Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Nine ways to implement the binomial method for option valuation in MATLAB

Higham, D.J. (2002) Nine ways to implement the binomial method for option valuation in MATLAB. SIAM Review, 44 (4). pp. 661-677. ISSN 0036-1445

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

In the context ofa 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.