Very High Order Lattice Methods for One Factor Models

27 Pages Posted: 15 Feb 2001

See all articles by Jonathan Alford

Jonathan Alford

University of Warwick - Warwick Business School

Nick Webber

University of Warwick - Warwick Business School

Date Written: January 18, 2001

Abstract

Lattice methods are often used to value derivative instruments. Multinomial lattice methods can in principle converge to the true value of the derivative to very high order. In this paper we describe how very high order multinomial lattices can be constructed and implemented when the SDE followed by the underlying state variable can be solved. We illustrate with comparisons between methods with branching order 3, 7, 11, 15 and 19 applied to a geometric Brownian motion. Incorporating both a terminal correction and appropriate truncation methods we find for the heptanomial lattice convergence rates at its theoretical maximum for European style options. With 50 time steps per year our errors are of order 10E-11. With 100 time steps per year our errors are of order 10E-13, approaching the practical limit of the accuracy obtainable in our implementation.

We discuss alternative methods of enabling the heptanomial lattice to achieve high convergence rates for payoff functions with a finite number of critical points. As an example we value a binary option to a high degree of accuracy. We also investigate applications to American and Bermudan options. Based on our comparisons, we conclude that the heptanomial lattice is the fastest and most accurate of the lattices of higher order, and recommend its use as standard in many one factor lattice implementations.

Keywords: Lattice, Multinomial, Derivatives, Heptanomial

JEL Classification: C13, C63, G13

Suggested Citation

Alford, Jonathan and Webber, Nick, Very High Order Lattice Methods for One Factor Models (January 18, 2001). Available at SSRN: https://ssrn.com/abstract=259478 or http://dx.doi.org/10.2139/ssrn.259478

Jonathan Alford

University of Warwick - Warwick Business School

Coventry CV4 7AL
United Kingdom

Nick Webber (Contact Author)

University of Warwick - Warwick Business School ( email )

Coventry CV4 7AL
United Kingdom
+(44) 24 7652 4664 (Phone)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
502
Abstract Views
2,148
Rank
94,867
PlumX Metrics