Corpus ID: 5676193

Basics of Levy processes

  title={Basics of Levy processes},
  author={Neil Shephard and Ole E. Barndorff-Nielsen},
This is a draft Chapter from a book by the authors on “Lévy Driven Volatility Models”. 
Lévy copulae for financial returns
Abstract The paper uses Lévy processes and bivariate Lévy copulae in order to model the behavior of intraday log-returns. Based on assumptions about the form of marginal tail integrals and a ClaytonExpand
Pricing Variance and Volatility Swaps for Barndorff-Nielsen and Shephard Process Driven Financial Markets
The objective of this paper is to study the arbitrage free pricing of variance and volatility swaps for Barndorff-Nielsen and Shephard type Levy process driven financial markets. One of the majorExpand
Pricing Covariance Swaps for Barndorff-Nielsen and Shephard Process Driven Financial Markets
The objective of this paper is to study the arbitrage free pricing of the covariance swap for Barndorff–Nielsen and Shephard (BN–S) type Levy process driven financial markets. One of the majorExpand
Comparing computational approaches to the analysis of high-frequency trading data using Bayesian methods
The central Chapters of the work are devoted to the illustration of Particle Filtering methods for MCMC posterior computations (or PMCMC methods), and a presentation of a semi-parametric version of the original model. Expand
Life distribution analysis based on Lévy subordinators for degradation with random jumps
For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumpsExpand
Evaluation of Hedging Strategies of Asian Options on Electricity at Nord Pool
This thesis empirically evaluates a geometric Brownian motion and a stochastic volatility model for modeling futures prices and hedging Asian call options on the electricity spot price. Estimation ofExpand
Essays on computational economics
This text consists of two parts. In chapters 2–3 the methods are developed that enable the application of tempered stable distributions to measuring and simulating macroeconomic uncertainties. InExpand
Lévy-driven non-Gaussian Ornstein–Uhlenbeck processes for degradation-based reliability analysis
ABSTRACT We use Lévy subordinators and non-Gaussian Ornstein–Uhlenbeck processes to model the evolution of degradation with random jumps. The superiority of our models stems from the flexibility ofExpand
Modeling Financial Swaps and Geophysical data Using the Barndorff-Nielsen and Shephard Model
This dissertation uses Barndoff-Nielsen and Shephard (BN-S) models to model swap, a type of financial derivative, and analyze geophysical data for estimation of major earthquakes to demonstrate the significance of BN-S models to phenomena that follow non-Gaussian distributions. Expand
Exact likelihood inference for autoregressive gamma stochastic volatility models 1
Affine stochastic volatility models are widely applicable and appear regularly in empirical finance and macroeconomics. The likelihood function for this class of models is in the form of aExpand


Calibration of Lévy Term Structure Models
The main purpose of this paper is to elaborate on calibration in the real world as well as in the risk-neutral setting. Expand
Lévy term structure models: No-arbitrage and completeness
It turns out that in a number of standard situations the martingale measure is unique. Expand
Option Pricing with Levy Process
In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristicsExpand
Time consistency of Lévy models
Time consistency of the models used is an important ingredient to improve risk management. The empirical investigation in this article gives evidence for some models driven by Lévy processes to beExpand
Lévy Processes in Finance: Pricing Financial Derivatives
Preface. Acknowledgements. Introduction. Financial Mathematics in Continuous Time. The Black-Scholes Model. Imperfections of the Black-Scholes Model. Levy Processes and OU Processes. Stock PriceExpand
Series Representations of Lévy Processes from the Perspective of Point Processes
Several methods of generating series representations of a Levy process are presented under a unified approach and a new rejection method is introduced in this context. The connection of suchExpand
Stochastic processes with Student marginals and various types of dependence structure, allowing for both shortand long-range dependence, are discussed in this paper. A particular motivation is theExpand
A general class of truncated Levy processes is introduced, and possible ways of fitting parameters of the constructed family of truncated Levy processes to data are discussed. For a market of aExpand
Integer-valued Lévy processes and low latency financial econometrics
Motivated by features of low latency data in financial econometrics we study in detail integer-valued Lévy processes as the basis of price processes for high-frequency econometrics. We propose usingExpand
Non-Gaussian Merton-Black-Scholes theory
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Levy processes of the exponential type) and related analytical methodsExpand