Consider a two-step binomial model with two no-arbitrage assets X and Y and parameters u > 1 >...

Consider
a two-step binomial model with two no-arbitrage assets X and Y and parameters u
> 1 > d > 0. Let A be a contract with a payoff

(a) Compute the prices VY (n) using the measure P Y . Note that

and it is a no-arbitrage
asset. Therefore there is a probability measure P A under which the prices of
no-arbitrage assets with respect to the reference asset A are martingales.
Determine P A by giving P A(HH), P A(HT ), P A(T H), P A(T T ). These are
functions of parameters u and d. The easiest way is to employ the
Radon–Nikod´ym derivative with respect to a martingale measure P Y . Recall
that