Papale on Option Parity

By Steve Papale

Happy 3rd day of unofficial spring!  Here around Chicago there is still snow on the ground with temps in the 30’s but the light of spring is definitely showing the end of the tunnel of winter.  Here in our house I at least mark the upcoming events – Big Ten tournament, bracket selection Sunday and NCAA tournament.  Mixed in there is something called St. Patrick’s Day which is big around here.  So here’s to warmer weather on the way.  It can’t get here soon enough.

Options trading, like all professions has its own terminology.  The terms help us function and communicate.  As I talk with students there is one term that seems to cause a bit of confusion so I thought I would try to clear it up today.  Often times, especially around expiration, we speak of an option trading at parity.

Parity simply refers to an option trading at its intrinsic value.  For example, suppose IBM is trading at $130.  The intrinsic value of the 110 calls is $20.  If those calls are trading at or close to $20, it is said to be trading at parity.  Of course, this generally happens around expiration or for very deep in the money options where extrinsic value is minimal.  The same idea for the puts.  The IBM 140 puts trading at parity are going for $10, their intrinsic value.  Out of the money options trade at parity too.  Close to expiration they are trading for 0, again their intrinsic value.

There is also something called put-call parity.  This gets into the concept of synthetics, which is simply the construction of an option or futures position using a combination of other options or futures.  For example, we can create a synthetic long stock position by combining a  long call with a short put at the same strike.  Say we do this for the at the money strike.  Buying one long call gives us a delta of +50.  When we sell one long put at the same strike we pick up another +50 deltas.  Together they add to +100 deltas, which is the same as 100 shares of stock.  If the underlying moves around the overall delta of this synthetic will behave the same as 100 shares of stock.  As the stock moves up and down, the deltas of the call and put will adjust and always add up to +100.

The concept of parity is important as it reminds us that the pricing relationship of options and underlying are always connected.  If for a short period there is a disconnect, traders will quickly come in and “arb” the inefficiency away, bringing prices back into line.  Even if we don’t have theoretical values we can use the parity relationships to determine if markets are in line.

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