Questions on arbitrage

I have the following questions about arbitrage that I am unsure of.

• Will an inverse term structure rate imply arbitrage possibilities?
• Will negative zero coupon rates imply arbitrage possibilities?
• Is it possible to have arbitrage possibilities in an incomplete market?

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 your market.

• Term structure rate is usually increasing. What if it was falling. – Peter0302 Jun 3 '16 at 16:26
1. If we are talking about zero rates, then any curve is arbitrage free.

2. No.

3. 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.