Subordination, Self-Similarity, and Option Pricing

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, fourparameter 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.