Understanding the difference in implied volatility surface of SPX PUTs and CALLs

[blueplayer]

Blue,
I'm not sure where you get that from. If I'm wrong, I'd like to know more. SPX closed at 2,049.58 Friday and the September ES contract settled at 2029.25. The difference is 20.33 points. SPX and ES option mirror each other. I think we can agree that any trading in ES will hedge with the future. I also think we can agree that hedging with the basket of 500 stocks is not efficient. What would you hedge an option position in Jul, Aug or September with? That hedge is the input price for the underlying in any model.

Robert I don't know why you fixate so much on the futures. The underlying for SPX options is the SPX index itself and you could hedge with the basket if you need too. I know that for convenience people prefer to hedge with the futures but that doesn't mean the futures are the underlying.

The discrepancies on closing quotes is very simple to understand if you take into account the following two things:

1. SPX closing price is reported at 4:00PM whereas ES mini closing price is reported at 4:15 PM
2. ES usually represents the forward price for SPX, so it will have a discount factor applied to it, that in the current low interest rates regime means it will be lower than SPX most of the time

 

[rmorse]

That is correct conceptually newurldmn, however when you use something like BSM to price the options it takes care of this for you as all the formulas are already in forward price mode. The input to the equations *should* be the current underlying spot price as most of the closed form solutions for BSM already take into account that. No need to do it twice (you will get wrong results).

As for the put call parity of course it needs to be adjusted by forward Strike

C-P = S-D*K

But even with that adjustment you will find that ITM options for SPX consistently violate put call parity. My whole point of the comment is that the quotes for those options are stale most of the time and therefore wrong.

I would not use the word stale for in the money options in SPX, as they do update. I would however say that you can't get meaning from the midpoint.

 

[blueplayer]

I would not use the word stale for in the money options in SPX, as they do update. I would however say that you can't get meaning from the midpoint.

Robert, I use stale because even though they update from time to time, it is very infrequent. So they can get stale for long periods of time. Case in point if you go deep ITM you might find strikes that quote bid and ask from the previous day for hours in a row. Of course the moment you want to trade them they get quoted more accurately.

That is the problem with the end of the day quotes from OPRA, ITM (in particular deep ITM) options might have quotes that were last updated at 3:30PM so you are missing quite sometime of action in the underlying. That is why plotting IV surfaces with that information will give you funky results.

 

[newwurldmn]

That is correct conceptually newurldmn, however when you use something like BSM to price the options it takes care of this for you as all the formulas are already in forward price mode. The input to the equations *should* be the current underlying spot price as most of the closed form solutions for BSM already take into account that. No need to do it twice (you will get wrong results).

As for the put call parity of course it needs to be adjusted by forward Strike

C-P = S-D*K

But even with that adjustment you will find that ITM options for SPX consistently violate put call parity. My whole point of the comment is that the quotes for those options are stale most of the time and therefore wrong.

Spx options are the most liquid and efficiently priced options on the planet. They never violate put call parity.

The black scholes equation has four market parameters: spot, vol, divs, and rates. The last two relate to the forward. Incorrect params will result in a violation of put call parity.

But in any complete market put call parity cannot be violated. In 2008 there were situations where it was violated but the condition of a complete market were violated with the banning of short selling and volatility in financing rates from counterparty to counterparty

 

[blueplayer]

Spx options are the most liquid and efficiently priced options on the planet. They never violate put call parity.

The black scholes equation has four market parameters: spot, vol, divs, and rates. The last two relate to the forward. Incorrect params will result in a violation of put call parity.

But in any complete market put call parity cannot be violated. In 2008 there were situations where it was violated but the condition of a complete market were violated with the banning of short selling and volatility in financing rates from counterparty to counterparty

We agree that put call parity in european options must never be violated newurldmn, however if you look at the OPRA feed (from yahoo or your favorite data provider) you will notice that it "looks" like it is violated for SPX ITM options (very obvious for deep ITM options), of course the moment you want to arb that free money the quotes magically update and PC parity is saved again.

So my point is that the apparent "violation" is due to quotes for ITM options propagating slower than their OTM counterparts (I have seen delays of hours). This same issue is what affects any end of day IV surface computation that uses ITM options (like the original poster discovered).

