Why SPX and E-Mini Option Theta Quotes Can Differ
Summary
The question compares broker-displayed theta for SPX index options and E-mini futures options with similar strikes and nearby expiries. Their quoted option prices are close, yet the reported theta differs, prompting a question about whether European versus American exercise explains the discrepancy.
The answer suggests that the difference may instead come from the pricing conventions used to calculate theta. Under a Black futures-option calculation, the futures price is held constant; under a Black-Scholes calculation for an index option, spot is held constant. With spot fixed, the forward price's movement toward spot contributes an additional component to reported theta, even though it is not simply time-value decay. The explanation is presented as a likely source of the discrepancy, not a verified account of the broker's settings. Thus theta values from different instruments or platforms may not be directly comparable without checking the model and underlying held constant.
Key ideas
- Similar option prices can have different displayed theta values when the calculations use different pricing conventions.
- A futures-option theta calculation may hold the futures price constant, while an index-option calculation may hold spot constant.
- Holding spot constant can include a forward-price movement component in reported theta.
- Confirm the model and theta convention before interpreting or comparing broker displays.
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Full text
# theta for SPX options vs. E-mini future options # theta for SPX options vs. E-mini future options Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: - calls: bid/ask 234.10/236.30, theta -0.362 - puts: bid/ask 146.70/148.40, theta -0.225 Then for E-mini future options with the same strike and expiring just one day later (2020-09-18, for both the option and the underlying future) the following: - calls: bid/ask 234.25/236.75, theta -0.279 - puts: bid/ask 146.75/148.50, theta -0.284 Why is theta -0.362 for SPX calls, but -0.279 for E-mini calls when they are practically the same intsrument? Is this to do with the fact the former are Europen-style and the latter American-style? (If so, why would American options decay faster? How does this tie in with the fact that the prices are almost the same and presumably still will be tomorrow?) ## Answer by dm63 (score 1) https://quant.stackexchange.com/a/49553 The theta for puts and calls at the same strike should be the same, so it seems the SPX theta is somehow wrong. Edit: thanks @maxim, I see now what the issue is. I think the difference is coming from the fact that the options on the e-mini futures are using the Black formula where the futures price is held constant when calculating the theta. However the options on SPX are using the classic Black Scholes formula which holds the spot index price constant. This latter model then gives a second component of theta corresponding to the move in the forward price of the stock towards spot, which has nothing to do with the decay of time value. Indeed a forward contract on SPX would have theta under that definition , even though it is not even an option. The two definitions of theta are inconsistent with each other conceptually but it wouldn’t surprise me if that is the standard treatment on a broker website.
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