Journal of Applied Mathematics and Decision Sciences
Volume 2008 (2008), Article ID 397028, 30 pages
doi:10.1155/2008/397028
Research Article
Subordination, Self-Similarity, and Option Pricing
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.
Abstract
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.