BLACK-SCHOLES OPTION PRICING MODEL
Enterprise Derivatives Pricing & Risk Analytics
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OPTION PARAMETERS BLACK-SCHOLES CALCULATIONS
Parameter Value Unit Component Formula Value
Spot Price (S) $100.00 $ d1 (ln(S/K)+(r-q+σ²/2)T) / (σ√T) 0.250000
Strike Price (K) $100.00 $ d2 d1 - σ√T 0.050000
Time to Expiration (T) 1.0000 Years N(d1) Cumulative normal of d1 0.598706
Risk-Free Rate (r) 5.00% % N(d2) Cumulative normal of d2 0.519939
Volatility (σ) 20.00% % N(-d1) 1 - N(d1) 0.401294
Dividend Yield (q) 2.00% % N(-d2) 1 - N(d2) 0.480061
Option Type Call Call / Put n(d1) [PDF] Standard normal PDF at d1 0.386668
      Discount Factor e^(-rT) PV factor 0.951229
    Dividend Factor e^(-qT) Dividend PV factor 0.980199
PRICING RESULTS      
Metric Value   GREEKS OVERVIEW
Call Option Price $9.23   Greek Call Put
Put Option Price $6.33   Delta (Δ) 0.5869 -0.3933
Selected Option Price $9.23   Gamma (Γ) 0.018951 0.018951
    Theta (Θ) /day -0.0139 -0.0063
Put-Call Parity Check 0.00000000 (should be 0) Vega (ν) /1% 0.3790 0.3790
Intrinsic Value $0.00   Rho (ρ) /1% 0.4946 -0.4566
Time Value $9.23   Vanna -0.094753 -0.094753
Moneyness (S/K) 1.0000   Volga (Vomma) 2.368822 2.368822
Moneyness Status At-the-Money   Charm (Delta Decay) -0.000162 -0.000108
Notes
1. Blue values are user inputs. Black values are calculated formulas. Modify blue cells to update the model.
2. The model uses the generalized Black-Scholes (Black-Scholes-Merton) formula with continuous dividend yield adjustment.
3. Greeks are computed analytically (closed-form). Theta is expressed per calendar day. Vega and Rho are per 1% move.
4. Put-Call Parity: C - P = S*exp(-qT) - K*exp(-rT). The check cell should equal zero (or near-zero due to rounding).