Question $1(23$ Marks$).$

$1\mathrm{.}1$ Suppose that the stock price on any given day can either be $5\%$ higher or $4\%$ lower than on the previous day. $,S(c)=15$ dollars

$1\mathrm{.}1\mathrm{.}1$ Find all the possible stock price movements over the next three days. $($Round to two decimal places$)$

$1\mathrm{.}1\mathrm{.}2$ How many different scenarios where distinguished on day $3.$

$1\mathrm{.}1\mathrm{.}3$ Sketch a tree representing possible price movements.

$(4)$

$1\mathrm{.}2$ Suppose that the return on all three scenarios is given by $K(1)=10\%,K(1)=-10\%,K(1)=-10\%$ and $K(0,2)=21\%,10\%$ or $-1\%$ respectively. Find the one step return $K(2)$ on all three scenarios. $($Show all steps$)$

Question $2(27$ Marks$)$

$(1+k_1{)}^2-1+k_{(0,2)}$

$2\mathrm{.}1$ Suppose that there are three possible scenarios, $=\{{}_1,{}_2,{}_3\}$

$\backslash$table$[[$Scenario$,S(0),S(1),S(2)$