“First， work out the cost of the box spread. Combine the two call options into a bull spread （buy the low strike call and sell the high strike call）， and the two put options into a bear spread （buy the high strike put and sell the low strike put）. Combining those two gives a box spread. To calculate the initial cost， work out the net premia：

　　Cost = c1 – c2 + p2 – p1 = 6 – 4 + 8.001 – 0.604 = $9.397

　　The payoff from the box spread will be the difference between the strike levels， ie 30 – 20 = $10.

　　If you borrowed $9.397 at the beginning in order to enter the box spread， how much would you have to pay back after 6 months？ You need to compound the cost at the risk-free rate：

　　$9.397 x e0.04 x 0.5 = $9.58683

　　So the arbitrage profit would be the difference between the payoff and what you have to pay back on the loan， ie $10 – $9.58683 = $0.41317”

　　8. Assume Felix Burrow is a US investor， holding some euro-denominated assets. Given the information below， calculate the domestic return for Burrow over the year.

　　Today Expected in 1 year

　　Euro asset 201.54 203.12

　　USD/EUR exchange rate 1.1133 1.1424

　　知名投行培训主管Nicholas Blain 解析：

　　“The domestic return （return in USD terms） depends on the EUR-return of the asset， as well as on the change in exchange rates：

　　RDC = （1+RFC） （1+RFX） -1

　　where RFX is the change in spot rates， using the domestic currency as the price currency （ie we require a USD/EUR quote）. In this example， the exchange rate is quoted as such， so we can use the quote provided （otherwise， if the domestic currency was the base currency， we would need to invert the quote first）.

　　RFC = -1 = 0.0078 = 0.78%

　　RFX = -1 = 0.0261 = 2.61%

　　RDC = （1 + 0.78%）（1 + 2.61%） – 1 = 3.41%

　　Burrow’s domestic currency return was higher than the underlying asset return， because he further benefits from the appreciation of the Euro （depreciation of the USD）.”