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The Black Scholes option pricing model is defined as follows:

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OV = option value.

S = spot price of the underlying asset.

= exercise price (strike).

= risk-free interest rate, expressed with continuous compounding.

vol = volatility of the relative price change of the underlying asset.

= time to maturity measured in years (actual/365 basis).

N(.) = cumulative normal distribution of (.).

iPC = 1 for call / -1 for put.






The continuous equivalent of the actual/365 risk-free interest rate is calculated as follows:

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Referring to the equations for d1 and d2 (see model definition), if S = 50, X = 60, r= 0.0677, vol = 0.25, and T = 1 (365/365 days), d1 = -0.3334 and d2 -0.5837.



As iPC = 1 (call), N(d1) is 0.3693 and N(d2) is 0.2797 (see oCumNorm( ) function), the Black Scholes equation becomes:


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As iPC = 1 (call), the delta equation simplifies to:


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As T = 1, the Gamma equation simplifies to:


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The n(d1) equation gives 0.3773, and since S = 50 and vol = 0.25, Gamma is 0.0302


As iPC = T = 1, the equation for Theta becomes:


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As T = 1, the equation for Vega becomes:


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As iPC = T = 1, the equation for Rho becomes:


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