Description 
Consider a European put option on a stock that has a current spot price of $120.00, a volatility of 35% and pays a continuous dividend of 3%. The option has a strike price of $110.00 and matures on 1 September 2003. The riskfree interest rate (on an actual/365 basis) is 6.0%. What is the value of this option as at 1 December 2002? 


Function Specification 
=oGBS(2, "1/12/02", "1/9/03", 120, 110, 0.35, 0.06, 0.03, 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 = 120, X = 110, r = 0.0583, b = 0.0287, vol = 0.35, and T = 0.7507 (274/365 days), d_{1} = 0.5096 and d_{2} = 0.2064.


As iPC = 1 (put), N(d_{1}) is 0.3052 and N(d_{2}) is 0.4182 (see oCumNorm( ) function), the oGBS( ) equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oGBS( ) Model Greeks: 
Delta 
0.29846 
Gamma 
0.00942 
Theta 
6.79811 
Vega 
35.62755 
Rho 
33.05876 
Phi 
26.88590 
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