A European call on the euro matures after T =0 90 days.The call pays on the maturity 100[S_A (T )-1.20] dollars if it ends in-the-money,zero otherwise,where 100 is the contract multiplier and $1.20 is the strike price K.The euro's volatility $\sigma$ is 15 percent per year.Today's spot exchange rate S_A is $1.3 per euro (in American terms).The continuously compounded annual risk-free interest rates are r = 4 percent in the United States (domestic)and r_E = 3 percent in the Eurozone.Then the Black-Scholes-Merton model gives a call option price of:

Question

Quizplus · Accepted Answer

We can use the Black-Scholes-Merton formula to calculate the call option price:

d1 = [ln(S0/K) + (r - q + 0.5*σ^2)*T]/(σ*sqrt(T)) = [ln(1.3/1.2) + (0.04 - 0.03 + 0.5*0.15^2)*0.25]/(0.15*sqrt(0.25)) = 0.7013
d2 = d1 - σ*sqrt(T) = 0.5356

N(d1) = 0.7581
N(d2) = 0.7047

C = S0*e^(-q*T)*N(d1) - K*e^(-r*T)*N(d2) = 1.3*e^(-0.03*0.25)*0.7581 - 1.2*e^(-0.04*0.25)*0.7047 = $10.84

Therefore, the option price is $10.84, so the best choice is D.

A European Call on the Euro Matures After T =0 σ\sigmaσ

A European Call on the Euro Matures After T =0 $\sigma$