 

[OddTrader]

I will attempt to explain. Typically, when you look for information on implied volatility surface you find reference to OTM and ATM options only, and this generally includes PUTs and CALLs, which when combined appear fairly simple and intuitive. However, if you instead observe all PUTs as a group separately from all CALLs as another group, the differences have me puzzled. To look at this, I pick some historic date (have looked at a number of dates), then use B&S to iterate on IV until I locate the IV that produced the observed price(since all other information is known, such as DTE, underlying price, interest rate (div=0 for SPX)). This is the method used to extract the IV for each option listed. Then I plot the IV on Z axis with moneyness on x axis and dte on y axis. I expected the plots to have fairly strong shape similarities, but find differences on the CALL IV that I do not understand. Some of these anomalies, may be unimportant, such as the downward curvature of deeper ITM CALL strikes (contribution to the option price is fairly negligible here, and probably low interest). However, I expected the IV with respect to DTE, to track closely with the IV with respect to DTE of PUT options, but often see a divergence. Also, the moneyness value of minimal IV for PUTs per expiration, seems to be nearly a constant for all DTE, but has a significant shift for CALL's, which I do not understand. There are other less bothersome differences, that may not be worth mentioning yet.
For moneyness I use the following formulas, which seem to be adequate:
CALL moneyness = log(price * exp(rt)/strike)/(t^.5)
PUT moneyness = log(strike * exp(rt)/strike)/(t^.5)
where r= interest rate
t= time to expiration
price = price of underlying
strike = strike price of the option
For reference I am attaching a graph of PUT IV, and then a graph of CALL IV for SPX on the same date.
View attachment 163065
View attachment 163066


View attachment 163063
View attachment 163064
It may be difficult to observe the IV with respect to DTE difference of the PUTs and CALLs -- The difference is slight, but still significant. I may poke around to find a better way to show the IV vs DTE difference.

Just 2 cents:

1. Have you considered asking CBOE your SPX questions? Afaik, their technical staff should be very happy to investigate and able to answer your questions. Please let us know their feedback in due course!

2. My guess is CBOE/SPX/MMs do not have to use the standard BSM or whatever parity for their options prices. Especially due to supply and demand for some particular strikes!!! Unless your calculation showed / proved uniformity across a whole series of over strikes! But I doubt it very much, since it seems you just picked a few days and a few strikes for why the oddity strikes, without saying any uniformity.

http://www.elitetrader.com/et/index...olatility-surface-oddity.298431/#post-4257585

It could be wrong prints, database errors, software bugs, etc. I saw several days ago a SPX price -5 for ask while a price like +10 for bid with the same strike call option. Lasting for perhaps overnight!

We can see often the open interest for individual strikes of SPX varies very greatly.

Maybe one MM just tried to attract you to buy certain options that they wanted to sell! If I am a MM, I could do this kind of tactics. And why not, because open interest, inventory supply, and the wide ask/bid spread?

3. What's your main purpose of your investigation about oddity, and using volatility surface? Any potential edge at all?

 

[stepandfetchit]

Thanks to all for your comments and feedback. There is a lot of information posted that is in conflict to what I currently believe to be fact (Hopefully I am wrong -- resulting in resolution, once I resolve). Three ideas that could potentially relate to the specific anomalies I am investigating (trying to understand).

1) Do SPX option prices account for the Dividends in SPY? -- I think NO, but some have indicated otherwise. (the Diva comment by newwurldmn ) --
2) Bob, indicates SPX options are NOT based on SPX as being the underlying, but something else (futures?). This is extremely important, and critical to my understanding. My lack of knowledge of Futures is making this non trivial to figure out.
3) The PUT CALL Parity relationship should provide a "sanity check" on the relationship of the PUT and CALL prices (and indirectly the IV of each), which I have not yet fully investigated.

All 3 of the above need to be resolved.

blueray: Thnx for your input. I understand your comments about liquidity, and pricing of deep ITM options. The issues I am currently pursuing are NOT specific to ITM options, but can be observed by examining the OTM and ATM as well. (my red-circled plot regions attempted to focus on the areas of interest) -- I will pursue the put-call parity relationship to hopefully tie up some loose ends, and provide a sanity check) Question: Should D, in the Call/Put parity equation include any Dividends in addition to interest?

OddTrader: My main purpose is to understand the (SPX option) IV behavior and relationship to known factors. My assumption is: If what I observe seems to be a "potential edge", then I must have an error or have bad data. There should be NO well defined trading edges found when observing static data. Once this is done, I should have a basic understanding, from which to build upon.

rmorse: My little spreadsheet section I posted was in error! I am continuing to try to resolve what underlying the SPX options are based on. My observations relating to what is the Underlying used for SPX options (small sample size so far of 17 samples): Using Put Call Parity equation, and solving for Underlying, { C + STRIKE*D - P} I find the following: Weekly options expiring within 5 minutes of closing bell resolve to within $1 of the price of SPX for Near the money strikes. There is a bit more play (but not much) with the monthlies. However, as the DTE increases, the PUT CALL Parity relationship diverges, which seems to correlate to one of the anomalies I mention in my opening comments. -- So, am now thinking there is a PUT CALL Parity deviation with time to expiration that is not understood. (Note: For the option and underlying prices above, I am using LAST traded prices for all) --- for "D" above, I am using "exp(-0.5%*DTE/365)" <- equation stolen from blueray

