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I'm trying to apply Black & Scholes formula for a real example to price a vanilla equity option but I'm strugling a little bit whith the dividend yield.

Let's assume I have a stock that trades at 50 dollar and the announced dividend in 100 days is 5 dollar, is the dividend yield = (100 / 252 days ) x 5 / 50 = 3.97% ? Am I right ?

The day after would it be (Assuming the stock price didn't change) : (99 / 252 days ) x 5 / 50 = 3.93% ?

Last question please, if the next divident is not announced yet, where do we get the dividend yield from ?

I don't have any problem with applying Black-Scholes formula but I'm just trying to apply it for a real example.

Cheers in advance.

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In real life, you imply the unknown dividend yields from the forwards and the discount curve.

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For European options you can utilise put-call parity and reverse out the implied dividend yield.

I.e.

F(T,K) = C(T,K) - P(T,K)

and obviously

F(T) = S(t)*e^[(r-d)*(T-t)]

Interestingly, you get mostly OK results for American ATM options also. Cf. Avellaneda's comments on this in one of his lecture's, page 18,

http://math.nyu.edu/faculty/avellane/DSLecture3.pdf

The one gotcha is when there is heavy shorting of the stock. In this case what you are actually measuring becomes clear - convenience yield - as now the stock holders earn a nice stock lending fee as well the dividend yield.

I created a Python script which grabs the data does this calculation, idivs.org. There's also an API available which you can use in spreadsheets etc.

I tested American ETF implied dividend yields against European Index dividend yields and they are pretty close.

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If it is a real example, then it may be unnecessary to consider the dividend explicitly. After all, the Gordon formula states that the stock price is equal to the discounted future cash flow of dividends.

For instance, if I have a call at strike K and the future dividend is announced when the market didn't expect it, then most likely the spot price will go up and my call will appreciate accordingly. That is, I would be making a mistake if I add the discounted dividend on top of that because the dividend has already been incorporated into the call price.

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Dividend estimation and forecast is not an easy problem. This paper describes and compares few approaches.

If the company pays dividend according to a certain scheme (quarterly, annually, etc.), it's easy to forecast a future dividend yield, using last known paid amount and the underlying price.

In some cases (like European and Asian companies), the forecasting becomes more tricky, as dividends pay outs are unequal (interim and final).

The correct answer here depends on what kind of underlying instruments you are dealing with.

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You could use the (time-scaled) trailing twelve month (TTM) dividend yield as it is a much easier number to get a hold of and can be a reasonable approximation. Also, while the upcoming dividends are not always published recent dividends should be easy to obtain and you can calculate the TTM yield yourself if you need to.

experquisite and user3264325 both have answers that are forward-looking rather than backward-looking like TTM, however, those values can be much harder to obtain and process.

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