Description 
Consider a European call option on a stock that has a current spot price of $50 and a volatility of 25%. The option has a strike price of $60 and matures on 1 April 2003. The riskfree interest rate (on an actual/365 basis) is 7%. What is the value of this option as at 1 April 2002? 


Function Specification 
=oBS(1, "1/4/02", "1/4/03", 50, 60, 0.25, 0.07, 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 = 50, X = 60, r = 0.0677, vol = 0.25, and T = 1 (365/365 days), d_{1} = 0.3334 and d_{2} 0.5837.


As iPC = 1 (call), N(d_{1}) is 0.3693 and N(d_{2}) is 0.2797 (see oCumNorm( ) function), the Black Scholes equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oBS() Model Greeks: 
Delta 
As iPC = 1 (call), the delta equation simplifies to: 


Gamma 
As T = 1, the Gamma equation simplifies to: 



The n(d_{1}) 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: 




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