Consider an instrument that will pay off S dollars in two years where S is the value
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Consider an instrument that will pay off S dollars in two years where S is the value of the Nikkei index. The index is currently 20,000. The yen/dollar exchange rate is 100 (yen 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 Nikkei index is 20% and the volatility of the yen-dollar exchange rate is 12%. The interest rates (assumed constant) in the U.S. 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 U.S. investor can create a portfolio that changes in value by approximately ΔS dollar when the index changes in value by ΔS yen by investing S dollars in the Nikkei and shorting SQ yen.
(c) Confirm that this is correct by supposing that the index changes from 20,000 to 20,050 and the exchange rate changes from 100 to 99.7.
(d) How would you delta hedge the instrument under consideration?
DividendA dividend is a distribution of a portion of company’s earnings, decided and managed by the company’s board of directors, and paid to the shareholders. Dividends are given on the shares. It is a token reward paid to the shareholders for their... Exchange Rate
The value of one currency for the purpose of conversion to another. Exchange Rate means on any day, for purposes of determining the Dollar Equivalent of any currency other than Dollars, the rate at which such currency may be exchanged into Dollars... Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...
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a We require the expected value of the Nikkei index in a dollar riskneutral world In a yen riskneutr...View the full answer
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