**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# The sources of sovereign risk: a calibration based on Levy stochastic processes

Abstract

Governments choose to issue risky or riskless debt depending on the nature of the stochastic process of output. We use Brownian motion and Poisson shocks a modeling method in the literature on corporate default known as Levy processes to approximate a decomposition of the output process into a smooth and a jump component. Using an Eaton and Gersovitz (1981) model of debt repudiation, we show that the Brownian part explains the counter-cyclical behavior of the current account, and the Poisson part explains the risk of default thus enabling our model to account for key stylized facts regarding sovereign risk. (C) 2019 Elsevier B.V. All rights reserved.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts

Loading

Related publications

Loading

Related publications (1)

Loading

Related concepts (8)

Risk

In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as heal

Stochastic process

In probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has

Brownian motion

Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas).
This motion pattern typically consists of random fluctuations in a particle's position inside a fluid s

The topic of this thesis is the study of several stochastic control problems motivated by sailing races. The goal is to minimize the travel time between two locations, by selecting the fastest route in face of randomly changing weather conditions, such as wind direction. When a sailboat is travelling upwind, the key is to decide when to tack. Since this maneuver slows down the yacht, it is natural to model this time lost by a "tacking penalty" which places the problem in the context of optimal stochastic control problems with switching costs. An objective of this work is to propose and to study mathematical models that capture some of the features of a sailing race, but which remain amenable to an explicit rigorous solution that can be proved to be optimal. We consider three different models in which the wind direction is described by a stochastic process. In the first model, we consider a wind that changes randomly only once. In the second model, the wind oscillates between two possible directions according to a continuous-time Markov chain. We exhibit a free boundary problem for the value function involving hyperbolic partial differential equations of Klein-Gordon type. The last model considers the wind direction as a Brownian motion. We prove the existence of a finite value function and exhibit a free boundary problem involving parabolic partial differential equations with non-constant coefficients. In these three models, the optimal solution consists of a partition of the state space into a region where it is optimal to tack immediately and a region where it is optimal to continue on the current tack. The boundaries between these regions are given by one or more "switching curves" and in the cases where we have been able to exhibit them, the optimality of the solution is established by a verification theorem based on the martingale method. We also solve two other control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle by controlling its drift and subject to a switching penalty. In each problem, the value function is written as the solution of a second order ordinary differential equations problem whose unknown boundaries are found by applying the principle of smooth fit. For both problems, we exhibit a candidate strategy as a function of the switching cost and we prove its optimality as well as its generic uniqueness.