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I want to find a way to long volatility of a future time period such as longing (march,april) vol from today. My idea is to short a straddle for march and long one for April for example. Will that work, what type of exposure will I get?

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Your strategy is called an options calendar spread (plenty of literature exists that you can consult). Basically, you do indeed have exposure to the implied volatility during the forward period (March-April in your example). Assuming you execute the same number of contracts of each, you will also receive time decay as the March option decays faster than the April. An important consideration is that your exposure to the forward volatility depends on where the underlying goes. If the underlying stays near the strike , you will have a large exposure to the forward volatility. If the underlying moves a long way from the strike in either direction, both options will be deep in the money, and you will have minimal exposure to the forward volatility.

To get a pure exposure to the forward volatility, you would have to execute a more exotic structure, such as a forward variance swap from March to April, which some dealers may offer. If you are a retail investor , you may not be able to access this strategy.

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A priori, I see no large risk on the underlying on your trade, since the (roughly null) deltas on both trades will offset each other. The breakeven move on a straddle is $\left|\tilde{\sigma} S \sqrt{\Delta t}\right|$; you should just have a residual exposure on the term structure of volatility.

Suppose that at some point $\tilde{\sigma}_\text{March} > \tilde{\sigma}_\text{April}$. If between two delta-rebalancings, your realised volatility is between the two, you will lock in a loss on both trades: gamma loss on the April straddle and theta loss on the March straddle.

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