Description 
Consider a European put option on a future that has a forward price (as of maturity) of $115 and a volatility of 30%. The option has a strike price of $90 and matures on 1 March 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(2, "1/6/02", "1/3/03", 115, 90, 0.3, 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 = 90, r = 0.0583, vol = 0.3 and T = 0.7479 (273/365 days), d_{1} = 1.0745 and d_{2} = 0.8150.


As iPC = 1 (put), N(d_{1}) is 0.1413 and N(d_{2}) is 0.2075 (see oCumNorm( ) function), the Black equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oBlack() Model Greeks: 
Delta 
0.135274 
Gamma 
0.007187 
Theta 
4.141495 
Vega 
21.325985 
Rho 
1.738260 
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