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Not sure if this is the right place to ask such question.

  1. How close to 1 should the delta be in order for the product to be classified as delta one. 2.What examples of delta one products are there?
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As indicated by the name, delta one products have a delta of exactly 1 (at least theoretically) with respect to the underlying; moreover, AFAIK the delta has to be constant, i.e. a product with optionality that happens to have $\Delta = 1$ for some period won't be classified as delta one (otherwise it would be a nightmare for traders to manage their books!). Some products that come to mind are forwards, futures, ETFs... You might want to take a look at Wikipedia's page.

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