Handling Missing Deltas in American Option Data
Summary
This note discusses missing delta values in a dataset of American-style calls and puts and distinguishes between market analysis and scenario repricing. For market studies, it recommends excluding observations with missing Greeks when the missingness may stem from stale quotes, especially for thinly traded, far out-of-the-money options. A quote can become inconsistent with the current underlying price after the underlying moves, preventing a valid implied-volatility calculation and therefore a delta calculation. Checking the quote’s timestamp and the underlying price at that time can help diagnose this issue.
For repricing or risk-management work, the note suggests estimating an implied-volatility surface from usable observations, extrapolating volatility to the affected contracts, repricing them at the current underlying level, and recalculating Greeks. It does not provide a specific interpolation method, uncertainty estimate, or reliable bounds for missing deltas. Any estimates therefore depend on the volatility-surface model and the quality and freshness of the input quotes.
Key ideas
- Missing option Greeks may signal stale or inconsistent option quotes rather than a simple data gap.
- For market analysis, dropping suspect observations can be more defensible than imputing deltas.
- Quote timestamps and the underlying price at the quote time can help identify stale data.
- For scenario repricing, an implied-volatility surface can be extrapolated and used to recalculate delta.
- The note gives no prescribed surface-fitting method or bounds for estimation uncertainty.
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# Estimate American-style option delta from similar options
# Estimate American-style option delta from similar options
I have a data set which looks something like this, referring to American-style put and call options:
```
> xyz
date undly EXPR_DT STRK_PRC PC delta shares_outstanding option_price stock_price
1: 2005-05-02 xyz 2005-05-21 22.5 C 0.236023 491164 0.250 20.97
2: 2005-05-02 xyz 2005-05-21 25.0 C 0.033663 491164 0.025 20.97
3: 2005-05-02 xyz 2005-11-19 20.0 C 0.650630 491164 2.850 20.97
4: 2005-05-02 xyz 2005-11-19 22.5 C 0.464808 491164 1.575 20.97
5: 2005-05-02 xyz 2005-05-21 17.5 P -0.096380 491164 0.150 20.97
6: 2005-05-02 xyz 2005-05-21 20.0 P -0.315730 491164 0.525 20.97
7: 2005-05-02 xyz 2005-05-21 22.5 P -0.780360 491164 1.725 20.97
8: 2005-05-02 xyz 2005-05-21 25.0 P NA 491164 4.000 20.97
9: 2005-05-02 xyz 2005-06-18 20.0 P -0.333370 491164 0.700 20.97
10: 2005-05-02 xyz 2005-08-20 20.0 P -0.350630 491164 1.050 20.97
11: 2005-05-02 xyz 2005-11-19 17.5 P -0.199830 491164 0.750 20.97
12: 2005-05-02 xyz 2005-11-19 20.0 P -0.357960 491164 1.550 20.97
13: 2005-05-02 xyz 2005-11-19 22.5 P -0.551720 491164 2.750 20.97
```
Unfortunately, some deltas are missing, but I need them for my calculations. Is there a convenient and reliable way to estimate the missing deltas, or at least upper/lower bounds, having all the other deltas?
I've stumbled over this book by Pierino Ursone, but it only provides methods for European-style options.
https://www.amazon.de/Calculate-Options-Prices-Their-Greeks/dp/1119011620?SubscriptionId=0H7E2ABGRZR51KQBN202&tag=universitat09-21&linkCode=xm2&camp=2025&creative=165953&creativeASIN=1119011620
## Answer by Aksakal almost surely binary (score 2)
https://quant.stackexchange.com/a/33991
I'll summarize my comments into an answer.
What you do with missing deltas depends on the purpose of the analysis. If the purpose is to study the market then I'm afraid the best is to drop these observations. In my experience the most likely reason for some deltas (greeks) to be missing in the market data feed is the stale price data that occurs with far OTM options which are thinly traded. In this case, the data providers may provide you with the price that no longer is relevant to the current underlying price. The underlying may move enough to make the quoted price impossible, i.e. you can't calculate the implied volatility, there's no solution for IV. Hence, you can't calculate the greeks either. This can be detected by pulling the trade date/time that corresponds to the price quote, and see if the last trade was done long ago and look at what was the underlying price at that date.
If the purpose of your analysis is something else, maybe re-pricing the option price under different scenarios, e.g. for risk management, then something can or should be done with deltas. For instance, you could build the IV surface from the existing data, then extrapolate the IV to the options with missing greeks, and re-price them using the current underlying price, and subsequently calculate the greeks.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.