The setting for this problem is the multi$-$period binomial model with T $=2,$ S$0=$ $$4,$

u $=2,$ d $=1/2,$ but now r $=1/4.$ Consider an American claim based on the payoff

sequence Y give by

Y$0=(4$ S$0)$

$+,$ Y$1=$

$4$

S$0+$ S$1$

$2$

$+$

$,$ Y$2=$

$4$

S$0+$ S$1+$ S$2$

$3$

$+$

$.$

$($This is like a put option based, not on the stock price itself, but on the average stock

price up to time t$.)$

$($a$)$ Construct the necessary wealth process U$0,$ U$1,$ U$2,$ for this claim, best displayed

as a tree.

$($b$)$ What is the no$-$arbitrage price for the claim?

$($c$)$ Describe a good time for the buyer of the claim to exercise the claim.