# Pair Trading Index Options

Suppose the trade is between Index Options of two Indices X and Y which are quite similar (but not exactly).

So for the equivalent strikes, one can quote option on Index X and cover in Index Y.

But these indices will have basis movements. How can one build a trading model to price options in say Index X based on Options of Index Y. How can one manage the risks.

Assumption (Volatility of Both Indices can be assumed to be same). For Simplicity assume, they have equally spaced Strikes.

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Do you know which uncertainties you're trying to exploit? Short term break down of correlations, net difference in vega, getting "free gamma", etc. Until you know what you're working to achieve, it's pretty difficult to give you specific, helpful information. – Rock Dec 6 '12 at 5:28

Are you trying to trade RV in delta (that is, conditional out-performance of one over the other) or identify RV in volatility (that is, you want to cover a delta-neutral vol position in one index with vol position in another index)? You approach would be very different for these two trades.

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The problem is with Delta management. So if the indices are trading around the same levels, and the options that I have bought on Index X and sold on Index Y, when the (Index X - Index Y) basis of say 10 points, now they move to a basis of 13 points. How do i manage that? That is something which will move the deltas. Does that clarify the scenario? – shoonya Oct 5 '12 at 17:06
So imagine that one index is Russel 3000 and other is Russel 1000. (The Russell 1000 represents approximately 92% of the Russell 3000 Index.) So these will track each other by construction. But this basis will be quite random. How does one handle that? – shoonya Oct 5 '12 at 17:30
Well, as I said, it would depend on the trade that you are actually doing. If you are trading them as a conditional spread, it's terminal beta neutral and will have delta through the life of the trade. In this trade you actually want the basis to move (hopefully in your favour). If you are trading them as a volatility pair, your are going to be managing deltas separaterly for each option and you want to separate what part of the volatility is idiosyncratic and what part of the volatility is driven by beta. Am I answering your question? – Strange Oct 5 '12 at 18:53
I agree to what you are saying. But then if this is the case, i.e. managing them as conditional spread, how can one manage it? Is there any paper that I can refer to? – shoonya Oct 6 '12 at 2:55

It really depends on the source of your signal. Since you're trading options I assume it is either volatility signal, or volatility + basis signal. If you have signal only on basis don't bother with options and just trade underlying.

Now if you are trading vol signal only, you will need to hedge all basis risk - so gamma hedge (dynamic hedging with underlying) each underlying separately, so your PL on each instrument is (hopefully) just vol mispricing.

If you are trading vol + basis, then you can implement them as offsetting trades - e.g. long 1M 25delta call in IWN and short equivalent call in IWO, no hedging (or just initial margin hedging) so this way you get PL from basis and from vol difference.

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