SUBORDINATION, SELF-DECOMPOSABILITY AND SEMI-STABILITY

Self-decomposability and Option Pricing

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 mat...

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 bo...

On the self-decomposability of the Fréchet distribution

Let {Γt, t ≥ 0} be the Gamma subordinator. Using a moment identification due to Bertoin-Yor (2002), we observe that for every t > 0 and α ∈ (0, 1) the random variable Γ t is distributed as the exponential functional of some spectrally negative Lévy process. This entails that all size-biased samplings of Fréchet distributions are self-decomposable and that the extreme value distribution Fξ is in...

Smoothness , semi - stability and alterationsby

Semi Stability Factors

A (semistability) factor [semifactor] of a matrix AE r: nn is a positive definite [positive semidefinite] matrix H such that AH + HA* is positive semidefinite. We give three proofs to show that if A has a semistability factor then it cannot be unique. We give necessary and sufficient conditions for a matrix H to be a (semi)factor of a given matrix. We also determine the dimension of the cone of...