Put Call Parity

Chuck · Post by **Chuck** » Sun Dec 02, 2007 5:11 am

Super basic: We have Ct + pv*K = Pt + St

Where Ct/Pt is market value of call/put at time t and St is market value at time t. pv*K can also be Ke^-rt (risk free rate multiplied by time to maturity).

I wanted to verify a price on puts, so I took the ask on the call and got the bid on the put as a result. In practice is this normally what's used? Or do most 'models'--however basic--use strictly bid/ask/mid?

dantes · Post by **dantes** » Sun Dec 02, 2007 6:34 am

I am not sure what you are asking, but it seems to me like you have verified that the market is pricing the stuff fairly. If the bid on the put was higher you would have an arbitrage, right? And if it was lower you could yourself put in a bid slightly higher hoping to get hit and do an arbitrage. If you should use bid/ask/mid will depend on your purpose and if you are looking to sell a put over parity you could use the ask of the call and the bid of the stock, knowing that is where you could do an immediate trade. Few markets offer such a treat, of course.

DrTarr · Post by **DrTarr** » Mon Dec 03, 2007 12:22 am

Assuming you are trying to sell the puts??

Chuck · Post by **Chuck** » Mon Dec 03, 2007 6:58 am

Not necessarily trying to sell...just experimenting. When I pop in the bid on the call I get 0 for the put, unfortunately I'm not a market maker and can't buy at the bid. The results were slightly off as I just remembered that parity only applies to European options; I was doing this on a dividend paying security.

FDAXHunter · Post by **FDAXHunter** » Mon Dec 03, 2007 7:16 am

Call-Put Parity holds with dividends. Where it doesn't hold is with American-style options.... which I presume is what you are looking at.

Baltazar · Post by **Baltazar** » Mon Dec 03, 2007 8:53 am

parity holds for europeans with dividends but obviously you have to include dividends in your formula.

and yes use the bid of the call to get a fair quote for the ask for the put