Description 
Consider a European call option on a forward contract with a forward price (as of maturity) of $115 and a volatility of 20%. The option has a strike price of $120 and matures on 1 June 2003. The riskfree interest rate (on an actual/365 basis) is 6%. What is the value of this option as at 1 June 2002? 




Function Specification 
=oBLACK(1, "1/6/02", "1/6/03", 115, 120, 0.2, 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 F = 115, X = 120, r = 0.0583, vol = 0.2, and T = 1 (365/365 days), d_{1} = 0.1128 and d_{2} = 0.3128.



As iPC = 1 (call), N(d_{1}) is 0.4551 and N(d_{2}) is 0.3772 (see oCumNorm( ) function), the Black equation becomes: 






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

Delta 
As the option is a call and T = 1 the Delta equation simplifies to 



Gamma 
As T = 1 and the n(d_{1}) equation gives 0.3964, the Gamma equation simplifies to: 



Theta 
As 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: 


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