Journal of Applied Mathematics and Decision Sciences
Volume 2008 (2008), Article ID 397028, 30 pages
Research Article

Subordination, Self-Similarity, and Option Pricing

Mack L. Galloway1 and Craig A. Nolder2

1Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
2Department of Mathematics, The Florida State University, Tallahassee, FL 32306-4510, USA

Received 17 February 2008; Accepted 27 October 2008

Academic Editor: Henry Schellhorn

Copyright © 2008 Mack L. Galloway and Craig A. Nolder. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We use additive processes to price options on the Standard and Poor's 500 index (SPX) for the sake of comparison of pricing performance across both model class and family of time-one distribution. Each of the additive processes in this study is defined using one of the following: subordination, Sato's (2002) construction of self-similar additive processes from self-decomposable distributions, or both. We find that during the year 2005: (1) for a given family of time-one distributions, four-parameter self-similar additive models consistently yielded lower pricing errors than those of four-parameter subordinated, and time-inhomogeneous additive models, (2) for a given class of additive models, the time-one marginal given by the normal inverse Gaussian distribution consistently yielded lower pricing errors than those of the variance gamma distribution. Market and model benchmarks for the additive models under consideration are obtained via the bid-ask spreads of the options and Lévy stochastic volatility model prices, respectively.