Question $6$: A market has two tradable assets which follow a trinomial model with the following param$-$

eters:

A$0=10$

Au $=12$

Am $=10$

Ad $=8$

B$0=20$

Bu $=25$

Bm $=20$

Bd $=15$

and strictly positive branching probabilities pu$,$ pm$,$ and pd such that pu $+$ pm $+$ pd $=1.$ A third asset has

terminal values Cu $=100,$ Cm $=90,$ and Cd $=0.$

$1.($easy$)$ Verify using the result of Question $3$ that the pair of assets A and B does not admit arbitrage.

$2.($medium$)$ What goes wrong when trying to find C$0$ by the replication argument in lecture?

$3.($very difficult$)$ Find all possible values of C$0$ such that there will not be an arbitrage in the market