uppose N $=2.1$

$2$

$($a$)$ You have a $($European$)$ security which pays you $$5$ if the stock price has

jumped up twice and $$0$ otherwise. Use the backward algorithm to find

Vn and $$n for n $=0,1.$

$($b$)$ You have a $($European$)$ security which pays you $$5$ if the stock price

has jumped up twice and $$0$ otherwise. Use the conditional expectation

method to find Vn for n $=0,1$