Academic journal article Journal of International Business Research

Currency Option Pricing Model Relevant to the Japanese Yen

Academic journal article Journal of International Business Research

Currency Option Pricing Model Relevant to the Japanese Yen

Article excerpt


The currency option pricing follows the exchange rate on the daily basis. In this work we studied the exchange rate for one Dollar in terms of Yen from January 1960 through January 2011. Several models for regression analysis such as Linear, Logarithmic, Inverse, Quadratic, Cubic, Compound, Power, S or S-curve, Growth, Exponential, and Logistic were employed. The regression analyses for these models were studied. Among these models S-curve was selected due to number of reasons that will be discussed later. Then regression analysis was performed to provide prediction of the exchange rate through year 2020. During the first quarter of 2011 exchange rate for 76 Yen per Dollar was tested which is even lower than our S-curve prediction for year 2012 but higher than year 2011 for other models. Some of the external forces will be mentioned and a few recommendations will be made for stability of Dollar versus Yen.

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Currency option pricing has been studied by a number of researchers. As a result several theories related to the exchange rate have been established. We discuss two of these theories. Purchasing power parity (PPP) quantifies the relation between inflation exchange rates between two countries that are being studied. There are two types of PPP theories.

The absolute form of PPP states that given the fact that there are no international trade barriers, then the consumers will tend to shift their purchases to the country that offers lower prices (as measured by common currency). As the result the exchange rate will adjust so that the same items will cost the same in both countries as measured by the same common currency. On the other hand, relative form of PPP is the exchange rate that is adjusted based on the relative inflation in the respective countries.

The second theory of exchange rate determination is the interest rate parity theory (IRO). In this theory the major assumption is that one should not make a greater profit by taking advantage of an interest rate differential in these two countries since the currency for the country with the higher interest rate has a tendency to depreciate either in the forward market or appreciate in the spot market.

The interest rate parity must hold based on the following equation, where di = domestic rate and F^sub i^ = foreign rate.


The exchange rate must be a direct quote, that is, it must be yen per dollar. It must be foreign currency per unit of domestic currency. Here the U.S. is considered domestic and Japan is considered foreign.

Black and Scholes (Black & Scholes, 1973) indicated that in deriving their formula for the value of an option in terms of the price of the stock, they made an assumption of "ideal conditions" in the market for the stock and for the option:

a) The short-term interest rate is known and is constant through time.

b) The stock price follows a random walk in continuous time with a variance rate proportional to the square of the stock price. Thus the distribution of possible stock prices at the end of any finite interval is log- normal. The variance rate of the return on the stock is constant.

c) The stock pays no dividends or other distributions.

d) The option is "European," that is, it can only be exercised at maturity.

e) There are no transaction costs in buying or selling the stock or the option.

f) It is possible to borrow any fraction of the price of a security to buy it or to hold it, at the short-term interest rate.

g) There are no penalties to short selling. A seller who does not own a security will simply accept the price of the security from a buyer, and will agree to settle with the buyer on some future date by paying him an amount equal to the price of the security on that date.

There are external factors that cannot be predicted or be quantified to include in the prediction exchange rate model. …

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