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Suppose I was interested in longing volatility. Suppose I bought a long straddle today which expires in 3 months. Suppose that volatility was very high in those 3 months, however, the stock expires at the money on expiration day. The straddle expires worthless but my PnL was still positive. How did I make money?

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    $\begingroup$ That question is not entirely clear IMO: if you can trade anything along with your open straddle position (e.g. dynamic delta hedge but also any other trading strategy whatsoever) then there is infinite many ways to generate P&L knowing vols are going to be high in the future (e.g. buy variance swaps,, buy options cheap/sell high). Although I agree of course that the expected answer is certainly the dynamic delta hedging one (accumulation of realised vs hedging vol discrepancies through the option Gamma). $\endgroup$ – Quantuple Sep 26 '17 at 7:34
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I think you would know better than me. But assuming this is some sort of riddle, I would say you made money by dynamically hedging the straddle. When the stock goes into the money your straddle delta goes positive and you sell stock to hedge. When the opposite happens you buy. You are buying low and selling high.

If on the other hand you just sat on the straddle you of course lost money overall (which doesn't necessarily mean it was a bad trade from an expected value perspective. Still this example shows if you want more volatility = more money guaranteed you need to dynamically hedge.)

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Another way to look at the riddle. You think volatility will be high during the next three months, so you buy a 6 months straddle. Three months from now, having been proven right, you sell your straddle (which has 3 months to go) at a high price, due to the high implied vol.

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  • $\begingroup$ Indeed. However we explicitly state that I hold the 3 month straddle till maturity. I think the dynamic hedging is the only sensible answer $\endgroup$ – Ryan J. Shrott Sep 25 '17 at 23:33

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