Exercises.

Three $2-$year bonds have the following cash flows and prices:

A$.(2,3),P_A=2\mathrm{.}5$

B$.(3,4),P_B=3\mathrm{.}6$

C$.(4,5),P_C=4\mathrm{.}8$

Is there any arbitrage opportunity?

How can you change $P_C$ so there is no arbitrage opportunity?

$2.$ Three $4-$year bonds have the following cash flows and prices:

A$.(2,2,2,3),P_A=2\mathrm{.}5$

B$.(3,3,3,4),P_B=3\mathrm{.}6$

C$.(4,4,4,5),P_C=4\mathrm{.}8$

Is there any arbitrage opportunity?

How can you change $P_C$ so there is no arbitrage opportunity?