36 lines
2.8 KiB
Plaintext
36 lines
2.8 KiB
Plaintext
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 |