This may be a question mostly for Ron B., but I don't know how to address him directly. When IV Smile is activated within TOS, the IV's for the call and put at a strike become the same. For example, on this Saturday morning, the IV for the Aug 26, NDX 4810 call and put, using Smile, is 9.85%. With Smile off and IIV on, the call is 8.93% and the put is 9.94%. What I don't understand is how these two methods do their calculations. According to B-S, doesn't an option, at a given strike, in a given term (DTE), with a given interest rate, at a given price provided by the market place, have to have a single, calculated IV? So, how can turning on Smile make the IV's suddenly different (and equal)? I have a separate, perhaps opposite, question about, given P/C parity, how the price for a put and a call with the same term/strike can be different in the first place (although they obviously are), but perhaps an answer to the first question will clarify this second question. Joe
With European options, the call and put IV needs to be exactly the same, due to put-call parity. With American options, under most normal circumstances, call and put IV should also be the same, but there are a few exceptions with equities (hard to borrow stock, dividends, etc). Here are some links which may help: http://screencast.com/t/er7mjBDIUgcV https://en.wikipedia.org/wiki/Putâ€“call_parity More: http://quant.stackexchange.com/questions/7604/does-implied-vol-vary-for-calls-vs-puts http://www.math.umn.edu/~bemis/finance/putcall.pdf
Most of the models use Black-Scholes to calculate the IV of each strike, and they do so by taking all of the various inputs (including the current market price of the option) and can then work out the IV for that option. But there are different models which can take other things into account as well, such as the "volatility surface" and "CEV" configs in OptionNetExplorer, "volatility smile" in TOS, and "combine put/call skew" in OptionVue. These models can either take put-call parity into account, or use some type of smoothing of IV data. Some models will then end up showing different IVs for the call and put of the same strike, and yet others (such as "TOS vol smile") will show the option chain where the call and put of a particular strike will have exactly the same IV. As you can see from the links I've listed above, plus many others you can find if you Google it, the options theory says that under most normal circumstances, the call and put IV for a particular strike should be the same, due to put-call parity. This should always be the case with European style options, but there are some exceptions with American style equity options, in cases where the stock may be hard to borrow, or there are upcoming dividends, etc.
I did read the links and wondered about these statements in the answer section of this link http://quant.stackexchange.com/questions/7604/does-implied-vol-vary-for-calls-vs-puts In practice there are bid-ask spreads and liquidity issues which implies that observable prices ofEuropean options do no align necessarily to the theory. and this one from the same link Implied volatility does not have to be equal (so yes, it can be different) for a call and put of same underlying, underlying borrow rates, time to expiration, strike if: If the underlying is a stock and the underlying cannot be easily borrowed for short selling If there are dividends or other costs of carry involved If there is not unlimited liquidity in the market In the absence of market turbulence. Which made me confused. Thanks for clearing it up.
This is a little off-topic from the original question but there seems to be an ever increasing propensity to quantify Implied Volatility and Greeks down to the decimal place across various platforms and computational models. I believe what's missing in the discussion is that these are simply models that more often than not provide a reasonable representation/estimate/educated guess of Implied Volatility (and therefore the Greeks as well). There are so many variables that are not accounted for in IV calculations...what is the IV between strikes? Is it linear? quadratic? does is smoothly transition from strike to strike as the underlying moves? Is continuous-time stochastic volatility jump diffusion are more accurate model, or do you buy volatility reverting to the mean and therefore leverage Volatility Clustering and change your model to leverage ARCH or GARCH? I think this is all very interesting...however... "In theory there is no difference between theory and practice; in practice there is." Check out NYU's Volatility Department's work on the subject: https://vlab.stern.nyu.edu/ They have implemented many volatility models, all correct, each providing a different "answer" This is a little off-topic from the original question but there seems to be an ever increasing propensity to quantify Implied Volatility and Greeks down to the decimal place across various platforms and computational models. I believe what's missing in the discussion is that these are simply models that more often than not provide a reasonable representation/estimate/educated guess of Implied Volatility (and therefore the Greeks as well). There are so many variables that are not accounted for in IV calculations...what is the IV between strikes? Is it linear? quadratic? does is smoothly transition from strike to strike as the underlying moves? Is continuous-time stochastic volatility jump diffusion are more accurate model, or do you buy volatility reverting to the mean and therefore leverage Volatility Clustering and change your model to leverage ARCH or GARCH?
