Description 
Consider a European option to sell AUD / buy USD. The current exchange rate is 0.57 USD per AUD, and the rate volatility is 18%. The 'domestic' riskfree rate in the USA is 7% while the 'foreign' riskfree rate in Australia is 8% (both expressed on an actual/365 basis). The option has a strike rate of 0.55 USD per AUD and matures on 1 August 2003. What is the value of the option as at 1 March 2003? 




Function Specification 
=oGK(2, "1/3/03", "1/8/03", 0.57, 0.55, 0.18, 0.07, 0.08, 0) 




Solution 
This option could be equivalently valued as either a call option or a put option. The following solution treats the option as a put on the AUD. The continuous equivalent of the actual/365 riskfree interest rates are calculated as follows: Referring to the equations for d_{1} and d_{2} (see model definition), if S = 0.57, X = 0.55, r = 0.0677, r_{f} = 0.077, vol = 0.18, and T = 0.4192 (153/365 days), d_{1} = 0.3313 and d_{2} = 0.2148.



As iPC = 1 (put), N(d_{1}) is 0.3702 and N(d_{2}) is 0.4150 (see oCumNorm( ) function), the Garman Kohlhagen equation becomes: 






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

Delta 
0.358457 

Gamma 
5.504513 

Theta 
0.029687 

Vega 
0.134940 

Rho 
0.092997 

Phi 
0.085647 
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