Consider a standard binomial model with the state space = {+,} and two base securities, risk-free bond B and risky stock S.

(a) Determine the portfolios [,] in the base assets B and S that replicate the payoffs of ArrowDebreu securities E = I{}.

(b) Determine the no-arbitrage prices 0(E).

(c) For an arbitrary payoff function X, we can write

X() = X(+)E+() + X()E(). Since the replicating portfolio (X , X ) is given by

[X , X ] = X(+)[+, +] + X()[, ] derive the formula for [X , X ] using the result of (a).