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If two indices are highly cointegrated, does it allow for some set of statistical arbitrage strategies for european options for which those indices are single underlyings ? Does answer change if assets are correlated rather then cointegrated ? Is this type of arbitrage a market practice ? Does it have its name ? It's not volatility surface arbitrage

I don't see possibility of using positive indices correlation for statictical arbitrage on implied volatility : 1. positive price shock of A indice in n-th day 2. large random price change od B indice in day n+1 3. Opening long straddle or Long Strangle between n and n+1 day with B-based options rather won't generate positive profit for n+1 day

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