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When I trade an index option (SPX), there is no actual trading going on in the underlying (as opposed to SPY).

But some option strategies (like covered call) by definition require a position in the underlying.

So how does one sell a covered call on SPX ?

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You can buy some S&P futures or go one step further and buy the underlying stocks that compose the index (which is what future/cash arbitrageurs do). But unless you are interested in a very specific arbitrage, buying SPY and selling calls on SPY would by and large achieve the same outcome.

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