Question

Suppose the current exchange rate is $ 1.80 divided by pound$1.80/£?, the interest rate in the United States is 5.25%?, the interest rate in the United Kingdom is 4.00 %, and the volatility of the? $/£ exchange rate is 10.0%. 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 $ 1.80.

The corresponding forward exchange rate is ?$_______/pound£. ?(Round to four decimal? places.) Using the? Black-Scholes formula d1 is _________ while Upper N1 is ___________. ?(Round to four decimal? places.) Using the? Black-Scholes formula d 2d2 is ________, while Upper N 2N2 is ________. ?(Round to four decimal? places.) The price of the call is ?$_________/pound£. ?(Round to four decimal? places.)

Answer 1

Formula to calculate forward rate is S₀e^(r-q)t

= 1.8 * e^{(5.25% - 4%)0.5}

= 1.8113

The formula to calculate D1 is :

d1= {ln(1.80/1.80) + 0.5 (0.0525 - 0.04) + 0.1²/2} / {0.1 * sqrt(0.5)}

d1 = 0.12374369

Hence the N(d1) = 0.5478

d2 = d1 - sqrt(t) * volatility.

d2 = 0.123 - sqrt(0.5) * 0.1

d2 = 0.05228932

Hence the N(d2) = 0.5200

To calculate the Call price, the formula used is :

C = (1.80 * e^{(-5.25% * 0.5)} * 0.5478) - (1.80 * e^{(-4.00% * 0.5)} * 0.5200)

C = 0.9605 - 0.9175

C = 0.043