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I'm trying to understand how to calculate the price and Greeks of XJO options.

XJO options are European, the underlying is an index and they don't pay a dividend. However the underlying drops when dividends in its constituents are paid out.

Using the Black Scholes Merton formula with and extension for options, see formulas here and on online calculator here, I get the correct price, but wrong Delta when I include the market dividend yield. If I set the dividend yield to zero I get the correct Delta but wrong price.

I guess the price is being discounted for the dividend, is this correct? Can anyone confirm I'm correct or show me a link which explains this hybrid calculation?

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Here is an answer from the ASX for anyone interested:

You might want to consider using the Black 76 model. https://en.wikipedia.org/wiki/Black_model

XJO options are over the XJO index however the market prices them using the SPI future (Futures contract over the S&P/ASX 200 index) as the underlying.

You can use Black Scholes but will need to create the forward value in the model using dividends and rates.

The important point to note using dividend yield is that it assumes a linear progression which is incorrect.

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