# 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

• Are there other greeks for this option? The reason I'm asking is because when the greeks are missing in the feed for us it's usually when the option can't be priced given the inputs, i.e. thinly traded options where the prices are either stale prices or quotes. – Aksakal Apr 30 '17 at 14:13
• No, there are no other greeks. What are possible reasons for missing deltas and can elaborate on your explanation ? – HJ Simpson Apr 30 '17 at 21:37
• In our feed if the option is thinly traded, you get the stale prices for options, i.e. prices from trades days ago. When you have far OTM options, the underlying often moves enough to make the option price impossible, you can't calculate IV. Without IV you can't calculate greeks – Aksakal Apr 30 '17 at 22:54
• Thank you for your help. I think you nailed the issue. As I recognized that many deltas are missing, I did an analysis for all observations with missing deltas. I tried to relate moneyness to the number of times the delta is missing. If your plot it, you see, that more often than not, moneyness is way above 1. In the end, I think it's fair to remove observations without deltas and continue with my analysis ! – HJ Simpson May 1 '17 at 8:25

## 1 Answer

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.

• yes, the first part of my analysis is studying the market. For this purpose I will drop the observations (as you mentioned). – HJ Simpson May 1 '17 at 21:16