Equivalent measure changes for subordinate diffusions. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: Li, Lingfei; Mendoza-Arriaga, Rafael
• Is Part Of: Stochastic models. Volume 35:Issue 4(2019)
• Page Start: 357
• Page End: 390
• Publication Date: 2019-10-02
• Subjects: Equivalent measure changes -- jump processes -- Markov processes -- subordination -- time-inhomogeneity; 60G30 -- 60J75; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2019.1606719
• Languages: English
• ISSNs: 1532-6349

Abstract

Abstract: A subordinate diffusion is a Markovian jump-diffusion or pure jump process obtained by time changing a diffusion process with an independent Lévy or additive subordinator. This class of processes has found many applications in financial modeling. In this paper, we develop sufficient conditions and necessary conditions for the distributions of two subordinate diffusions to be equivalent, which are important for derivatives pricing and calibration. We obtain asymptotics for the jump intensity of a large class of subordinate diffusions near zero, which allow us to reduce these conditions to explicit restrictions on the model parameters that can be directly checked in applications. These asymptotics are also useful in detecting finiteness of the jump variation for these processes.