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Basic delta hedging question

Discussion in 'Options' started by matrisking, Oct 27, 2008.

1. matrisking

Hi,

Quick question about hedging delta in a situation where options with varying expirations are being used to create a delta-neutral position:

If you short some at-the-money calls (lets say 100 contracts) that expire in 9 months, and want to buy calls expiring in 6 months with the same strike price (at-the-money) to hedge delta, then how many calls do you buy? Is it 100? Or is it more than that, because you need to take into consideration the fact that, at the money, shorter time until expiration results in a smaller delta... meaning more 6 month calls would need to be bought to bring the net delta position to 0?

I have a pretty good grasp of what it means to be delta neutral, but in a situation like this I'm really not sure.

Thanks!

2. dagnyt

Delta neutral means you own as many deltas as you are short.

Take the delta of the call you are selling and multiply by 100 (# of contracts).

Divide that number by the delta of the option you are buying to determine the quantity you need to become 'delta neutral.'

I assume you know how to use an option calculator.

Mark

3. MTE

Based on your question, you don't seem to have a good grasp of what it means to be delta neutral!

Unless you are using futures options, you can add up the deltas across expirations. So just add up all the deltas on the short side and then go long the same amount of deltas.

If you ARE using futures options then you cannot just add up deltas across expirations when the underlying futures contract is not the same. I mean, you can still do it, but you are assuming additional risk that the two underlying futures contracts won't move identically.

The delta of the 6 month options will depend on whether they are itm, otm or atm. As a general rule, if itm then their delta will be higher (relative to the 9 month expiry options) and thus you will need fewer contracts to get neutral. If they're otm then delta will be lower and you'll need more contracts. If atm then delta will be very similar.
The easy way is to just look up the delta of the option you want to buy and divide it into the TOTAL short position delta to get the number of options you need to buy to neutralise.
db

5. curtains

Err... you assume that same strike for 6 months options will be ATM? Interest, divs?

Anyway - delta of contact * contract = Delta of position. Then just hedge that many deltas with whatever else you want to trade.
This advice does not take into account second order derivatives.

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