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