)
• r: Risk-free interest rate (annualized)
• σ: Volatility of the underlying asset (annualized)
• C: Option price for Call options (or P for Put options)

Formulas for Options Greeks

1. Delta

Call Option:

= NORM.S.DIST(d1, TRUE)

Put Option:

= NORM.S.DIST(d1, TRUE) - 1

Where:

d1 = (LN(S/K) + (r + (σ^2)/2) * T) / (σ * SQRT(T))

2. Gamma

= NORM.S.DIST(d1, TRUE) / (S * σ * SQRT(T))

3. Theta

Call Option:

= -(S * NORM.S.DIST(d1, TRUE) * σ) / (2 * SQRT(T)) - r * K * EXP(-r * T) * NORM.S.DIST(d2, TRUE)

Put Option:

= -(S * NORM.S.DIST(d1, TRUE) * σ) / (2 * SQRT(T)) + r * K * EXP(-r * T) * NORM.S.DIST(-d2, TRUE)

4. Vega

= S * NORM.S.DIST(d1, TRUE) * SQRT(T)

5. Rho

Call Option:

= K * T * EXP(-r * T) * NORM.S.DIST(d2, TRUE)

Put Option:

= -K * T * EXP(-r * T) * NORM.S.DIST(-d2, TRUE)

Practical Example

Given Values

• Current Price of Underlying Asset (S): 100
• Strike Price (K): 95
• Time until expiration (T): 30 days / 365 (0.08219 years)
• Risk-Free Interest Rate (r): 5% (0.05)
• Volatility (σ): 20% (0.20)

Calculation Steps

1. Calculate d1 and d2:

d1 = (LN(S/K) + (r + (σ^2)/2) * T) / (σ * SQRT(T))
d2 = d1 - σ * SQRT(T)

2. Substitute values into Delta, Gamma, Theta, Vega, and Rho formulas.

Conclusion

The formulas for calculating the Greeks in Excel can help traders manage risk and assess the pricing sensitivity of options effectively.

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