MULTIVARIATE SUBORDINATION OF MARKOV PROCESSES WITH FINANCIAL APPLICATIONS

Rafael Mendoza-Arriaga*, Vadim Linetsky

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

This paper develops the procedure of multivariate subordination for a collection of independent Markov processes with killing. Starting from d independent Markov processes Xi with killing and an independent d-dimensional time change T, we construct a new process by time, changing each of the Markov processes Xi with a coordinate Ti. When T is a d-dimensional Lévy subordinator, the time changed process (Yi ≔ Xi(Ti(t))) is a time-homogeneous Markov process with state-dependent jumps and killing in the product of the state spaces of Xi. The dependence among jumps of its components is governed by the d-dimensional Lévy measure of the subordinator. When T is a d-dimensional additive subordinator, Y is a time-inhomogeneous Markov process. When Ti = ∫t0 Visds with Vi forming a multivariate Markov process, (Yi, Vi) is a Markov process, where each Vi plays a role of stochastic volatility of Yi. This construction provides a rich modeling architecture for building multivariate models in finance with time- and state-dependent jumps, stochastic volatility, and killing (default). The semigroup theory provides powerful analytical and computational tools for securities pricing in this framework. To illustrate, the paper considers applications to multiname unified credit-equity models and correlated commodity models.

Original languageEnglish (US)
Pages (from-to)699-747
Number of pages49
JournalMathematical Finance
Volume26
Issue number4
DOIs
StatePublished - Oct 1 2016

Keywords

  • JDCEV model
  • additive subordinators
  • multiparameter semigroups
  • multiple commodities
  • multivariate subordination
  • stochastic volatility
  • subordinators
  • time-inhomogeneous

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'MULTIVARIATE SUBORDINATION OF MARKOV PROCESSES WITH FINANCIAL APPLICATIONS'. Together they form a unique fingerprint.

  • Cite this