Investigating Impacts of Self-exciting Jumps in Returns and Volatility
Author : Andras Fulop
Publisher :
Page : pages
File Size : 13,11 MB
Release : 2012
Category :
ISBN :
The Impact of Jumps in Volatility and Returns
Author : Michael S. Johannes
Publisher :
Page : 47 pages
File Size : 48,94 MB
Release : 2011
Category :
ISBN :
Book Description
This paper examines a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility. We develop a likelihood-based estimation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using both Samp;P 500 and Nasdaq 100 index returns. Estimates of jumps times, jump sizes and volatility are particularly useful for disentangling the dynamic effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998. Using both formal and informal diagnostics, we find strong evidence for jumps in volatility, even after accounting for jumps in returns. We use implied volatility curves computed from option prices to judge the economic differences between the models. Finally, we evaluate the impact of estimation risk on option prices and find that the uncertainty in estimating the parameters and the spot volatility has important, though very different, effects on option prices.
Testing for Self-exciting Jumps in Bitcoin Returns
Author : Chuanhai Zhang
Publisher :
Page : 27 pages
File Size : 25,36 MB
Release : 2020
Category :
ISBN :
Book Description
Cryptocurrencies, especially Bitcoin (BTC), have drawn extraordinary worldwide attention. The characteristics of the BTC include a high level of speculation, extreme volatility and price discontinuity. In this paper, we investigate the self-excitation jumps in Bitcoin prices by using a new nonparametric self-excitation jumps test proposed by Boswijk et al. (2018). This paper investigates the strength of the self-excitation, the asymmetry between self-excitation triggered by positive and negative jumps and the possible different features of self-excitation in bear and bull markets. We summarize the main findings as follows. (1) There exists some degree of self-excitation effects in Bitcoin returns, which do not increase monotonically with jump size; the most self-excitation events occur with mild-sized jumps. (2) There exists asymmetry phenomenon between self-excitation when news is good and bad, i.e., the proportion of self-excitation triggered by negative jumps is larger than positive jumps. (3) Self-excitation activities are different in bear and bull markets. (4) Further empirical results show that the self-excitation effects are more pronounced if we detect the locations of jumps before implementing the self-excitation tests. The empirical findings in this paper has great significance for risk management and Bitcoin options pricing that takes into account self-exciting jump clustering.
A Multifactor Self-Exciting Jump Diffusion Approach for Modelling the Clustering of Jumps in Equity Returns
Author : Donatien Hainaut
Publisher :
Page : 52 pages
File Size : 40,22 MB
Release : 2017
Category :
ISBN :
Book Description
This paper introduces a new jump diffusion process where the occurrence and the size of past jumps have an impact on both the instantaneous and the long term propensities of observing a jump instantaneously. Here, the intensity of jump arrival is a multifactor self-excited process whereas the jump size is a double exponential random variable. This specification capture many dynamic features of asset returns; it can for instance handle with the jump clustering effects explored by Ait-Sahalia et al. (2015). Moreover, it remains analytically tractable, as we can prove that these multifactor self-excited processes are similar to single factor processes whose kernel function is the sum of two exponential functions. We can derive various closed and semi-closed form expressions for the mean and the variance of the intensity as well as for the moment generating of log returns. We also find a class of changes of measure that preserves the dynamics of the process under the risk neutral measure. To motivate empirically the multifactor model, we calibrate the model by a peak over threshold approach and filter state variables by sequential Monte Carlo algorithm. We also investigate if self-excitation is induced by positive, negative or both jumps. So as to illustrate the applicability of our modeling for derivatives, we next evaluate European options and analyze the sensitivity of implied volatilities to parameters and factors.
Causality Effect of Returns, Continuous Volatility and Jumps : Evidence from the U.S. and European Index Futures Markets
Author : 廖志偉
Publisher :
Page : pages
File Size : 35,34 MB
Release : 2017
Category :
ISBN :
Book Description
Modeling Financial Contagion Using Mutually Exciting Jump Processes
Author : Yacine Aït-Sahalia
Publisher :
Page : 0 pages
File Size : 50,43 MB
Release : 2010
Category : Economics
ISBN :
Book Description
Abstract: Adverse shocks to stock markets propagate across the world, with a jump in one region of the world seemingly causing an increase in the likelihood of a different jump in another region of the world. To capture this effect mathematically, we introduce a model for asset return dynamics with a drift component, a volatility component and mutually exciting jumps known as Hawkes processes. In the model, a jump in one region of the world or one segment of the market increases the intensity of jumps occurring both in the same region (self-excitation) as well as in other regions (cross-excitation). The model generates the type of jump clustering that is observed empirically. Jump intensities then mean-revert until the next jump. We develop and implement an estimation procedure for this model. Our estimates provide evidence for self-excitation both in the US market as well as in other world markets. Furthermore, we find that US jumps tend to get reflected quickly in most other markets, while statistical evidence for the reverse transmission is much less pronounced. Implications of the model for measuring market stress, risk management and optimal portfolio choise are also investigated
Hidden Correlations
Author : Laura Ballotta
Publisher :
Page : 33 pages
File Size : 18,38 MB
Release : 2018
Category :
ISBN :
Book Description
The aim of this paper is to investigate the dependence between exchange rates and their volatility from the information synthesised into currency options quotes. To this purpose, we propose an affine stochastic volatility model with self-exciting structure under a timechanged pure jump Lévy framework. In particular, we construct a mechanism inducing dependence effects via systematic jumps. The performance analysis shows that this factor construction marginally improves the pricing of FX options in terms of calibration and fit of the implied volatility surface, indicating that this dependence is of moderate nature. Therefore, we have evidence to claim that there exists a mild correlation between exchange rates and their volatility.
Continuous Time Processes for Finance
Author : Donatien Hainaut
Publisher : Springer Nature
Page : 359 pages
File Size : 13,79 MB
Release : 2022-08-25
Category : Mathematics
ISBN : 3031063619
Book Description
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.
An Introduction to the Theory of Point Processes
Author : D.J. Daley
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 37,62 MB
Release : 2006-04-10
Category : Mathematics
ISBN : 0387215646
Book Description
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes)
Author : Cheng Few Lee
Publisher : World Scientific
Page : 5053 pages
File Size : 50,51 MB
Release : 2020-07-30
Category : Business & Economics
ISBN : 9811202400
Book Description
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.
