1. (Comparing binomial and trinomial option pricing) This problem asks you to create one Excel
add-in which has functions for the Black-Scholes formula, binomial option pricing and trinomial
option pricing. You can use the C code you created in the solutions to previous homework assign-
ments or the code provided in the solutions or lecture les. The three Excel functions created in
this problem should be placed in a single Excel add-in called xllp bs.xll. Make sure that the
.xll is compiled in Release mode. The XLL+ source code should be in a le named xllp [url removed, login to view]
and the non-XLL+ source code (e.g., which contains the option pricing and supporting routines)
should be in a separate le bs [url removed, login to view] with corresponding header le bs routines.h.
You might also want to have a separate le containing NR routines nr [url removed, login to view] and cor-
responding header le nr routines.h.
B9122: Homework Assignment #8
(a) Use XLL+ to create an Excel function bs call(S, , , r, T, K) which returns the Black-
Scholes price of a European call option. Test the function with the parameters: S = 100,
= 0:6, = 0:01, r = 0:05, T = 3, and K = 102.
(b) Use XLL+ to create an Excel function binomial call(S, , , r, T, K, n) which returns
the binomial approximation to the price of a European call option using n time steps and
the CPU time in seconds. The function binomial call is an Excel array function because
it returns two results in an array. The results should appear in a column. Test the function
with the same parameters as in (a) together with n = 100.
(c) Use XLL+ to create an Excel function trinomial call(S, , , r, T, K, , n) which returns
the trinomial approximation to the price of a European call option using the trinomial
stretch parameter and n time steps and also returns the CPU time in seconds. The two
results should be returned in a column array. Test the function with the same parameters
as in (a) together with =
3=2 and n = 100.
(d) (Extra credit) This part asks you to create a graph in Excel of average absolute error versus
average CPU time. The graph should contain two series, one corresponding to the binomial
method and the other corresponding to the trinomial method. Each series of results should
correspond to n = 2000; 4000; 8000; and 16000 time steps. For each value of n, price
European call options using the binomial method, with the same parameters as in (a), but
for the eleven strikes 90, 92, : : : ; 110. For each strike compute the absolute value of the
error (where the error is the binomial price compared to the Black-Scholes price), and then
average the results to compute the average absolute error. Also average the CPU time over
the eleven options priced. Then repeat for each of the four values of n, giving four values of
average absolute error and average CPU time for the binomial method. Repeat the process
for the trinomial method. Plot the resulting two series of binomial and trinomial results
of the average absolute error versus average CPU time with the axes both in logarithmic
Hint: Set up the spreadsheet and graph for smaller values of n, e.g, n = 200; 400; 800 and
1600. When this is working properly, change the values of n to the larger set.
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