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If we are talking about zero rates, then any curve is arbitrage free. No. Yes. Although in general arbitrage and incompleteness are in different directions (not enough tradeable instruments --> incomplete, too many traceable instruments --> potential arbitrage), it's of course possible for a model to be incomplete in one place and arbitrageable in another.


1) not sure to see what you mean by inverse term structure rate 2) no if $r>-100\%$, $r<0$ means having cash on you will cost you something 3) If there is an unhedgeable risk in your market, it is not complete. So you cannot build an arbitrage based on this risk (since it is unhedgeable, it is pure bet). However, you could have arbitrage elsewhere in ...

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