Pricing ASX 200 Index Options with Futures and Discrete Dividends

Summary

The document addresses pricing European options on the ASX 200 index when dividends paid by constituent companies affect the index level. It reports that using a continuous dividend yield in Black–Scholes–Merton produced a price consistent with the observed market but a delta that did not match, while setting the yield to zero reversed that result. The question is whether this apparent hybrid treatment is appropriate.

The answer says the market prices these options using the SPI futures contract as the underlying and suggests Black 76 as a suitable model. Alternatively, Black–Scholes can be used by constructing the forward value from rates and dividends. A continuous dividend yield assumes dividends accrue linearly, which may be inaccurate when actual constituent payments occur at specific times. The discussion gives modeling guidance but no derivation, calibration details, or quantitative comparison; the appropriate setup depends on the market convention and dividend inputs.

Key ideas

• ASX 200 index options are described as being priced with the SPI futures contract as the underlying.
• Black 76 is suggested for pricing options using the futures price.
• Black–Scholes can also be applied by constructing a forward that accounts for rates and dividends.
• A continuous dividend yield assumes a linear progression that may not match discrete constituent dividend payments.
• The document gives no detailed derivation or comparison of model performance.

Tags

# Dividend yield on ASX 200 (XJO) index options


# Dividend yield on ASX 200 (XJO) index options












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?

## Answer by Zeus (score 1, accepted)

https://quant.stackexchange.com/a/39817

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.