In this problem you will price various options with payoffs based on the Eurostoxx index and the dollar/euro exchange rate. Assume that Q= 2750 (the index), x = 1.25 ($/=C), s = 0.08 (the exchange rate volatility), σ = 0.2 (index volatility), r = 0.01(the U.S. risk-free rate), rf = 0.03 (the euro-denominated risk-free rate), δQ = 0.02 (the dividend yield on the index), ρ = 0.25 (the index exchange rate correlation), and T = 1. Verify the following prices (all are in dollars):
a. Equity index call denominated in euros: max (QT − K, 0), K = 2500 ($457.775)
b. Foreign equity call struck in domestic currency: max (xTQT − Kd, 0), Kd = $3200 ($414.574)
c. Fixed exchange rate foreign equity call: max(QT − K, 0); = 1.25, K = 2500 ($456.988)
d. Equity-linked foreign exchange call: max (xTQT − KQT, 0), K = $1.20 ($152.561)