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I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets since the underlying of SPX is SP500, while the underlying of SPY is a ETF which tracks sp500 index

A very simple idea would be : with the same expiration date (while one is AM and the other one is PM), for the strike at the same log moneyness, i.e. $\log(\frac{K}{F})$, I assume the vol should be the same.

Anyone has any suggestions?

Motivation: SPY is a much tighter market, if I know the vol curve of SPY, and I can somehow convert the vol of SPY to the vol of SPX, then I would claim I get a more accurate vol curve for SPX.

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    $\begingroup$ You seriously could have taken a bit more time writing the question with decent formatting and grammar. $\endgroup$
    – SRKX
    Feb 10, 2012 at 15:43
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    $\begingroup$ They will be about the same but beware of the differing borrow rates. $\endgroup$
    – Brian B
    Feb 10, 2012 at 15:59
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    $\begingroup$ being new here. I'll rewrite the question. Thanks for your advice. $\endgroup$
    – DeepRed
    Feb 10, 2012 at 16:03
  • $\begingroup$ Hi Brian, thanks for your comment. You mean I should use different interest rates here? What I am doing now is: I get the interest rate from Eurodollar future, and use it for both market. But I use dividend yield for SPX, while make assumptions on the discrete cash dividend for SPY. $\endgroup$
    – DeepRed
    Feb 10, 2012 at 16:11
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    $\begingroup$ The differences will be driven by technical details in the differences between the two markets, such as interest rates and dividend yields. Not a very interesting quant question, more of an annoying practical trading problem, kinda like the headache that is adjusting for day count conventions in fixed income. $\endgroup$ Feb 10, 2012 at 16:41

2 Answers 2

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They'll be correlated, and generally close to one another, but rarely identical. In fact differences of 2 points in implied vol are common.

The reason for the differences comes down to the portfolio construction and tracking error of the SPY ETF. While generally quite low over a long period of time, the tracking error on a 1-day or less basis can be noticeable. Even though SPY is designed to track SPX, you can look at the SPY prospectus to see that the weights are slightly different. (They don't say it explicitly, but they're most likely not trading all 500 stocks). This is another source of differences in implied vol.

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  • $\begingroup$ Thanks glyphard. I understand there is no exact math solution to this practical problem. As a practitioner, I should be familiar with these markets in detail. Your comment is helpful. Thanks. $\endgroup$
    – DeepRed
    Feb 14, 2012 at 19:46
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The above answers are somewhat correct but do not contemplate the main source of discrepancy between the surfaces which is the exercise type. SPX options are european while SPY options are american. For most strikes and maturities, this does not yield much difference but can create large discrepancies when you goo deep OTM -- where the effect of the "americanity" is more pronounced, and it becomes more likely for options to have their early exercise feature enforced.

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  • $\begingroup$ Usually you de-americanize before building a vol surface but it will naturally be different. It makes little sense to proxy SPY with SPX when SPY itself is so liquid, unless you don't have the capability to build a surface from american options, in which case simply plugging in the SPX vol should give a reasonable estimate. On the other hand, SPY options are directly price quoted so you have plenty of prices and data available. $\endgroup$
    – AKdemy
    Dec 22, 2022 at 6:14
  • $\begingroup$ When you "de-americanize" the options, do you use the de-americanized OTM or ITM options? $\endgroup$
    – Rodrigo
    Dec 22, 2022 at 13:30

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