NDLI: Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB

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Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Higham, Desmond J.
Copyright Year	2002
Abstract	In the context of a real-life application that is of interest to many students, we illustrate how the choices made in translating an algorithm into a high-level computer code can affect the execution time. More precisely, we give nine MATLAB programs that implement the binomial method for valuing a European put option. The first program is a straightforward translation of the pseudocode in Figure 10.4 of The Mathematics of Financial Derivatives, by P. Wilmott, S. Howison, and J. Dewynne, Cambridge University Press, 1995. Four variants of this program are then presented that improve the efficiency by avoiding redundant computation, vectorizing, and accessing subarrays via MATLAB's colon notation. We then consider reformulating the problem via a binomial coefficient expansion. Here, a straightforward implementation is seen to be improved by vectorizing, avoiding overflow and underflow, and exploiting sparsity. Overall, the fastest of the binomial method programs has an execution time that is within a factor 2 of direct evaluation of the Black--Scholes formula. One of the vectorized versions is then used as the basis for a program that values an American put option. The programs show how execution times in MATLAB can be dramatically reduced by using high-level operations on arrays rather than computing with individual components, a principle that applies in many scientific computing environments. The relevant files are downloadable from the World Wide Web.
Starting Page	661
Ending Page	677
Page Count	17
File Format	PDF
ISSN	00361445
DOI	10.1137/S0036144501393266
e-ISSN	10957200
Journal	SIAM Review (SIREAD)
Issue Number	4
Volume Number	44
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-04
Access Restriction	Subscribed
Subject Keyword	underflow vectorization American option Black--Scholes overflow optimization Complexity and performance of numerical algorithms Instructional exposition algorithm European option
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computational Mathematics

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