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What is the difference in exposures between delta hedged options, ATM straddles and delta hedged straddles. They all seem to provide the same thing, which is exposure to volatility.

What are the differences? When would you use each?

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The best of these for pure vol exposure is the delta hedged straddle: it is delta neutral while requiring very few delta-hedging transactions, because the delta of the call is positive while the delta of the put is negative so they partly offset each other, and the overall delta changes only slowly. The ATM straddle does not always stay ATM and therefore acquires some delta, even if it starts out delta-neutral. The individual option requires constant delta hedging and therefore is more costly to implement. Only delta hedge straddle achieves both zero delta and low hedging costs.

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