Assume the following:

- Annual risk-free rate on US dollars \(=4 \%\).

- Annual risk-free rate on British pounds \(=2 \%\).

- \(\$ /\) BP spot exchange rate \(=\$1.30 / \mathrm{BP}\).

- Mean annualized logarithmic return (for \(\$ / B P\) exchange rate) \(=\mu^{\mathrm{A}}=0\).

- Annualized logarithmic return's standard deviation \(=\sigma^{\mathrm{A}}=\)0.25 .

- BP futures contract expiring in 120 days.

- The BP futures price is determined by the interest-rate-parity condition:

\[f_{0}=E_{0} e^{\left(R_{\$}-R_{B P}\right) n_{f} \Delta t}\]
Determine the following:

a. The price of a European BP futures call option with an exercise price of \(\$1.30\) and expiration of 60 days using the Black futures option model.

b. The price of a European BP futures call with an exercise price of \(\$1.30\) and expiration of 60 days using the binomial Excel program for the case of \(n=30\) subperiods of length \(\Delta t=\) \(2 / 365\).

c. The price of a European BP futures put with an exercise price of \(\$1.30\) and expiration of 60 days using the Black futures option model.

d. The price of an European BP futures put with an exercise price of \(\$1.30\) and expiration of 60 days using the binomial Excel program for the case of \(n=30\) subperiods of length \(\Delta t=\) \(2 / 365\).