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Answers to Questions and Problems
1. Explain why interest payments on a foreign currency can be treated as analogous to a dividend on a common
stock.
For a stock, dividends represent a leakage of value from the asset. If dividends were not paid, the stock price
would continue to grow at a higher rate, compounding the value of the dividends. The same is true for a cur
rency. The interest rate paid by a currency represents a leakage of value from the currency. Therefore, divi
dends from common stock and interest payments from a currency can be treated in the same way for option
pricing purposes.
2. Why do we assume that the costofcarry for a futures is the same as the riskfree rate?
For pricing options on futures, the important consideration is that the futures price follow the costofcarry
relationship very closely. This adherence to the costofcarry model is much more important than the exact
amount of the costofcarry. The option pricing model for futures does not work well if there is not an adher
ence to the costofcarry model. Thus, it is mainly a matter of convenience that we assume the costofcarry
to equal the riskfree rate. In the real world, this assumption performs very well for financial futures, but it
performs less well for futures on agricultural goods.
3. Explain how to adjust a price lattice for an underlying good that makes discrete payments.
The text considers three types of dividend payments: constant proportional payments, occasional payments
equal to a percentage of the asset value, and occasional payments of a fixed dollar amount. In every case, the
presence of the dividend requires an adjustment in the stock price lattice. In essence, the nodes in the stock
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 Spring '08
 Danısoglu
 Dividends, Interest, Options

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