Suppose the following:

- Spot S\&P 500 is currently at 3,000

- Continuous annual dividend yield of \(\psi=5 \%\)

- Annualized standard deviation is \(\sigma^{\mathrm{A}}=0.25\)

- Annual risk-free rate is \(R=4 \%\).

- European call and put options on the S\&P 500 each with an exercise price of 3,000 and expiration of 180 days

a. Determine the equilibrium prices of the call and put options using Merton's dividend adjusted B-S OPM. Use the B-S Excel program.

b. Determine both the American and European options prices using Merton's dividend adjusted binomial model for \(n=100\) subperiods. Use the Excel program.

c. Compare the price for Merton's European binomial with Merton's B-S model.

d. Compare the prices for Merton's American binomial with the European binomial value. Is there any early exercise advantage?