Hi, I have a question on implied volatility surfaces (IVSs). If one constructs two IVSs separately using calls only and puts only, would the two surfaces normally very close to each other?From the theory, it should be due to the put-call parity. But I'd wonder if in reality this is the case or not. If not, what are the explanations? Also in such cases, what would one do if the mode in use is the local volatility model?Thanks in advance,TW813

In general both vollies are very simular. Remember call-put parity only works for european style options.Furthermore, implied-vollies are model dependent. So, if I have same vollie for both the call and the put, does not mean someone else should have the same, if he/she uses different pricing models. What do you mean with your question about local vollie model ? Why would you do something else with these models ?

I do not quite understand your point "implied vol is model dependent". Wat I understood is implied vols are always obtained by inverting the Black-Scholes formulas given market option prices as inputs, though I do realize that different people may have different model assumptions such as the discount curve.Regarding local vol question, I was just wondering if one were to price an option under the local vol model which has to be calibrated using implied vol surface. So if puts alone and calls alone produce two quite different surfaces, what should one do for calibrating the local vol model for pricing the option in hand?- thanks,Tw813

Generally, quite liquid options exist only on markets with liquid underlying or forward.So, put-call parity must stand (else a child or someone would arbitrage the market)The option markets I know are among the most liquid ones : the Eurostoxx and SP ones.Midprices volatilities from puts and calls are not exactly the same, but not to be arbitrageable, the bid-ask put and call ranges (which are about 1%) must have a common part, what forces the two vols to be less than 1% far too...If you can't retrieve this, you can be sure that you don't agree with the market assumptions (the anticipated dividends, for example, or more obvisous ones)

Call-Put parity only stands when options are european excercise style. What I mean with model dependent is, you can handle dividends, for example, in different ways. This will influence the implied volatilities you will obtain.just compare the implied volatities you will get when you use a non-recombining binomial tree with a binomial tree where you subtract the present value of the dividend.

From a practical point of view, the dividends, yields and the borrowing rate can influence the call/put parity - thus I would expect that these parameters are not the same as the other market participants expectations.If underlyings are not liquid, then usually the bid/ask spread will be too wide, so that the ask call vol will be still above the bid put vol and vice versa.It is very uncommon to look at calls and puts differently - I know an option trading system though which allows this setting and I have seen some guys using this setting.

eye51 is of course correct.one other point that people tend to not focus on is that american option models normally only accept one single volatility figure. in fact they are a type of barrier option, so are sensitive to more than just one "european-style implied vol".in other words if there was a market which had a full set of liquid european options, then the correct pricing of American options (including skew) on the same underlying would not in general produce prices which give the same "binomial tree implied vol". so american puts and calls could easily have different IVs on a binomial just due to skew or term structure effects.an example of this can be seen when pricing an american put on a zero div stock. you can get a highly accurate approximation for this option by pricing a down and out put with barrier below strike, and with rebate equal to strike minus barrier. to find the barrier level corresponding to your desired american put, just move the barrier up and down until you have maximised the option value. this is not exact, but you will find very good agreement. this demonstrates how american options are like barrier options, and shows that in reality skew ought to be used to price american options.