1. Create an Excel worksheet to compute and compare the values of the following three types of call options on foreign assets: (i) call options struck in foreign currency, (ii) call options struck in domestic currency, and (iii) quanto call options¹. Prompt the user to input X(0), S(0), K, r, T, σs, σx, ρ, q, and T̄. Take the strike price of the option struck in foreign currency to be Kx, take the strike price of both the option struck in domestic currency and the quanto option to be X(0)K (so K is interpreted as an amount in foreign currency), and take the fixed exchange rate in the quanto to be X̄ = X(0). You should be able to confirm that if r = rf and ρ ≥ 0, then (i) the option struck in domestic currency is more valuable than the option struck in foreign currency, and (ii) the option struck in foreign currency is more valuable than the quanto.
2. Create an Excel worksheet in which the user inputs rs, rf, and the exchange rate. Compute the forward exchange rate at maturities T = 0.1, 0.2, …, 2.0, and plot the forward rate against the maturity in a scatter plot. A market is said to be in “contango” if this curve is upward sloping and to be in “backwardation” if this curve is downward sloping. For currencies, what determines whether the market is in contango or in backwardation?
3. Create a VBA subroutine to simulate a path of the exchange rate and the forward exchange rate under the risk-neutral measure, prompting the user to input X(0), T, rs, σx, the maturity T of the forward contract, and the number of periods N. Plot the simulated exchange rate and forward exchange rate together. Note that you need to first derive the process of X with the risk-free asset as the numeraire (recall what you learned in Chapter 2), then write the VBA codes to implement the simulation, and lastly, make the plot.
4. Create a VBA subroutine to simulate a path of the exchange rate under the actual probability measure, prompting the user to input X(0), σx, and the expected rate of growth μs of the exchange rate. Prompt the user also to input S(0), T, rs, σs, q, ρ, the fixed exchange rate X̄, the maturity T, the number of periods N, and the expected rate of growth μs of the asset in the foreign currency. Note that both μx and μs are under the actual probability measure, and μs includes the dividend (so μs – q is the expected rate of price appreciation). Use the subroutine also to generate a path of the foreign asset price along with the exchange rate. Then, calculate the gain/loss from the portfolio that promises to pay X(T) at date T and uses a discretely rebalanced hedge, rebalancing at dates t1, …, tN = T, where ti – ti-1 = T/N, similar to the calculation in the function Simulated_Delta_Hedge_Profit. Use the money-market hedge, which means investing V(0) at date 0, holding the number of shares of the foreign asset shown in Equation (9) [also Equation (6.14) in the textbook] at each date ti, and having a short position in the foreign risk-free asset of the same value at each date ti. Cash flow generated at each date from buying/selling the foreign asset and lending/borrowing at the foreign risk-free rate should be withdrawn/deposited in the domestic risk-free asset. Note that because of discrete rebalancing, this is not a perfect hedge, and the investment in the domestic risk-free asset will not always equal V(t).

Save your VBA codes and results (including plots and narrative answers) for all four problems in an Excel Macro-Enabled Workbook with the file extension “.xlsm”. Also, name the worksheets “Problem 1,” “Problem 2,” “Problem 3,” and “Problem 4,” respectively. Submit your Excel file electronically on Canvas with the rest of your work [i.e., derivation of the process of X with the risk-free asset as the numeraire in Problem 3].