We assume we live in a two$-$period binomial world. We will use the same notations in the lecture i$.$e$.$ we assume

that there are only two possible scenarii between t$0=0$ and T the maturity, where the asset S can only go

up or down.

The initial value of the asset is S$0=$ S$,$ and its value ST $($wu$)=$ Su and ST $($wd$)=$ Sd $($e$.$g$.$ u $=1\mathrm{.}1$ and

d $=0\mathrm{.}92).$ We Further assume that P$($ST $=$ Su$)=$ p and P$($ST $=$ Sd$)=1$ p where $0<$ p $<1$ represents

the historical probability.

A client is asking us to give a quote for a forward price i$.$e$.$ a fair strike K for the forward contract. We

would like to study the hedge and the pricing of this problem in this peculiar single binomial world.

$1.$ What is the payoff of this derivative contract at each terminal state at maturity T$?$

$2.$ From the lectures, what is the $($a priori$)$ price at the inception date T$0$ of any fair forward contract?

$3.$ Since you are starting with a zero premium, derive a delta $$ and a strike K so that you end up with

zero pnl in all scenarios.

$4.$ Summarize your replication strategy of this contract at each step.