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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.
X = exercise price (strike).
r = risk-free interest rate, expressed with continuous compounding.
vol = volatility of the relative price change of the underlying asset.
T = time to maturity measured in years (actual/365 basis).
N(.) = cumulative normal distribution of (.).
iPC = 1 for call / -1 for put.
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Solution
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The continuous equivalent of the actual/365 risk-free interest rate is calculated as follows:
Referring to the equations for d1 and d2 (see ), if S = 50, X = 60, r= 0.0677, vol = 0.25, and T = 1 (365/365 days), d1 = -0.3334 and d2 -0.5837.
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As iPC = 1 (call), N(d1) is 0.3693 and N(d2) is 0.2797 (see ), the Black Scholes equation becomes:
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Greeks
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Delta
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As iPC = 1 (call), the delta equation simplifies to:
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Gamma
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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
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Theta
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As iPC = T = 1, the equation for Theta becomes:
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Vega
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As T = 1, the equation for Vega becomes:
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Rho
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As iPC = T = 1, the equation for Rho becomes:
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For more information see our pricing plans.
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