 

[rmorse]

1) Do SPX option prices account for the Dividends in SPY? -- I think NO, but some have indicated otherwise. (the Diva comment by newwurldmn ) --

The S&P Index as represented by the 500/501 stocks that are the index. You can buy the basket yourself, or buy it in a few ways. SPX is 100X the cash index, SPY is 10X the index and ES is 50X the index. Since they can all be hedged with any of the other products, including a basket of stocks, you have to include interest and dividends in all of them. The only one you can't directly buy is the cash index.

 

[blueplayer]

Thanks to all for your comments and feedback. There is a lot of information posted that is in conflict to what I currently believe to be fact (Hopefully I am wrong -- resulting in resolution, once I resolve). Three ideas that could potentially relate to the specific anomalies I am investigating (trying to understand).

1) Do SPX option prices account for the Dividends in SPY? -- I think NO, but some have indicated otherwise. (the Diva comment by newwurldmn ) --
2) Bob, indicates SPX options are NOT based on SPX as being the underlying, but something else (futures?). This is extremely important, and critical to my understanding. My lack of knowledge of Futures is making this non trivial to figure out.
3) The PUT CALL Parity relationship should provide a "sanity check" on the relationship of the PUT and CALL prices (and indirectly the IV of each), which I have not yet fully investigated.

All 3 of the above need to be resolved.

blueray: Thnx for your input. I understand your comments about liquidity, and pricing of deep ITM options. The issues I am currently pursuing are NOT specific to ITM options, but can be observed by examining the OTM and ATM as well. (my red-circled plot regions attempted to focus on the areas of interest) -- I will pursue the put-call parity relationship to hopefully tie up some loose ends, and provide a sanity check)

OddTrader: My main purpose is to understand the (SPX option) IV behavior and relationship to known factors. My assumption is: If what I observe seems to be a "potential edge", then I must have an error or have bad data. There should be NO well defined trading edges found when observing static data. Once this is done, I should have a basic understanding, from which to build upon.

rmorse: My little spreadsheet section I posted was in error! I am continuing to try to resolve what underlying the SPX options are based on. My observations relating to what is the Underlying used for SPX options (small sample size so far of 17 samples): Using Put Call Parity equation, and solving for Underlying, { C + STRIKE*D - P} I find the following: Weekly options expiring within 5 minutes of closing bell resolve to within $1 of the price of SPX for Near the money strikes. There is a bit more play (but not much) with the monthlies. However, as the DTE increases, the PUT CALL Parity relationship diverges, which seems to correlate to one of the anomalies I mention in my opening comments. -- So, am now thinking there is a PUT CALL Parity deviation with time to expiration that is not understood. (Note: For the option and underlying prices above, I am using LAST traded prices for all) --- for "D" above, I am using "exp(-0.5%*DTE/365)"

Just a comment about dividends. Because SPX options use the basket of SP500 stocks as its reference underlying, then it would be possible to do dividend arbitrage if the SPX options didn't incorporate it in their pricing. So yes, when pricing SPX options please include continuous paying dividends otherwise you can be arbed away.

 

[rmorse]

rmorse: My little spreadsheet section I posted was in error! I am continuing to try to resolve what underlying the SPX options are based on. My observations relating to what is the Underlying used for SPX options (small sample size so far of 17 samples): Using Put Call Parity equation, and solving for Underlying, { C + STRIKE*D - P} I find the following: Weekly options expiring within 5 minutes of closing bell resolve to within $1 of the price of SPX for Near the money strikes. There is a bit more play (but not much) with the monthlies. However, as the DTE increases, the PUT CALL Parity relationship diverges, which seems to correlate to one of the anomalies I mention in my opening comments. -- So, am now thinking there is a PUT CALL Parity deviation with time to expiration that is not understood. (Note: For the option and underlying prices above, I am using LAST traded prices for all) --- for "D" above, I am using "exp(-0.5%*DTE/365)"

Yes, the SPX, as it approached expiration will match the SPX cash, as that is the settlement value and there is no longer any cost of carry or dividends. You don't really have to understand futures. You only need to calculate a daily interest/dividend cost to see how how much to adjust the cash index to match the correct underlying value. I don't use Bloomberg, but my guess is that it is there somewhere. The only reason you will need to make these adjustments is if you have your own auto-quoter that runs off your vol numbers and skew and you want to be independent from any platform or market values.