Description 
Consider a European put option on Gold that has a current spot price of $300.00 per ounce and a volatility of 15%. The storage cost of gold (expressed as a yield) is 1%, while the convenience yield is 2% (net convenience yield is thus 1%). The option has a strike price of $280.00 and matures on 1 April 2004. The riskfree interest rate (on an actual/365 basis) is 6.0%. What is the value of this option as at 1 April 2002? 


Function Specification 
=oGBS(2, "1/4/02", "1/4/04", 300, 280, 0.15, 0.06, 0.05, 0) 


Solution 
The continuous equivalents of the actual/365 riskfree interest rate and the cost of carry are calculated as follows (see special cases): Referring to the equations for d_{1} and d_{2} (see model definition), if S = 300, X = 280, r = 0.0583, b = 0.0483, vol = 0.15, and T = 2.0027 (731/365 days), d_{1} = 0.8870 and d_{2} = 0.6747.


As iPC = 1 (put), N(d_{1}) is 0.1875 and N(d_{2}) is 0.2499 (refer to the oCumNorm( ) function), the oGBS( ) equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oGBS() Model Greeks: 
Delta 
0.183835 
Gamma 
0.004144 
Theta 
1.115770 
Vega 
112.031028 
Rho 
124.710844 
Phi 
110.452131 
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