Question

# Suppose the current exchange rate is \$ 1.83 divided by pound​, the interest rate in the...

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​ Black-Scholes formula to determine the price of a​ six-month European call option on the British pound with a strike price of \$ 1.83 divided by pound.

Strike Rate St = \$1.83

Current Rate X = \$1.83

Time T = 6 month/12 months = 0.5

Domestic Interst Rate Id = 5.45% = 0.0545

Foreign Interest Rate If = 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} =

 0.044836
/

0.074953 =

 0.598186

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 (d1) = 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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