Consider instrument that will pay off S dollars is 2 years, where S is the value of the Nikkel indes. The index is currently 20,000. The yen dollar exchange rate is 100 (yes per dollar). The correlation between the exchange rate and the index is 0.3 and the dividend yield on the index is 1% per annum. The volatility of the Nikkel index is 20% and the volatility of the yen dollar exchange rate is 12%. The interest rates (assumed constant) in the US and Japan are 4% and 2%, respectively.

(a) What is the value of the instrument?

(b) Suppose that the exchange rate at some point during the life of the instrument is Q and the level of the index is S. Show that a US investor can create a portfolio that changes in value by approximately AS dollar when the index changes in value by AS yen by investing S dollars in the Nikkei and shorting 50 yen.

(c) Confirm that this is correct by supposing that the index changes from 20,000 10 20,050 and the exchange rate changes from 1:00 to