Question: 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

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?

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