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Let $B(t,T)$ denote the cost at time t of a risk-free 1 euro bond, at time T. Assume that the interest rate is a deterministic function. Show that the absence of arbitrage requires that:

$ B(0,1) B(1,2) = B(0,2)$

For instance, could you give a detailed explanation of what to do if $B(0,1)B(1,2) > B(0,2)$ ?

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  • $\begingroup$ What have you tried to solve this problem? $\endgroup$ – Bob Jansen Mar 31 '20 at 13:35
  • $\begingroup$ I have to suppose two cases: $B(0,1)B(1,2) >B(0,2) $ and $B(0,1)B(1,2) <B(0,2) $ and show that both lead to an arbitrage $\endgroup$ – Babado Mar 31 '20 at 13:37
  • $\begingroup$ As usual, to make a profit you sell the thing(s) which is most expensive and buy the thing(s) which is cheaper. $\endgroup$ – noob2 Mar 31 '20 at 15:38
  • $\begingroup$ Yeah ok, but I don't understand in real life, what does it mean for example to sell $B(0,1)B(1,2) $ and buy $B(0,2)$ $\endgroup$ – Babado Mar 31 '20 at 16:03
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    $\begingroup$ Try thinking of borrowing money instead of selling a bond and of lending money instead of buying a bond $\endgroup$ – simzoor Mar 31 '20 at 16:08

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