Download This PaperMethod of Lines Approach for Pricing American Spread Options
28 Pages Posted: 11 Mar 2012
Date Written: December 5, 2011
Abstract
A numerical technique for the evaluation of American spread call options where the underlying asset dynamics evolve under the influence of a single stochastic variance process of the Heston (1993) type is presented. The numerical algorithm involves extending to the multi-dimensional setting the method of lines approach first presented in the option pricing framework by Meyer and van der Hoek (1997) when pricing the standard American put option. We transform the pricing partial differential equation to a corresponding system of ordinary differential equations with the aid of the Riccati transformation. We use the implicit trapezoidal rule to solve the resulting Riccati equations. Numerical results are presented outlining the effectiveness of the algorithm. The effects of stochastic volatility are explored by making comparisons with the geometric Brownian motion results.
Keywords: American Options, Method of Lines, Riccati Transformation
JEL Classification: C61, D11
Suggested Citation: Suggested Citation
Jonathan Ziveyi
University of New South Wales; ARC Centre of Excellence in Population Ageing Research and School of Risk & Actuarial Studies ( email )
School of Risk and Actuarial Studies
UNSW Business School
Sydney, NSW 2000
Australia
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