Hello,Since, in the equity world, the implied volatility is different for a call than for a put (same strike), I was wondering if one should have a call implied volatility surface to calibrate to when it's for pricing an exotic call option (the same holding for a put). Or is it possible from both call and put to obtain a unique and consistent volatility surface using call put parity identity. What is the market practice to solve for that problem (if any) ? Do you have any useful references or papers ?I really need some enlightment.Thanks in advance,zzbool.

why do you think that the implied vol is different for calls and puts of the same strike & maturity?

the put call parity relationship implies the volatility for puts and calls of same strike and maturity are equal - see Hull!

Some [big] shops do not calculate different equity vol. surfaces for Calls and Puts but use the Out-of-the-Money options for Calls and Puts and then use that---i.e. OTM Calls become also ITM Put and visa-versa. At least if they don't have a 'big' model. Without a 'big' model for the surfaces they may solve for Delta, Gamma, Vega.

I do agree with you, tibbar & apine, from a theoritical point of view. But I came to this question, when looking at listed options traded on the DJ EuroStoxx 50 index. I observed that for a put and a call with the same expiry & the same strike, the implied volatility was different (using Bloomberg OMON & OV command). Which is why I asked how the market was treating that kind of discrepancy. How do you explain that the theory is not verified in practice (the tests I conducted, have been made on several options and several underlyings and the difference has been verified for each of these options) and what are the practical day to day answers ?Thanks for inputs !

In my experience, it's almost always a data problem.The ideal data will be based on option bid/asks simultaneouswith a good index quote, say from the futures market to pickup the best cost-of-carry factors. Tothe extent that your data deviates from this, it may be problematic.My suggestion: nail down the times when the option quotes were generated.Assuming they are all at the close, there is probably some hope.Get the closing index value, project dividends, and compare yourimplied futures price with the actual futures price. If there is a difference here, figure out why. If this doesn't work, feel free to post some actual numbers for more suggestions.regards,

Alan is, of course, correct. it is a data problem or you are using an incorrect (or at least different) set of assumptions. perhaps your rates are different or dividend streams. i make my living from pricing the vol surface correctly, so i can assure you that this is more than a merely theoretical issue.

So, apine & alan, from your experience it's not practically possible for a call & a put with same strike and expiry to have different implied volatilities ?

Post your analysis along the lines I suggested. Let's see if it translates into asignficant put/call parity violation that should have been exploited. Then, youshould be able to draw your own conclusion.

Thanks Alan !I'll post it tomorrow when I'll get the informations needed from Bloomberg.Regards.

When you use Bloomberg, the implied vols are computed with the yield dividend assumption (meaning, last year divs). So basically, if the implied vols are not the same, it simply means that you are off on the divs. On a stock, it could also be the repo, but on indices, it is usually that you are not using the correct implied dividends.

I agree with Alan that significant differences are almost always data problems, and also with apine and volare that small theoretical differences are possible due to uncertain dividends and different borrowing and lending rates; plus another one they did not mention, early exercise possibility.I would add one point. With options far from the money, a small price difference can result in a large implied volatility difference. For example, suppose a stock is selling for $95, while interest rates are 3%. The $100 call expiring tomorrow sells for $0.001627, giving an implied volatility of 30%. By put/call parity, the $100 put should sell for $4.99 but, because it is American, it sells for $5.00. That $5.00 price put into a European implied volatility model gives 37.72%. So it looks as if there is a large implied volatility difference between the put and call, due to the small theoretical feature of American exercise.If the implied volatilty calculation is American then the put has inderminant volatility. Also, you could generate the same problem with small uncertainties or asymmetries.

I am facing the same problem: I am posting the trade data for 4th June 07 on S&P. Th options are European, both call and put. 100% strike corresponds to ATM. Prices are mentioned as a % of underlying. Notice the difference in vols. for 100% call and 100% put. Is there any dividend issue on S&P 500, please excuse my ignorance, but does is there any dividend on this index at all.I have taken the risk-free interest rate = 0, is that a wrong thing to do?Also, if I am to believe jfuqua, my surface will be against moneyness not strikes... what should I call as a vol. surface, one against strike on the x-axis or moneyness?Thanks very much.SPX as of 04 June 2007 Call PricesStrikes >Expiry V 90% 100% 110% 120% 130% 140% 150% 15-Jun-07 10.0892% 0.8397% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000% 20-Jul-07 10.5763% 1.9438% 0.0018% 0.0000% 0.0000% 0.0000% 0.0000% 17-Aug-07 10.9373% 2.6379% 0.0239% 0.0000% 0.0000% 0.0000% 0.0000% 21-Sep-07 11.4312% 3.4108% 0.1124% 0.0000% 0.0000% 0.0000% 0.0000% 21-Dec-07 12.6585% 5.0612% 0.7998% 0.0257% 0.0001% 0.0000% 0.0000%Put Prices Strikes >Expiry V 50% 60% 70% 80% 90% 100% 110% 15-Jun-07 0.0000% 0.0000% 0.0000% 0.0001% 0.0091% 0.7434% 9.8875% 20-Jul-07 0.0000% 0.0000% 0.0014% 0.0251% 0.1637% 1.4636% 9.4539% 17-Aug-07 0.0000% 0.0004% 0.0087% 0.0706% 0.3299% 1.9217% 9.1990% 21-Sep-07 0.0001% 0.0021% 0.0233% 0.1299% 0.5376% 2.3574% 8.8992% 21-Dec-07 0.0015% 0.0162% 0.0899% 0.3408% 1.0785% 3.1903% 8.6379%

its almost always a data problem. there is a paper(not by a well established guy though) about how to handle non-simultaneity of data, in captured data.there is another paper which empirically proves that average pnL generated(net of txn cost) by executing these strategies is negative.

Please allow me to revive this old thread... With imposition of generalized put-call parity, i can use the market data to find unknown embedded risk-free rate and also the unknown implied dividend yields, such that put and call implied volatilities are same strikes are the same. Here, I need only two strikes in order to find the unknown risk-free rates and the dividend yield.In an over-specified problem, like that with 3-4 overlapping market traded put-call strikes, I have a choice which two strikes to choose.Is there a guideline for this choice?Better still, are there more no-arbitrage boundary conditions that I can apply, so that it does not remain an over-specified problem.