Option Volatility and Pricing by Sheldon Natenberg

Author:Sheldon Natenberg
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2015-01-14T16:00:00+00:00

Boxes

What else acts like an underlying contract but isn’t an underlying contract? Another possibility is to replace the underlying position with a synthetic position, but a synthetic with a different exercise price. For example, suppose that we have a June 100 conversion:

–1 June 100 call

+1 June 100 put

+1 underlying contract

At the same time, we also execute a June 90 reversal. The combined position is

The long and short underlying contracts cancel out, leaving

We have a synthetic long underlying position at the 90 exercise price and a synthetic short underlying position at the 100 exercise price. This position, known as a box, is similar to a conversion or reversal except that we have eliminated the risk associated with holding a position in the underlying contract. A trader is long the box when he is synthetically long at the lower exercise price and synthetically short at the higher exercise price. He is short the box when he is synthetically short at the lower exercise price and synthetically long at the higher exercise price. The example position is long a June 90/100 box.

Like a conversion or reversal, a box is an arbitrage—we are buying and selling the same contract but in different markets. In our example, we are buying the underlying contract in the 90 exercise price market and selling the same underlying contract in the 100 exercise price market.

How much is a box worth? Ignoring pin risk, at expiration, a trader who has a box will simultaneously buy the underlying contract at one exercise price and sell the underlying contract at the other exercise price. The value of the box at expiration will be exactly the amount between exercise prices. In our example, at expiration, the 90/100 box will be worth exactly 10.00 because the trader will simultaneously buy the underlying contract at 90 (exercise the 90 call or be assigned on the 90 put) and sell the underlying contract at 100 (exercise the 100 put or be assigned on the 100 call). If the box is worth 10.00 at expiration, how much is it worth today? If the options are subject to futures-type settlement, the value today is the same as the value at expiration. If, however, the options are subject to stock-type settlement, the value of the box today will be the present value of the amount between exercise prices. If our 90/100 box expires in three months with interest rates at 8 percent, the value today is

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.