Subordination, Self-Similarity, and Option Pricing

摘要

We use additive processes to price options on the Standard and Poor's500 index (SPX) for the sake of comparison of pricing performance acrossboth 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 fromself-decomposable distributions, or both. We find that during the year2005: (1) for a given family of time-one distributions, four-parameterself-similar additive models consistently yielded lower pricing errors thanthose of four-parameter subordinated, and time-inhomogeneous additivemodels, (2) for a given class of additive models, the time-one marginalgiven by the normal inverse Gaussian distribution consistently yieldedlower pricing errors than those of the variance gamma distribution. Marketand model benchmarks for the additive models under considerationare obtained via the bid-ask spreads of the options and Lévy stochasticvolatility model prices, respectively.valued generalizedw