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I have been thinking about this one for last couple of days. With options on share we hedge on cash and the underlying equity as per Black-Scholes formulation.

But I am confused on Index options. There is a basket of equities (often large number) to hedge. I don't find the cash and equities hedging technique to be convincing. The reasons:

1) Large number of equities
2) Transaction costs

Anyone here who has some experience or can direct me to any relevant literature. I am curious how market makers deal with index options.

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Most index options are options on futures, so to delta hedge a single option position, you trade the corresponding future.

For example, say you sell 10 delta 50 calls on the CME Emini S&P. To delta hedge them, you'd buy 5 CME Emini S&P Futures with the same expiry date as the options.

As you say, you could hedge with the basket instead, but for practical purposes the futures are usually easier. If the futures go out of line with the basket you can always trade an index arb strategy.

Now market makers normally dont just trade one option - they build a portfolio of options by buying and selling both call and put options at different strikes. Once you start combining option positions for the same expiry, you can sum the delta for your portfolio and just hedge the remaining delta.

Options have other risk sensitivities though, so to a certain degree you also need to hedge gamma, vega, etc. That's normally done by adjusting your prices so that if for example you are long vega (you've bought a lot of options), you adjust your prices down for both calls & puts to make it more likely that you'll sell options (and hence reduce your overall vega).

It's obviously a bit more complex than that in practice, but you get the general idea.

Btw, you can check out some example index option/future contract specs here:

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I am not sure I fully understand your question.

Options it just derivative contracts (wager) between two parties, there is no ‘real’ assets bought to support the +/- value change the option might have during its duration.

When the exercise date is upon the option, and you are the winner, you are paid according to the WAMC of the index – e.g. 3.4% of your winnings is an Exxon Mobile stock, 1.6% is Bank of America stock and so on…

In short: There is no problems with transaction cost or the number of equities, since the option is just a contract.

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  • $\begingroup$ My question is in market making part of it. How market makers hedge this option? $\endgroup$ – user3001408 Dec 29 '14 at 9:10
  • $\begingroup$ They use a derivative with the opposite risk e.g. a future. If none exist they ether use a synthetic position strategy, or simply add the directional risk the index option opposes, to their dynamic hedging strategy. I think the keywords for your further research is “synthetic position” and “dynamic hedging” in a combination with the synonym of market makers “liquidity providers”. $\endgroup$ – chjortlund Dec 29 '14 at 12:10

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