SELF‐DECOMPOSABILITY AND OPTION PRICING

Peter Carr, Hélyette Geman, Dilip B. Madan and Marc Yor

Mathematical Finance, 2007, vol. 17, issue 1, 31-57

Abstract: The risk‐neutral process is modeled by a four parameter self‐similar process of independent increments with a self‐decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and maturities at a point of time. Considerations of parameter stability over time suggest a preference for two of these models. Currently, there are several option pricing models with 6–10 free parameters that deliver a comparable level of performance in synthesizing option prices. The dimension reduction attained here should prove useful in studying the variation over time of option prices.

Date: 2007
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