Why SPX and SPY Implied Volatility Curves Differ
Summary
The document asks whether SPX and SPY options should have matching implied volatility at the same expiration and log-moneyness, given that SPY tracks the S&P 500. It explains that the curves are generally correlated and often close, but need not match. ETF tracking error and differences in portfolio construction can contribute to short-horizon discrepancies, even when the ETF tracks its index closely over longer periods.
A further source is the options’ exercise style: SPX options are European, while SPY options are American. Early exercise can affect their values and implied volatilities, with the answer identifying deep out-of-the-money options as a place where the difference may become more pronounced. The discussion offers qualitative explanations rather than a conversion formula or empirical analysis. It therefore cautions against assuming that a tighter SPY market gives an exact SPX volatility curve simply by matching expiration and log-moneyness; settlement timing and contract features also matter.
Key ideas
- SPX and SPY implied volatility curves are usually related but are not necessarily identical.
- ETF tracking error and portfolio construction can contribute to differences between the curves.
- SPX options are European style, while SPY options are American style.
- Early exercise effects can make implied volatility differences more pronounced for some options, including deep out-of-the-money contracts.
- Matching log-moneyness alone does not guarantee equivalent implied volatilities.
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Full text
# What's the connection between implied vol curve of SPX and SPY?
# What's the connection between implied vol curve of SPX and SPY?
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.
## Answer by glyphard (score 4)
https://quant.stackexchange.com/a/2965
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.
## Answer by Rodrigo (score 1)
https://quant.stackexchange.com/a/74159
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.