Description 
Consider a European option to buy GBP / sell USD. The current exchange rate is 1.56 USD per GBP, and the rate volatility is 12%. The 'domestic' riskfree rate in the USA is 6% while the 'foreign' riskfree rate in the UK is 8% (both expressed on an actual/365 basis). The option has a strike rate of 1.60 USD per GBP and matures on 1 May 2003. What is the value of the option as at 1 November 2002? 




Function Specification 
=oGK(1, "1/11/02", "1/5/03", 1.56, 1.60, 0.12, 0.06, 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 call on the GBP. 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 = 1.56, X = 1.60, r = 0.0583, r_{f} = 0.077, vol = 0.12, and T = 0.4959 (181/365 days), d_{1} = 0.3670 and d_{2} = 0.4516.



As iPC = 1 (call), N(d_{1}) is 0.3568 and N(d_{2}) is 0.3258 (see oCumNorm( ) function), the Garman Kohlhagen equation becomes: 






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

Delta 
Given the above parameters, the delta equation becomes: 

Gamma 
As n(d_{1}) = 0.3730, the Gamma equation becomes: 



Theta 
The equation for Theta becomes: 



Vega 
The equation for Vega becomes: 



Rho 
As r <> r_{f}, the equation for Rho becomes: 



Phi 
The equation for Phi becomes: 

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