Option Trading Blog

This is part II of the last post on reducing risks with synthetic options. In the last topic we talked about the the box technique. As we have said earlier, with the box technique, we don’t buy anymore the stock, just a combination of options on different strike prices. Let’s consider again the following portfolio

• long a 1 month 90 call
• short a 1 month 90 call
• short a 1 month 100 call
• long a 1 month 100 put

What happens if the stock finishes at 95$? We receive 5$ for the 100 put and 5$ for the 90 call for a total profit of 10$. What happens if the stock finishes at 105$? We receive 15$ for the 90 call and pay 5$ for the short put for a profit of 10$. Actually, no matter what happens, we receive 10$! This means that The portfolio itself must be worth 10$ minus the cost of interest rates. Note that you can create other boxes as well for different strike prices.

When to utilize it

Suppose the interest rate for 1 month is 1%. This means our box should be valued at . What happens if not? We know we are guranteed to get with the box technique 10$. If the price of the execution of the box is lower than 9.9, it is cheap to execute it. This means we could buy the portfolio of the box and sell a bond with 1% interest rate at 9.9$. At the end, we have to pay the bond owner 10$, but we will receive that amount from the box technique. We will end up with the difference to our pocket!(The bond we sold minus the box portfolio we bought) 

Consider this real life example of April options trading in the TASE (Israeli Stock Market):

At this moment, the TA25 stands at 1028.81 points. How much the box technique costs for the following portfolio (note that we can chose other strike prices as well)

• short April 1030 call - 1491 
• long Aprial 1030 put - 1290
• long April 1020 call - 2132
• short April 1020 put - 931

Buying the portfolio would cost us 1290+2132-1491-931 = 1000 shekels. We are guranteed to receive (1030-1020)*100 = 1000 shekels at the 26th, when the stocks expire(we have multiplied by 100 because on the index, the options have a multiplier of 100). We can see that the market is very efficient because even when discounting the 1 month interest rate from 1000, it will almost still equal 1000 shekels! This means that in this situation, it won’t be profitable to execute the box technique.

So when is it profitable? when there is a lot of uncertainty and confusion, there is a chance of finding arbitrage opportunities. At the 12th of july, 2006, the war with Lebanon has started. Consider again the following long box portfolio:

• long call 800 - 840
• short put 800 - 2682
• short call  900 - 3
• long put 900 - 11,553

 This would cost us 3 + 2682 - 11,553-840= 9708 shekels to buy, and gurantees us 10,000 shekels (900-800 = 100 * multiplier) in return! This means it was profitable to execute the box!