Given the following futures and spot information:

- The S\&P 500 futures option expiring at the end of 60 days.

- The S\&P 500 futures contract expiring at the end of 60 days.

- The current spot index is at \(S_{0}=3,000\).

- The estimated annualized volatility and mean of the spot index's logarithmic return are \(\sigma^{\mathrm{A}}=0.25\) and \(\mu^{\mathrm{A}}=0\).

- The annual risk-free rate is \(R_{f}=3 \%\).

- The futures price is determined by the carrying-cost model:
\[ f_{0}=S_{0} e^{\left(R_{f}-\psi\right) n_{f} \Delta t}\]
- \(\Psi=\) continuous annual dividend yield \(=5 \%\).
Determine the following option prices for a 30-period binomial option model using the BOPM Excel program:

a. American futures call

b. European futures call

c. American spot call

d. European spot call

e. American futures put

f. European futures put g. American spot put h. European spot put Based on your findings, comment on the relations between American and European futures options and spot options.