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Chapter 27: Arbitrage 423
BASIC PUT AND CALL ARBITRAGE ("DISCOUNTING")
The basic call and the basic put arbitrages are two of the simpler forms of option arbi­
trage. In these situations, the arbitrageur attempts to buy the option at a discount
while simultaneously taking an opposite position in the underlying stock. He can then
exercise his option immediately and make a profit equal to the amount of the discount.
The basic call arbitrage is described first. This was also outlined in Chapter 1,
under the section on anticipating exercise.
Example: XYZ is trading at 58 and the XYZ July 50 call is trading at 7¾. The call is
actually at a discount from parity of ¼ point. Discount options generally either are
quite deeply in-the-money or have only a short time remaining until expiration, or
both. The call arbitrage would be constructed by:
1. buying the call at 7¾;
2. selling the stock at 58;
3. exercising the call to buy the stock at 50.
The arbitrageur would make 8 points of profit from the stock, having sold it at 58 and
bought it back at 50 via the option exercise. He loses the 7¾ points that he paid for
the call option, but this still leaves him with an overall profit of¼ point. Since he is
a member of the exchange, or is trading the seat of an exchange member, the arbi­
trageur pays only a small charge to transact the trades.
In reality, the stock is not sold short per se, even though it is sold before it is
bought. Rather, the position is designated, at the time of its inception, as an "irrevo­
cable exercise." The arbitrageur is promising to exercise the call. As a result, no
uptick is required to sell the stock.
The main goal in the call arbitrage is to be able to buy the call at a discount from
the price at which the stock is sold. The differential is the profit potential of the arbi­
trage. The basic put arbitrage is quite similar to the call arbitrage. Again, the arbi­
trageur is looking to buy the put option at a discount from parity. The put arbitrage
is completed with a stock purchase and option exercise.
Example: XYZ is at 58 and the XYZ July 70 put is at 11 ¾. With the put at ¼ discount
from parity, the arbitrageur might take the following action:
1. Buy put at 11 ¾.
2. Buy stock at 58.
3. Exercise put to sell stock at 70.