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 The Black Scholes option pricing model is defined as follows: 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.

Solution

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

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:

Greeks

###### Delta

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

###### Gamma

As T = 1, the Gamma equation simplifies to:

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

###### Theta

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

###### Vega

As T = 1, the equation for Vega becomes:

###### Rho

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