Suppose the current exchange rate is $ 1.83 divided by pound, the interest rate in the United States is 5.45 %, the interest rate in the United Kingdom is 3.77 %, and the volatility of the $/£ exchange rate is 10.6 %. Use the BlackScholes formula to determine the price of a sixmonth European call option on the British pound with a strike price of $ 1.83 divided by pound.
Strike Rate S_{t} = $1.83
Current Rate X = $1.83
Time T = 6 month/12 months = 0.5
Domestic Interst Rate I_{d} = 5.45% = 0.0545
Foreign Interest Rate I_{f} = 3.77% = 0.0377
Volatility = 10.6% = 0.106
d1 = [Ln (1.83/1.83) + {0.0545  0.0377 + 0.5 (0.106)^{2} }/ 0.5] / {(0.106 * (0.5)^{1/2}} =

0.074953 =

d2 = [Ln (1.83/1.83) + {0.0545  0.0377  0.5 (0.106)^{2} }/ 0.5] / {(0.106 * (0.5)^{1/2} =
0.022364/ 
0.074953 =
0.298372 
N (d_{1}) = N(.595186) = 0.617291
N (d2) = N(.298372) = 0.725142
Call Option Price C = 1.83 * 0.617291 * e^{ 0.0377}* ^{0.5}  1.83 * 0.725142 * e^{ 0.0545}* ^{0.5}
^{=}
0.18279 
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