Author: Mawuli SegnonPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Multifractal Models, Intertrade Durations and Return Volatility
Author: Mawuli SegnonMultifractal Models, Intertrade Durations and Return Volatility
Author: Multifractal Volatility
Author: Laurent E. CalvetPublisher: Academic Press
ISBN: 0080559964
Category : Business & Economics
Languages : en
Pages : 273
Book Description
Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime changes of heterogeneous durations. Using the intuition that some economic phenomena are long-lasting while others are more transient, they permit regimes to have varying degrees of persistence. By drawing on insights from the use of multifractals in the natural sciences and mathematics, they show how to construct high-dimensional regime-switching models that are easy to estimate, and substantially outperform some of the best traditional forecasting models such as GARCH. The goal of Multifractal Volatility is to popularize the approach by presenting these exciting new developments to a wider audience. They emphasize both theoretical and empirical applications, beginning with a style that is easily accessible and intuitive in early chapters, and extending to the most rigorous continuous-time and equilibrium pricing formulations in final chapters. Presents a powerful new technique for forecasting volatility Leads the reader intuitively from existing volatility techniques to the frontier of research in this field by top scholars at major universities The first comprehensive book on multifractal techniques in finance, a cutting-edge field of research
Volatility Forecasting with the Multifractal Model of Asset Returns
Author: Terrence Y. ZhangPublisher:
ISBN:
Category :
Languages : en
Pages : 24
Book Description
This paper presents an empirical application of the Multifractal Model of Asset Returns (MMAR) to intraday stock prices, with a goal of generating accurate volatility forecasts. Intraday stock volatility exhibits long tails, persistence, and strong evidence of moment scaling. This allows us to apply the MMAR. A forecasting method for the MMAR is implemented through Monte Carlo simulation, and this forecasting method is compared to Generalized Autoregressive Conditional Heteroskedasticity (GARCH) alternatives over several testing samples. The MMAR significantly outperformed the GARCH models. This suggests that the framework of multifractality has a large potential for further development and application within finance.
A Multifractal Model of Assets Returns
Author: Laurent E. CalvetPublisher:
ISBN:
Category :
Languages : en
Pages : 56
Book Description
This paper investigates the Multifractal Model of Asset Returns, a continuous-time process that incorporates the thick tails and volatility persistence exhibited by many financial time series. The model is constructed by compounding a Brownian Motion with a multifractal time-deformation process. Return moments scale as a power law of the time horizon, a property confirmed for Deutschemark / U.S. Dollar exchange rates and several equity series. The model implies semi-martingale prices and thus precludes arbitrage in a standard two-asset economy. Volatility has long-memory, and the highest finite moment of returns can have any value greater than two. The local variability of the process is characterized by a renormalized probability density of local Houml;lder exponents. Unlike standard models, multifractal paths contain a multiplicity of these exponents within any time interval. We develop an estimation method, and infer a parsimonious generating mechanism for the exchange rate series. Simulated samples replicate the moment-scaling found in the data.
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II
Author: David CarfiPublisher: American Mathematical Soc.
ISBN: 0821891480
Category : Mathematics
Languages : en
Pages : 384
Book Description
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
New Advances in Statistics and Data Science
Author: Ding-Geng ChenPublisher: Springer
ISBN: 3319694162
Category : Mathematics
Languages : en
Pages : 355
Book Description
This book is comprised of the presentations delivered at the 25th ICSA Applied Statistics Symposium held at the Hyatt Regency Atlanta, on June 12-15, 2016. This symposium attracted more than 700 statisticians and data scientists working in academia, government, and industry from all over the world. The theme of this conference was the “Challenge of Big Data and Applications of Statistics,” in recognition of the advent of big data era, and the symposium offered opportunities for learning, receiving inspirations from old research ideas and for developing new ones, and for promoting further research collaborations in the data sciences. The invited contributions addressed rich topics closely related to big data analysis in the data sciences, reflecting recent advances and major challenges in statistics, business statistics, and biostatistics. Subsequently, the six editors selected 19 high-quality presentations and invited the speakers to prepare full chapters for this book, which showcases new methods in statistics and data sciences, emerging theories, and case applications from statistics, data science and interdisciplinary fields. The topics covered in the book are timely and have great impact on data sciences, identifying important directions for future research, promoting advanced statistical methods in big data science, and facilitating future collaborations across disciplines and between theory and practice.
The Oxford Handbook of Computational Economics and Finance
Author: Shu-Heng ChenPublisher: Oxford University Press
ISBN: 0199844380
Category : Business & Economics
Languages : en
Pages : 785
Book Description
The Oxford Handbook of Computational Economics and Finance provides a survey of both the foundations of and recent advances in the frontiers of analysis and action. It is both historically and interdisciplinarily rich and also tightly connected to the rise of digital society. It begins with the conventional view of computational economics, including recent algorithmic development in computing rational expectations, volatility, and general equilibrium. It then moves from traditional computing in economics and finance to recent developments in natural computing, including applications of nature-inspired intelligence, genetic programming, swarm intelligence, and fuzzy logic. Also examined are recent developments of network and agent-based computing in economics. How these approaches are applied is examined in chapters on such subjects as trading robots and automated markets. The last part deals with the epistemology of simulation in its trinity form with the integration of simulation, computation, and dynamics. Distinctive is the focus on natural computationalism and the examination of the implications of intelligent machines for the future of computational economics and finance. Not merely individual robots, but whole integrated systems are extending their "immigration" to the world of Homo sapiens, or symbiogenesis.
Multifractality and Long-range Dependence of Asset Returns
Author: Ruipeng LiuForecasting Multifractal Volatility
Author: Laurent E. CalvetPublisher:
ISBN:
Category :
Languages : en
Pages : 48
Book Description
This paper develops analytical methods to forecast the distribution of future returns for a new continuous-time process, the Poisson multifractal. Out model captures the thick tails and volatility persistence exhibited by many financial time series. We assume that the forecaster knows the true generating process with certainty, but only observes past returns. The challenge in this environment is long memory and the corresponding infinite dimension of the state space. We show that a discretized version of the model has a finite state space, which allows an analytical solution to the conditioning problem. Further, the discrete model converges to the continuous-time model as time scale goes to zero, so that forecasts are consistent. The methodology is implemented on simulated data calibrated to the Deutschemark/US Dollar exchange rate. Applying these results to option pricing, we find that the model captures both volatility smiles and long-memory in the term structure of implied volatilities.