Assume a binomial, risk-neutral world where \(n=1, \mathrm{~S}_{0}=\$ 100, R_{f}=0.05, u=\) 1.10 , and \(d=0.95\).

a. What are the risk-neutral probabilities of the stock increasing in one period and decreasing in one period?

b. Solve for the probabilities using the equation: \(S_{0}=P V\left(E\left(S_{T}\right)\right.\) ).

c. Using risk-neutral pricing, determine the equilibrium price of a call on a stock with an exercise price of \(\$ 100\) and expiration at the end of the period.

d. Using risk-neutral pricing, determine the equilibrium price of a put on the stock with an exercise price of \(\$ 100\) and expiration at the end of the period.

e. Are your answers in \(\mathrm{c}\) and \(d\) consistent with the BOPM's replicating approach?