hi all,i have a question related to implied volatility of call and put .i m getting different implied volatilities for call and put options (european) with same strike and expiration .i) why they are different ? as per the no arbitrage rule, call and put options with same strike and expiration should have same volatility.ii) how to find a single volatility number ?

1. Do you have the correct risk-free rate?2. Have you accounted for dividends correctly?3. Are you ATM or deep ITM or deep OTM?4. How wide is the bid/ask spread?Some suggestions:1. If you are unsure of the risk-free rate/dividend to use, you can find out what market-makers are using by adjusting it so that the implied volatilities for put and call are the same.2. Ignore deep ITM contracts. Their implied volatilites are unreliable. Use OTMs for the wing volatilities.

put call parity (sighs)basically the market is telling you that your forward price is wrong. yes, i repeat your forward price is wrong. no doubt the call implied is lower than the put implied. what you have to do is use the call and put price to figure out the markets forward price for the asset and the use that forward price to get the implied vol. hth.

On a related note: be careful about bid/ask spreads. Put/call parity is only enforceable if you can put on the arbitrage and profit after transactions costs.I have had people in the past tell me put call parity's being violated when the violation was small enough to fit within bid/ask spreads or when the violation was similar magnitude to the uncertainty in constructing mid prices.

dave,is there any good book that will go into what you are saying. i think your point is an interesting one but i need some help in figuring out the right equation. thanks, anish

any options book will tell you what you have to do.but here goes anywayuse put call parity relationship for european optionsc - p = exp(-rt)*(f-K)hence f = K + exp(rt)*(c-p)now use f as the input into your iv calculator for either the call or put or bothyou should get the same number back

Hello Everyone,I found the same situation in some index options market. I found a difference of 5-6% in volatility of ATM puts and calls, and thought there could be some arbitrage. As Daveangel mentioned, I agree with the fact that forwards (or futures) in those markets are mispriced and they are mispriced. But now I am wondering, how one could profit from this mispricing? Especially in market where, spot (cash) index is hard (and also shorting index ETF is not as efficient), if not impossible.Does anyone have any idea? If I didnt do good job in giving explanation, please let me know, I will try again.Thanks,

He didn't say the forwards are mispriced, he said YOUR forward price is wrong.If you are dealing with a market where you can't short PC parity won't hold anyway.

Dave didn't say that forwards are misprices, he told the other guy he used the wrong forward. The fact that trading spot is hard is probably the reason for your forward not being what you expected. Edit: seems like TinMan just beat me to the reply

Thank you for quick responses from both of you.I am little new to this field. I was wondering if there is anyways, I can sell "expensive" puts volatility and buy "cheap" call volatility (doing this at ATM would be similar synthetic long forward) or make a volatility arbitrage position, by selling "expensive" puts and hedging the positions, assuming this high implied volatility will not be realized.Any views on this?Thanks,

The problem with PC parity is that people get it the wrong way round.You assume it holds and work from there.Look at the front page of the site for the article on volatility arbitrage, it's also covered in Wilmott in some depth.The book comes with a spreadsheet to that gives you a feel for the ideas.

Which book of Wilmott are you referring to?