Question

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.

Answer 1

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} =

0.044836 /

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