016 - 16 Options on Stock Indexes, Foreign Currency, and...

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163 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 cost-of-carry for a futures is the same as the risk-free rate? For pricing options on futures, the important consideration is that the futures price follow the cost-of-carry relationship very closely. This adherence to the cost-of-carry model is much more important than the exact amount of the cost-of-carry. The option pricing model for futures does not work well if there is not an adher- ence to the cost-of-carry model. Thus, it is mainly a matter of convenience that we assume the cost-of-carry to equal the risk-free 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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016 - 16 Options on Stock Indexes, Foreign Currency, and...

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