Index equivalents

[grantx]

Comparing options on indexes (indices?) with strong correlation, eg DOW/S&P, DAX/STOXX but different strikes, how is equivalence determined?

Is it by deltas, ie .25 call delta on DAX is equivalent to .25 call delta on STOXX?

Further, how is the correct ratio determined (dividing deltas)?

I know this should be in the "Options" section but seems "Futures" provides a better response (some devious people around).

Thank you in anticpation.

Grant.

 

[Profitaker]

Grant

Your Q is probably more suited in the options section. I rarely look in here.

The $Delta method works quite well...

$Delta = Spot x Option Delta x Option Qty

Where the correlation between indices is +1 (unlikely, but hey) the $Delta values should be the same. Correlation +0.5 then one should be half the $Delta value of the other.

Hope that helps.

 

[grantx]

Profitaker,

Thank you for info but I’m a bit confused. Perhaps you could clarify?

Presumably, we shouldn’t compare two indices in point terms. For example, DAX and Stoxx are closely correlated (except today) in relative (percentage), not absolute (point), terms:

If DAX is 6300 and Stoxx is 4000, 100 points DAX = 0.16%; 100 points Stoxx = 2.5%.

Alternatively, 6300/4000 = 1.57, ie 1 DAX = 1.57 Stoxx, or 1 Stoxx = 0.625 DAX. In other words, 1 x 0.50 delta Dax is equivalent to a 1.57 x 0.50 delta Stoxx. That is, for every 1.57 point move on the Dax, Stoxx will move 1 point, or 16:10 DAX:Stoxx ratio .

I’m not sure what $Delta = Spot x Option Delta x Option Qty refers to. For example,

6300 x 0.50 x 1 = 3,150
4000 x 0.50 x 1 = 2000.

Could you expand?

Out of interest, why is the spot used as opposed to the future?

Thanks, once again.

Grant.

 

[Profitaker]

Grant.

I’m not sure what $Delta = Spot x Option Delta x Option Qty refers to. For example,

6300 x 0.50 x 1 = 3,150
4000 x 0.50 x 1 = 2000.

Could you expand?

You were asking about equivalence and ratios between two indices using options as an instrument to trade them, I think ? Using $Delta you adjust your exposure as required. For example, suppose you have two indices highly correlated (6300 & 4000) and you took the view that the vol was too high on one when compared to the other. You’d want to short one index option and buy the other. How many ?

Spot x Delta x Qty = $Delta
6300 x 0.40 x 10 = 25200
4000 x 0.30 x 21 = 25200

In the above example, your exposure to each index is matched, which is what you want. You could change the exposure by a combination of Qty and / or different delta options. Depends what you want to do and why.

Yes, strictly speaking you should use the forward price (spot + carry cost – dividends) rather than spot. But depending how far out in time you go the difference is often negligible.

 

[grantx]

Profitaker,

Thank you for the clarification.

You probably guessed my maths isn't brilliant, and to help me improve by discovering for myself you omitted the determination of the second (4000) quantity.

I worked it out (go to the top of the class):

$delta/(underlying x delta):

25,200 / (4000 x 0.3) = 21

Which gives:

4000 x 0.3 x 21 = 25,200.

Thanks for the excellent info (and self-improvement).

Grant.