A Bayesian Analysis of Return Dynamics with Lévy Jumps

A Bayesian Analysis of Return Dynamics with Lévy Jumps
Author: Haitao Li
Publisher:
Total Pages:
Release: 2010
Genre:
ISBN:
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We have developed Bayesian Markov chain Monte Carlo (MCMC) methods for inferences of continuous-time models with stochastic volatility and infinite-activity Leacute;vy jumps using discretely sampled data. Simulation studies show that (i) our methods provide accurate joint identification of diffusion, stochastic volatility, and Leacute;vy jumps, and (ii) the affine jump-diffusion (AJD) models fail to adequately approximate the behavior of infinite-activity jumps. In particular, the AJD models fail to capture the ldquo;infinitely manyrdquo; small Leacute;vy jumps, which are too big for Brownian motion to model and too small for compound Poisson process to capture. Empirical studies show that infinite-activity Leacute;vy jumps are essential for modeling the Samp;P 500 index returns.

Handbooks in Operations Research and Management Science: Financial Engineering

Handbooks in Operations Research and Management Science: Financial Engineering
Author: John R. Birge
Publisher: Elsevier
Total Pages: 1026
Release: 2007-11-16
Genre: Business & Economics
ISBN: 9780080553252
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The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.

Detecting Jumps from Levy Jump Diffusion Processes

Detecting Jumps from Levy Jump Diffusion Processes
Author: Suzanne S. Lee
Publisher:
Total Pages: 0
Release: 2009
Genre:
ISBN:
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Recent asset pricing models incorporate jump risk through Levy processes in addition to diffusive risk. This paper studies how to detect stochastic arrivals of small and big Levy jumps with new nonparametric tests. They allow for robust analysis on their separate characteristics and facilitate better estimation of return dynamics. Empirical evidence based on our tests suggests that models for both individual equities and overall market indices require Levy-type jumps due to our finding of many small jumps as well as big jumps. This evidence of small jumps also offers a resolution for the puzzle: why are jumps in the index uncorrelated with jumps in its component equities?

Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities

Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities
Author: Anatoliy Swishchuk
Publisher: World Scientific
Total Pages: 326
Release: 2013-06-03
Genre: Business & Economics
ISBN: 9814440140
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Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.

Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes)

Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes)
Author: Cheng Few Lee
Publisher: World Scientific
Total Pages: 5053
Release: 2020-07-30
Genre: Business & Economics
ISBN: 9811202400
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This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

Handbook of Economic Forecasting

Handbook of Economic Forecasting
Author: Graham Elliott
Publisher: Newnes
Total Pages: 719
Release: 2013-08-23
Genre: Business & Economics
ISBN: 0444536841
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The highly prized ability to make financial plans with some certainty about the future comes from the core fields of economics. In recent years the availability of more data, analytical tools of greater precision, and ex post studies of business decisions have increased demand for information about economic forecasting. Volumes 2A and 2B, which follows Nobel laureate Clive Granger's Volume 1 (2006), concentrate on two major subjects. Volume 2A covers innovations in methodologies, specifically macroforecasting and forecasting financial variables. Volume 2B investigates commercial applications, with sections on forecasters' objectives and methodologies. Experts provide surveys of a large range of literature scattered across applied and theoretical statistics journals as well as econometrics and empirical economics journals. The Handbook of Economic Forecasting Volumes 2A and 2B provide a unique compilation of chapters giving a coherent overview of forecasting theory and applications in one place and with up-to-date accounts of all major conceptual issues. Focuses on innovation in economic forecasting via industry applications Presents coherent summaries of subjects in economic forecasting that stretch from methodologies to applications Makes details about economic forecasting accessible to scholars in fields outside economics

Continuous Time Processes for Finance

Continuous Time Processes for Finance
Author: Donatien Hainaut
Publisher: Springer Nature
Total Pages: 359
Release: 2022-08-25
Genre: Mathematics
ISBN: 3031063619
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This book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management. The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed. A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets. These processes recently receive a lot of attention from researchers and we focus here on its econometric estimation and its simulation. A chapter is dedicated to estimation of stochastic volatility models. Two chapters are dedicated to the fractional Brownian motion and Gaussian fields. After a summary of their features, we present applications for stock and interest rate modeling. Two chapters focuses on sub-diffusions that allows to replicate illiquidity in financial markets. This book targets undergraduate students who have followed a first course of stochastic finance and practitioners as quantitative analyst or actuaries working in risk management.

Estimation of Stochastic Volatility Models with Markov Chain Monte Carlo Methods

Estimation of Stochastic Volatility Models with Markov Chain Monte Carlo Methods
Author: Maximilian Richter
Publisher:
Total Pages:
Release: 2016
Genre:
ISBN:
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Markov Chain Monte Carlo (MCMC) methods are a Bayesian approach to tackle one of the main obstacles encountered in the estimation of modern-day stochastic volatility models: the curse of dimensionality induced by the increasing number of latent variables. This thesis strives to study the performance of affine jump-diffusion models in comparison to state-of-the-art Lévy-based return dynamics. Thus MCMC methods are applied to a novel dataset of S & P500 returns that comprises different periods of economic turmoil, such as the subprime crisis. The subordinate research goal is to address difficulties in the implementation of the MCMC methodology. In line with previous studies, the results indicate that jump components are indeed crucial for capturing complex patterns like skewness and excess kurtosis of the return distributions. Moreover, infinite-activity Lévy jumps prove to be superior to discrete compound Poisson jumps.