Consider a one-period, two-state case in which ABC stock is trading at \(S_{\mathrm{O}}=\) \(\$ 100, u=1.1\), and \(d=0.95\), the period risk-free rate is \(5 \%\), and the stock is expected to go ex-dividend at the end of the period with a dividend worth \(\$ 1.00\) at the ex-dividend date.

a. Using the BOPM, determine the equilibrium price of an \(\mathrm{ABC} 100\) European call option.

b. Using the BOPM, determine the equilibrium price of an \(\mathrm{ABC} 100\) European put option.

c. Using the put-call parity model, show that the put price is equal to BOPM's put value.

d. What is the equilibrium price of the call option if it was American and therefore could be exercised just before the expiration date?