How to Profit from Mispriced Options

04/09/2010 12:01 am EST


Many traders do not know this, but if one looks at the profit/loss (P&L) chart of a covered call and a cash-secured put on the same strike, they are borderline identical (save any differences in margin use). This is proven in a formula called put-call parity.

Put-Call Parity

Put-call parity is kind of like the duct tape of the options world; it holds the entire options universe together. No matter how complex the model is in the programmed trade, if this simple formula isn't taken into account, the complex model is likely to cause its operator a lot of problems.

Put-call parity proves that if a call is trading at a given price, then the put has a direct quantifiable value that the trader can calculate. The formula for put-call parity is:

C-P = S-X + (I-D)

C = call
P = put
S = Stock
X = Strike
I = Interest
D = Dividends

This likely sounds crazy in the day and age of computers, but up until about 2003, floor traders spent a majority of their floor time looking up at the option screens and converting calls into puts and vice versa. If the trader found a call or a put that was mispriced, the trader would then trade that option. The idea was the trader was trying to lock in "edge." "Edge" is a term professional traders use for the value the trader enters an option trade above or below its theoretical value. 

Here is an example. Suppose stock XYZ is trading at $56, the April 55 call is trading at $4, there is 5 cents in interest to collect (we are pretending rates are a lot higher than they currently are), and the stock has a 25-cent dividend between today and expiration. What should the value of the put be? 

Using the put-call parity formula, the equation is:

4-P = 56-55 + (.05-.25)
4-P = 1 + (-0.2)
P = 3.20

The put should be worth $3.20. If the put is $3.30 bid or $3.10 offered, the trader knows that one of the options is mispriced. The trader would then typically look at the screen and see a public bid or offer in either the call or put that was throwing off the parity between puts and calls.

This is all well and good, but how can retail traders use this formula to their advantage?

Certainly, retail traders do not have the ability to sit in front of a computer and scan for mispriced options, but there are actually a few ways that traders can use put-call parity to their advantage. I am going to present the simplest ways, credit and debit spreads. 

Credit and Debit Spreads

If there is a formula that holds puts and calls together, then put and call credit spreads are also held together by the same formula.

Take a moment to look at a long IBM May 130/135 call spread. Now compare the spread to a short May 130/135 put spread. Once inspected, the trader should notice that they are exactly the same spread. And a long 125/130 put spread is the same as a short 125/130 call spread.

Here is the simple rule: The difference between the strikes, less the value of the call spread, should equal the put spread, and vice versa.

How can traders use this knowledge to their advantage? Throw out the idea that a trader should only trade credit spreads or only trade debit spreads. Traders should understand that they are exactly the same thing!  

Take a little time to do some math before entering a particular debit or credit spread. There may be an opportunity to take advantage of a mispriced spread (and yes, this happens often).

Back to IBM. Suppose I decide that I want to get long a debit spread. I look at the IBM May 130/135 call spread. If I can buy that spread for $1.50, what price should I be able to sell the IBM May 130/135 put spread at? The answer is $3.50.

But what if I could sell the put spread at $3.55 instead of $3.50? I would be getting long the exact same spread at five cents less per spread. The same holds on the put side if I wanted to get long an IBM put spread.

This may not sound like a lot, but it adds up over time. While the savings at first might pay for a foot-long sub, if the trader repeats this process and can save that five cents many times in a year, he or she will be able to pay for dinner for two at a very nice restaurant relatively quickly.

By Mark Sebastian of

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