Problem BIN$-318$B

We are given a three$-$period binomial tree for the price of a non$-$dividend$-$paying stock.

With our usual notation,

$S(0)=$$$50$

$R=1\mathrm{.}0125$

$u=1\mathrm{.}02$

$d=0\mathrm{.}96$

The risk$-$neutralized probability:

$=$

Complete the following binomial trees.

$($a$)$ A security which pays $[S(3){]}^2$ in cash.

$($b$)$ A share$-$or$-$nothing call which expires at time $3,$

with strike

$K=48$

$($c$)$ A security which pays max$\{1\frac{1}{2}(S)(2)+\frac{1}{2}(S)(3)-K,0\}$

uuu

und

udu

udd

duu

dud

ddu

ddd