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International Financial Management

Notes If there are two options that are otherwise alike, the option with the longer time to expiration
must sell at an amount equal to or greater than the option that expires earlier.
For example, consider the two options on the same stock:
(a) Strike price = ` 100, maturity = 6 months, price = ` 8
(b) Strike price = ` 100, maturity = 3 months, price = ` 10

The transactions made by an arbitrageur would be:
Buy the 6 months option (` 8)
Sell the 3 months option +` 10
Net cash flow ` 2
The only risk against the ` 2 profit is that the option which was sold might be exercised. In that
case, the position can be squared up by selling the six months options. The ` 2 profit would
materialise even in this case.
Hence, the six months option has to sell at a price ≥ ` 10.

Interest Rates
Let us consider an example.
Assume that a stock now sells for ` 100 in the market and over the next year its value can change
10% in either direction. Risk free rate of interest is 12% and a call option exists on the stock with
a value of ` 100 and an expiration date one year from now. Two portfolios can be constructed.
Portfolio A: 100 shares of stock worth ` 10,000.
Portfolio B: ` 10,000 pure discount bond maturing in one year with a current value of ` (10000/
1.12) = ` 8929. And one option contract, with an exercise price of ` 100 per share.
Consider the values of the two portfolios one year from now.

+10% -10%
Portfolio A (Stock) ` 11000 ` 9000
Maturing Bond B ` 10000 ` 10000
Call Option ` 1000 0
As can be seen from the table, portfolio B is a better portfolio to hold as it gives better results
than portfolio A under both conditions. If stock prices go down, portfolio B is worth ` 1000 more
than portfolio A; otherwise, both have the same value. Since portfolio B has more value than
portfolio A, its cost must equal or exceed that of portfolio A to deny riskless arbitrage opportunity.
Thus, bond price + call option price = Cost of portfolio A = ` 10000. Thus, call option price =
` 10000 – ` 8929 = ` 1071.
Hence, to deny arbitrage opportunity, C ≥ S – Present Value(E). The call price must be greater
than or equal to the stock price minus the present value of the exercise price. Also, if the interest
rate were higher, say 20%, value of the call option will be – (` 10000/1.2) = ` 1667.
Based on this line of reasoning, another principle can be stated: ‘other things being equal, the
higher the risk-free rate of interest, the greater must be the price of the call option.’

8.6.1 Speculating with Currency Options

Investors may speculate in the currency options market based on their expectations of the future
movements in a particular currency. For example, if the speculators expect that the Japanese yen
will appreciate, they will purchase Japanese yen call option. When the spot rate of Japanese yen

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