FIN 452 & 537, Spring 2022 Advanced Derivative Securities
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Homework #7
Due Tuesday, March 29, 2022


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 (0),
(0), , , , σ, σ, ρ, , and . Take the strike price of the option struck in foreign
currency to be , take the strike price of both the option struck in domestic currency and the
quanto option to be (0) (so is interpreted as an amount in foreign currency), and take
the fixed exchange rate in the quanto to be � = (0). You should be able to confirm that if
= 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 , , and the exchange rate. Compute
the forward exchange rate at maturities = 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 (0), , , σ, the maturity
of the forward contract, and the number of periods . Plot the simulated exchange rate
and forward exchange rate together. Note that you need to first derive the process of 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 (0), σ, and the expected rate of growth of the
exchange rate. Prompt the user also to input (0), , , σ, , ρ, the fixed exchange rate �,
the maturity , the number of periods , and the expected rate of growth of the asset in


1 According to Chapter 6, a “quanto call” is a European call option on a foreign asset, with strike set in the domestic
currency and the value of foreign asset being converted to domestic currency at a fixed exchange rate �. Thus, the
value of the quanto call at maturity is max(0,�() − ). We have learned that the portfolio with value defined
in Equation (2) [also Equation (6.7) in the textbook] replicates the payoff �(), that is, in each state of the world,
() = �(). Therefore, the quanto call is equivalent to a standard European call on the portfolio with domestic
currency price . From Equation (7) [also Equation (6.9) in the textbook], we can see that the volatility of is the
same as that of . Furthermore, the portfolio is non-dividend-paying as it is the value of a claim to �() at date
with no interim cash flows. Putting all pieces together, we can use the Black-Scholes formula to calculate the
value of the quanto call = (0)(1) − −(2), and we input as the volatility and zero as the dividend
yield in the formula.
FIN 452 & 537, Spring 2022 Advanced Derivative Securities
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the foreign currency. Note that both and are under the actual probability measure, and
includes the dividend (so − 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 �() at date and uses a discretely
rebalanced hedge, rebalancing at dates 1, …, = , where − −1 = ⁄ , similar to the
calculation in the function Simulated_Delta_Hedge_Profit. Use the money-market hedge,
which means investing (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 , and having a short position
in the foreign risk-free asset of the same value at each date . 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 ().


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 by 7 p.m. on the due date with the rest of your work [i.e., derivation of
the process of with the risk-free asset as the numeraire in Problem 3].