MULTIVARIATE SUBORDINATION OF MARKOV PROCESSES WITH FINANCIAL APPLICATIONS

Abstract

This paper develops the procedure of multivariate subordination for a collection of independent Markov processes with killing. Starting from d independent Markov processes with killing and an independent d‐dimensional time change , we construct a new process by time, changing each of the Markov processes with a coordinate . When is a d‐dimensional Lévy subordinator, the time changed process is a time‐homogeneous Markov process with state‐dependent jumps and killing in the product of the state spaces of . The dependence among jumps of its components is governed by the d‐dimensional Lévy measure of the subordinator. When is a d‐dimensional additive subordinator, Y is a time‐inhomogeneous Markov process. When with forming a multivariate Markov process, is a Markov process, where each plays a role of stochastic volatility of . 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.