Hi guys,A big part of my job concerns building volatility surfaces. I use gatheral's SVI technique and I consider it works real fine.Although, I'm facing some permanent little problems when working with the data. The obvious one is outliers for which I don't have much hope honestly. I'll continue to think about potential quick (one of our main focus is being fast in the surfaces building process) automatic tests to irradicate some of them and I would be graceful for any idea you guys would have.The other one is put-call parity not holding. Let me first explain that, for any maturity, I build the smile from out of the money options implied volatilities (i.e. calls to the right of ATM strike, puts to the left). From a put-call parity stand point, we would expect those volatilities to "touch" each other around the ATM strike but that's not the case. In fact, we sometimes get two distinct curves having pretty similar slopes near the ATM strike but being at quite different levels.Then the fitting doesn't make much sense. It tolds me that, to be consistent, we should build distinct surfaces for calls and puts. Then the debate is open as to how we should do it (using in-the-money data? using out-of-the-money data of the other C/P type and shifting it in some way to the appropriate level?).If we stick to only one surface for calls and puts together, what should we do? I used to shift both curves half a step towards each other so that their level is the same around the ATM strike but that means that my final vols are a few points away from market vols. Also, if we consider a maturity for which we only have like 4 data points, we cannot really estimate the appropriate shift. I also thought of tweaking the risk-free rate used to compute the implied vols (kind of like using a risky rate). There's always a rate for which the the two curves will touch each other. But how can we obtain that magic rate? And, beside, when the surface is used for pricing, the risk-free rate will be used and that takes us away from market prices.Any thoughts about those issues?

First, what is the underlying?. I suspect you need to spend a lot more time fine tuning your cost of carry parameters. At the end of the day, gross violations of put/callparity are unlikely if the underlying is liquid and not hard to borrow.

Hi Alan,Indeed I forgot to specify the underlyings.I'm working with equities. Mainly the big names we find in the US/Europe indices. So liquidity is not really an issue most of the time.So it would come down to using the right rates... I usually use as input the finance rate and dividend yield that Bloomberg associates with each option. That was a practical choice.So then should I calibrate the cost of carry parameters from options prices or should I seek fo any data source that would provide better risk-free rates and dividend yields?Thanks!

I would first use discrete dividends, which you may have to project for longer dated maturities.Then, when you have the dividends right, I would back out an implied interest rate foreach maturity. Can you construct a yield curve from these implied rates with, say, US equities, thatis fairly independent of the specific underlying? If so, and these rates make sense as a market rate,then your problem seems solved. If not, what do you find?. p.s. Of course, your US options are amer-style, not euro-style so that is a complicating factor, too.Perhaps you should try to reconcile things with non-dividend payers first. Since rates are so low,both the call and the put should be priced very close to the euro-style value if there is no dividend and the maturity is not too long.

I think I should calibrate a risk-free rate curve from my non-dividend underlying options. For each maturity available, I would use the closest to ATM options (like 0.95 to 1.05 moneyness, maybe tighter) for which I have both call and put prices. Then I calculate an implied risk-free rate by minimizing the total distance between each pair of call and put volatilities.I guess that I should have little problem thereafter if I use this rate curve with other underlyings paying dividends.I'll finish testing this method on monday and give you some feedback.Thanks for the talk Alan.

There has been some talk (c.f. Derivatives Week) about how the put spread collar trade has altered skew dynamics. In short, historically the longs bought puts and sold calls (downside protection; selling away upside). As puts got too expensive they started writing puts too. Recently, you can see traces of supply and demand behavior in Bloomberg's vol surface for FTSE100. Check 2y; there is a reasonably big vol gap between puts and calls.

You're using wrong underlying price to calculate implied volatility. Change underlying price, let's say down -1% to + 1% from you're using now. And draw the call side and put side skew. There will be a point that two sides match. That is the correct underlying price you should use. Or, the other traders would make money since put-call parity holds.

I would tend not to doubt my underlying price honestly. Cost of carry parameters are far less trackable than equities spot prices in my mind. That's why I'm leaning toward using some kind of implied rates.

New Underlying Price = Your Underlying Price + Price Offset(including cost of carry, market situation, ... )Calculate IV from the New Underlying Price, and compare. Give it a shot. When you trade, if the skew of call and put differs significantly, that is the time when you should change price offset. Or if you believe that the market is wrong, then that is the time when you should take the profit from put-call parity. Underlying the above is hard to short sell. When you think about hedging, you'd better consider the other underlying that you can synthetically make and trade.