Nonparametric Estimation In Model With Levy Type Jumps And Stochastic Volatility
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High-Frequency Financial Econometrics
| Author | : Yacine Aït-Sahalia |
| Publisher | : Princeton University Press |
| Total Pages | : 683 |
| Release | : 2014-07-21 |
| Genre | : Business & Economics |
| ISBN | : 0691161437 |
A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.
Parameter Estimation in Stochastic Volatility Models
| Author | : Jaya P. N. Bishwal |
| Publisher | : Springer Nature |
| Total Pages | : 634 |
| Release | : 2022-08-06 |
| Genre | : Mathematics |
| ISBN | : 3031038614 |
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Handbook of Computational Finance
| Author | : Jin-Chuan Duan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 791 |
| Release | : 2011-10-25 |
| Genre | : Business & Economics |
| ISBN | : 3642172547 |
Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods
| Author | : Milan Fičura |
| Publisher | : |
| Total Pages | : 25 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
We are comparing two approaches for stochastic volatility and jumps estimation in the EUR/USD time series - the non-parametric power-variation approach using high-frequency returns, and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We find that both of the methods do identify continuous stochastic volatility similarly, but they do not identify similarly the jump component. Firstly - the jumps estimated using the non-parametric high-frequency estimators are much more numerous than in the case of the Bayesian method using daily data. More importantly - we find that the probabilities of jump occurrences assigned to every day by both of the methods are virtually no rank-correlated (Spearman rank correlation is 0.0148) meaning that the two methods do not identify jumps at the same days. Actually the jump probabilities inferred using the non-parametric approach are not much correlated even with the daily realized variance and the daily squared returns, indicating that the discontinuous price changes (jumps) observed on high-frequencies may not be distinguishable (from the continuous volatility) on the daily frequency. As an additional result we find strong evidence for jump size dependence and jump clustering (based on the self-exciting Hawkes process) of the jumps identified using the non-parametric method (the shrinkage estimator).
