Chapter 27: Arbitrage 439 
Example 1: XYZ is sold short at 60, and a January 50 call is bought for 10¼ points. 
Assume that the prevailing interest rate is 1 % per month and that the position is 
established one month prior to expiration. XYZ pays no dividend. The total credit 
brought in from the trades is $4,975, so the arbitrageur will earn $49.75 in interest 
over the course of 1 month. If the stock is above 50 at expiration, he will exercise his 
call to buy stock at 50 and close the position. His loss on the security trades will be 
$25 the amount of time value premium paid for the call option. (He makes 10 
points by selling stock at 60 and buying at 50, but loses 10¼ points on the exercised 
call.) His overall profit is thus $24.75. 
Example 2: A real-life example may point out the effect of interest rates even more 
dramatically. In early 1979, IBM April 240 calls with about six weeks of life remain­
ing were over 60 points in-the-money. IBM was not going to be ex-dividend in that 
time. Normally, such a deeply in-the-money option would be trading at parity or even 
a discount when the time remaining to expiration is so short. However, these calls 
were trading 3½ points over parity because of the prevailing high interest rates at the 
time. IBM was at 300, the April 240 calls were trading at 63½, and the prevailing 
interest rate was approximately 1 % per month. The credit from selling the stock and 
buying the call was $23,700, so the arbitrageur earned $365.50 in interest for 1 ½ 
months, and lost $350 - the 3½ points of time value premium that he paid for the 
call. This still left enough room for a profit. 
In Chapter 1, it was stated that interest rates affect option prices. The above 
examples of the "interest play" strategy quite clearly show why. As interest rates rise, 
the arbitrageur can afford to pay more for the long call in this strategy, thus causing 
the call price to increase in times of high interest rates. If call prices are higher, so 
will put prices be, as the relationships necessary for conversion and reversal arbitrage 
are preserved. Similarly, if interest rates decline, the arbitrageur will make lower 
bids, and call and put prices will be lower. They are active enough to give truth to the 
theory that option prices are directly related to interest rates. 
THE BOX SPREAD 
An arbitrage consists of simultaneously buying and selling the same security or equiv­
alent securities at different prices. For example, the reversal consists of selling a put 
and simultaneously shorting stock and buying a call. The reader will recall that the 
short stock/long call position was called a synthetic put. That is, shorting the stock 
and buying a call is equivalent to buying a put. The reversal arbitrage therefore con­
sists of selling a (listed) put and simultaneously buying a (synthetic) put. In a similar