Elite Trader Forum
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Here's a recent question that resulted in a bit of difficulty for the person who asked the question:
"Selling ITM strangles is equivalent to selling OTM strangles with the same strike prices: True or Not? Why?"
Example: Assume SPX is 900
ITM strangle:
OTM strangle:
You are having a problem comparing these positions. Try this:
Consider the difference between the two strangles. To do that,subtract one strangle from the other. For example, Add the legs from the ITM strangle and subtract the legs from the OTM strangle,
Take the four legs from both strangles.
Add them to make a single position.
Theat position is now a long box.
Short Jan 950 Call
Long Jan 950 Put
Short Jan 850 Put
A box is a riskless (ok, there is pin risk) position that varies very slightly in price as time passes (or interest rates change) by the cost of carrying the position to expiration.
Next, break that box into a call spread and a put spread, instead of two strangles. That gives you the SPX Jan 850/950 call spread and the SPX Jan 850/950 put spread.
It's easy to see that at expiration, no matter what the price of the underlying, the call spread plus put spread equals the distance between the strikes, or 100 in this example. Thus, the price of the box is constant.
If the value of the box is constant, that means the difference between the two strangles is also constant the value of the box because that difference is a box spread.
Sell either strangle - and the P/L must be identical. Why? Because the difference between the strangles remains constant. So if one strangle loses $5,000 then the other must also lose $5,000.
This assumes you collect the value of the box as the extra premium when selling the ITM strangle. In other words, you should collect almost $10,000 extra (fair value is $10,000 less interest through expiration) when selling the ITM strangle when compared with the OTM strangle. When expiration arrives and you are assigned one or two exercise notices on your short options, you will repay that extra $10,000 if you sold the ITM strangle.