Thank you, Ron, for this very helpful answer. Lots to think about. Thanks to the others, too, for comments and the additional web site. Joe
This is a great discussion. There's lots of info to chew on. But let me jump in to offer what I know. I have some experience calculating implied volatility in excel using the black scholes. I realized dividend and risk free rate play a big role, ie a slight difference in the input will create significant discrepancies. This might be the reason why we see so much Put Call IV deviation. Let's look at some examples : Firstly - TOS Put Call IV discrepancy is quite large - 8.99% vs 10.29% ATM strike - below. I think that's because TOS assumes zero dividend for SPX and I've no idea how much is the rfr they use. In reality, stocks in SPX do pay dividend. Hence, the actual Put options prices will be higher and Call lower than what TOS is expecting and that is reflected in IVs. However, If you change the TOS modeling to Vol Smile, yes, you'll get the same IV for Put and Call, but that's merely using the average IV for both. Let's look at OV : 11.6% vs 11.1%, much closer. But let's look at their dividend and risk free rate assumptions. OV does let you know what they are and let you change them. That's what I like ! This is their default settings : Now, if I change the interest rate from 0.29% to 0.80%, I got something really close. Next - I set dividend to zero to mimic what what TOS does. No surprise - I get a huge discrepancy like TOS : So... in summary, my take is this : 1. For a liquid underlying like SPX, RUT, Put Call parity has to hold. Put Call IVs might not be exactly the same, but they should be quite close. 2. The reason there is a discrepancy has to do with what dividend and risk free rate the software use - ie, the assumed inputs are different from market. 3. IV calculation should not depend on the modeling that the software uses. IV is a straight forward calculation from option mid price by using the black scholes formula or a variation of it. The proprietary IV modeling and regression curve fitting done by the software is applied AFTER IV has been calculated. That means projected IVs, CEV, skew tweaking etc.. are all done post IV and done in order to calculate greeks as well as to draw the T+n lines. 4. Having said the above, the list of conditions that Paul Demers posted above still stand. In those cases, Put Call parity can still be broken. I have experience trading stocks that cannot be shorted, the Put IV can be significantly higher than Call IV. Let me know what you guys think. It's a great discussion topic.
Great explanation Kevin. That is what I have seen in my spreadsheet when I calculate the IV and Greeks and zero out the dividends.
Kevin, I had a discussion a while back with TOS support about their RFR. I don't recall the details of the discussion, but I concluded that the best approximation was to look at what the TOS Analyze tab defaults to when you open it up. In this screenshot, it is 0.50%. This may be nothing more than mimicking the Fed Funds target rate, but the fact that it is adjustable and has a default is interesting. I also want to recall that this moved from 0.25 to 0.50 at the last rate hike, but it may be my faulty memory. I'll try to watch again if the Fed hikes in September and see if it happens. Joe
Thanx for point that out. But that setting seems to only affect simulated trades but not the option chain above.
For the risk free rate I have been using the three month treasury yield found here https://www.treasury.gov/resource-c...interest-rates/Pages/TextView.aspx?data=yield
This is fascinating stuff. Kevin, you mention Dividends with SPX which seems to have a discrepancy. If you use line graph in TOS Charts for a year or more and graph (SPX/10 - SPY), it seems to fairly clearly show SPX price does NOT track the Dividend (the computed price difference is the Dividend). SPY reflects the Dividend, as it must, but the SPX price does not. I may be missing something, so please point out my error if so. I am trying to get a handle on the IV of PUTs and CALLs as well, and seems to be like holding a Greased Pig on reconciling some differences. I am not yet able to explain the discrepancies with option price & individual IV with CALL/PUT parity. (This seems to be my greased pig for now) I find that if I use the SPX spot price and assume no dividends, then the PUT IV surface (from using Mid point) and solving using B&S with the proper interest for each expiry, the surface seems ideal. Using a Forward price (via CBOE VIX white-paper Forward price method) for SPX also seems to produce a "reasonable looking" PUT IV surface. However, the CALL IV surface seems to have inflections I do not understand (I observe the same inflections from TOS IV)
For the risk free rate (for B&S interest input), I have been using Quandl's "USTREASURY/BILLRATES" daily downloads for 4 wk, 13 wk, 26 wk, and 52 week, and selecting the appropriate fit based on the DTE of each option. -- It is identical data. Sorry for the duplication.
It is my understanding that the dividends, splits and mergers are adjusted into the SPX pricing on a daily basis as explained to me by Jim Riggio and would use continuous dividend vs discreet dividend.
Gary, I plotted the SPX/10 - SPY graph but I don't know how to interpret it to conclude that SPX does not include dividend. But I googled it and found this article http://www.investopedia.com/ask/answers/040915/does-sp-500-index-include-dividends.asp Seem to suggest it does.