This document contains complementary material of section 6 of the article "Marshall-Olkin Distributions, Subordinators, Efficient Simulation, and Applications to Credit Risk". In particular, we provide the time-inhomogeneous extensions of Theorems 4.1 and 4.2 of the main document. These results...

The paper presents a novel construction of Marshall-Olkin (MO) multivariate exponential distributions of failure times as distributions of the first passage times of the coordinates of multidimensional Levy subordinator processes above independent unit-mean exponential random variables. A...

To capture mean reversion and sharp seasonal spikes observed in electricity prices, this paper develops a new stochastic model for electricity spot prices by time changing the Jump Cox-Ingersoll-Ross (JCIR) process with a random clock that is a composite of a Gamma subordinator and a...

We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Levy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Levy measure, local stochastic volatility and have a local stochastic default intensity....

A subordinate diffusion is a Markov jump-diffusion or pure jump process obtained by time changing a diffusion process with an independent Levy or additive subordinator. This class of processes has found many applications in finance. In this paper, we derive sufficient conditions for equivalent...

Motivated by the need to model time-dependent behavior, this paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner's subordination, which...

The Basic Affine Jump Diffusion (BAJD) process is widely used in financial modeling. In this paper, we develop an exact analytical representation for its transition density in terms of a series expansion that is uniformly-absolutely convergent on compacts. Computationally, our formula...

The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process of the diffusion state variable and default indicator process (X,D) in the diffusion intensity model...

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...