Description 
Consider a European call option on a stock that has a current spot price of $100, a volatility of 30% and pays no dividends. The option has a strike price of $100 and matures on 1 September 2003. The riskfree interest rate (on an actual/365 basis) is 6%. What is the value of this option as at 1 September 2002? 




Function Specification 
=oGBS(1, "1/9/02", "1/9/03", 100, 100, 0.3, 0.06, 0.06, 0) 




Solution 
The continuous equivalent of the actual/365 riskfree interest rate is calculated as follows: Referring to the equations for d_{1} and d_{2} (see model definition), if S = 100, X = 100, b = r = 0.0583 (see special cases), vol = 0.30, and T = 1 (365/365 days), d_{1} = 0.3442 and d_{2} = 0.0442.



As iPC = 1 (call), N(d_{1}) is 0.6347 and N(d_{2}) is 0.5176 (see oCumNorm( ) function), the Generalized Black Scholes equation becomes: 






Greeks 
The following Greeks are computed using the formulas specified in oGBS( ) Model Greeks: 

Delta 
As the underlying asset is a nondividend paying stock, delta is equal to N(d_{1}) or 0.5699. This can be confirmed by referring to the Delta equation, where the first part of the equation, equals 1.0. 

Gamma 
As b = r and T = 1, the Gamma equation simplifies to: 




The n(d_{1}) equation gives 0.3760, and since S = 100 and vol= 0.30, Gamma is 0.0125. 

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



Vega 
As b = r and T = 1, the equation for Vega becomes: 



Rho 
As b <> 0 and iPC = T = 1, the equation for Rho becomes: 



Phi 
As b = r = and iPC = 1, the equation for Phi becomes: 
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