Description 
Consider a European call option on the New Zealand Dollar which has a current exchange rate of 2.100 (expressed in USD/NZD) and a volatility of 25%. The (local) American riskfree interest rate is 6.0% while the (foreign) New Zealand riskfree rate is 7.5% (both expressed in actual/365 terms). The option has a strike price of 2.000 and matures on 1 October 2002. What is the value of this option as at 1 February 2002? 


Function Specification 
=oGBS(1, "1/2/02", "1/10/02", 2.100, 2.000, 0.25, 0.06, 0.015, 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 = 2.1, X = 2.0, r = 0.0583, b = 0.0141 , vol = 0.25, and T = 0.6630 (242/365 days), d_{1} = 0.2957 and d_{2} = 0.5367.


As iPC = 1 (call), N(d_{1}) is 0.6163 and N(d_{2}) is 0.5367 (refer oCumNorm( ) function), the oGBS( ) equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oGBS( ) Model Greeks: 
Delta 
0.587416 
Gamma 
0.851489 
Theta 
0.088309 
Vega 
0.622415 
Rho 
0.684713 
Phi 
0.817876 
Copyright 2013 Hedgebook Ltd.