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Upon close reading, this appears to be 3 (interesting) questions, not one. I'm not sure if the mods have the tools needed to split it up, so I'm just going to write down the three questions as I see them and then deal with them one by one. Note, it is simpler for me to talk about variance instead of volatility. This has no material impact on the answer. ...


Normal distribution makes most sense these days for ratesthat are very low, or even negative, like euribor, chf libor Normal distribution is what is assumed by option brokers impliedvolatility quotes for these currencies

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