American Option Dividends and Implied Volatility Estimates
Summary
The document discusses why an implied volatility computed with a European Black-Scholes model may differ from a quoted estimate for Microsoft options. The response points out that these options are American style, so they can be exercised before expiration, and that a dividend expected before expiration can make early exercise relevant, particularly for an in-the-money call. It recommends an American-option valuation approach, such as a PDE grid, rather than treating the observed price as a European option price.
The answer applies this reasoning to the stated example: a dividend goes ex shortly before expiration, which may make exercise just before that date likely and shorten the economically relevant option life. It suggests trying a European calculation with a shorter effective time to expiry as an approximation, while noting that expected exercise timing may be slightly later. This is a case-specific explanation, not a general recipe for estimating early exercise or a confirmation of the data source’s exact implied-volatility methodology. Funding and borrow assumptions can also affect comparisons.
Key ideas
- American options can be exercised before expiration, unlike European options.
- A dividend before expiration can affect the value and exercise decision for an in-the-money call.
- A European Black-Scholes calculation may not match the price of an American option.
- A PDE grid can be used to solve for implied volatility under an American option model.
- Using a shorter effective time to expiry is suggested as an approximation for the example, not a universal method.
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# Formula behind pandas.Options() implied volatility # Formula behind pandas.Options() implied volatility I noted that implied volatility (IV field) from pandas.Options class is very different (especially, for out of money options) than what I compute with Black-Scholes model. (risk free rate is pulled from FRED and matches the time to expiry on the option). Can anyone describe or provide references on how `pandas.Options()` computes its IV? An example. as of 11/13/15: MSFT's close is 52.84, call's close 5.80, expiry 12/04/2015 (0.0575 year), K=48.5, r=0.0001 (rate). pandas IV = 0.3569, my BS-implied IV=0.6712. Difference is 0.3143 (mine is greater). Another example. Without getting into code (unless someone asks for it), here is a visual for the context background. This is for educational purpose, not live trading. - Left-most image is my BS-implied IV. - Center image is IV from `pandas.Options()` - Right-most image is the difference between the two. My calculations match pandas, but only for in the money and at the money, not out of money, where my IV values are very high (while pandas are nearly zero). Below are These are computed for MSFT call options using 10/28/15 Yahoo data. Please let me know, if further clarification is needed. Thanks in advance. ## Answer by FinanceGuyThatCantCode (score 1) https://quant.stackexchange.com/a/33131 I don't see such a package in pandas, but MSFT options are American, so you need a PDE grid to solve for the IV. Black Scholes is for European options. MSFT has dividends so American Price > European Price. If it did not have dividends, then it would be safe to say that MSFT is very easy to borrow, so the European should be very close to the American price barring any weird funding irregularities (I once saw AAPL imply a negative dividend before they had dividends mostly due to strange stuff with funding). In your case MSFT did have a 0.36 dividend that went ex on Nov 17, 2015 - that must factor into the price - especially since your option is fairly deep ITM. The likelihood of early expiry is very high and would occur on Nov 16, 2015 - so almost as if this is a 3 day option. Try to back out the European implied vol as if this were a three day option - should get you closer. Really you want the expected time to exercise which should be slightly longer than 3 days.
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