Approximating Volatility Diffusions with Cev-Arch Models PDF Download
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Author: Fabio Fornari
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
Aim of this article is to judge the empirical performance of Arch as diffusion approximations to models of the short-term rate with stochastic volatility and as filters of the unobserved volatility. We show that the estimation of the continuous time scheme to which a discrete time Arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time coefficients. A natural substitute of a global specification test for just-identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias. Unlike previous literature in which standard Arch models approximated only specific diffusions, our estimation strategy relies on a new Arch model that approximates any CEV-diffusion model for the conditional volatility. A Monte-Carlo study reveals that the filtering performances of this model are remarkably good, even in the presence of an important kind of misspecification.
Author: Fabio Fornari
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
Aim of this article is to judge the empirical performance of Arch as diffusion approximations to models of the short-term rate with stochastic volatility and as filters of the unobserved volatility. We show that the estimation of the continuous time scheme to which a discrete time Arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time coefficients. A natural substitute of a global specification test for just-identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias. Unlike previous literature in which standard Arch models approximated only specific diffusions, our estimation strategy relies on a new Arch model that approximates any CEV-diffusion model for the conditional volatility. A Monte-Carlo study reveals that the filtering performances of this model are remarkably good, even in the presence of an important kind of misspecification.
Author: Fabio Fornari
Publisher:
ISBN:
Category : Interest rates
Languages : en
Pages : 76
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Book Description
Author: Fabio Fornari
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Aim of this article is to judge the empirical performance of Arch as diffusion approximations to models of the short-term rate with stochastic volatility and as filters of the unobserved volatility. We show that the estimation of the continuous time scheme to which a discrete time Arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time coefficients. A natural substitute of a global specification test for just-identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias. Unlike previous literature in which standard Arch models approximated only specific diffusions, our estimation strategy relies on a new Arch that approximates any Cev-diffusion model for the conditional volatility. A Monte-Carlo study reveals that the filtering performances of this model is remarkably good, even in the presence of an important kind of misspecification.
Author: G. Gregoriou
Publisher: Springer
ISBN: 0230625843
Category : Business & Economics
Languages : en
Pages : 401
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Book Description
This important book brings together an edited series of papers about risk management and the latest developments in the field. Covering topics such as Stochastic Volatility, Risk Dynamics and Portfolio Diversification, this book is vital for optimal portfolio allocation for private and institutional investors, and is an indispensable tool.
Author: Fabio FORNARI
Publisher:
ISBN:
Category :
Languages : en
Pages : 68
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Book Description
Author: Robert F. Engle
Publisher:
ISBN:
Category : Diffusion processes
Languages : en
Pages : 34
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Book Description
Author: Yacine Ait-Sahalia
Publisher: Elsevier
ISBN: 0080929842
Category : Business & Economics
Languages : en
Pages : 809
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Book Description
This collection of original articles—8 years in the making—shines a bright light on recent advances in financial econometrics. From a survey of mathematical and statistical tools for understanding nonlinear Markov processes to an exploration of the time-series evolution of the risk-return tradeoff for stock market investment, noted scholars Yacine Aït-Sahalia and Lars Peter Hansen benchmark the current state of knowledge while contributors build a framework for its growth. Whether in the presence of statistical uncertainty or the proven advantages and limitations of value at risk models, readers will discover that they can set few constraints on the value of this long-awaited volume. Presents a broad survey of current research—from local characterizations of the Markov process dynamics to financial market trading activity Contributors include Nobel Laureate Robert Engle and leading econometricians Offers a clarity of method and explanation unavailable in other financial econometrics collections
Author: John B. Guerard, Jr.
Publisher: Springer
ISBN: 3319339761
Category : Business & Economics
Languages : en
Pages : 480
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Book Description
This volume, inspired by and dedicated to the work of pioneering investment analyst, Jack Treynor, addresses the issues of portfolio risk and return and how investment portfolios are measured. In a career spanning over fifty years, the primary questions addressed by Jack Treynor were: Is there an observable risk-return trade-off? How can stock selection models be integrated with risk models to enhance client returns? Do managed portfolios earn positive, and statistically significant, excess returns and can mutual fund managers time the market? Since the publication of a pair of seminal Harvard Business Review articles in the mid-1960’s, Jack Treynor has developed thinking that has greatly influenced security selection, portfolio construction and measurement, and market efficiency. Key publications addressed such topics as the Capital Asset Pricing Model and stock selection modeling and integration with risk models. Treynor also served as editor of the Financial Analysts Journal, through which he wrote many columns across a wide spectrum of topics. This volume showcases original essays by leading researchers and practitioners exploring the topics that have interested Treynor while applying the most current methodologies. Such topics include the origins of portfolio theory, market timing, and portfolio construction in equity markets. The result not only reinforces Treynor’s lasting contributions to the field but suggests new areas for research and analysis.
Author: Carl J. Ullrich
Publisher:
ISBN:
Category :
Languages : en
Pages : 38
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Book Description
How does currency return volatility evolve over time and what are the properties of volatility dynamics? What forms of non-linearities are admitted in the drift and diffusion functions? The purpose of this study is to estimate a large class of volatility processes and explore these issues using weekly observations on U.S. dollar-based Japanese yen and British pound options data. The approach is based on maximum-likelihood estimation that relies on closed-form density approximations (Ait-Sahalia, 1999; Ait-Sahalia, 2002). Based on volatility implied by currency options, the affine square root specification for the variance of variance function commonly adapted in the literature is misspecified. The constant elasticity of variance (CEV) specification provides a reasonable characterization of the variance of variance function. Unlike previous findings for equity volatility, extending the diffusion function beyond the CEV specification does not improve the fit of the model, regardless of the assumed form of the drift function.
Author: Alexandre Antonov
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Stochastic volatility models are widely used in interest rate modeling to match the option smiles -- the two most popular are the Heston model and the SABR one. These have been incorporated into arbitrage-free term structure frameworks, Heston-LMM and SABR-LMM respectively.In this paper we consider the CEV model with a general stochastic volatility. Assuming that rate-volatility correlation is zero we are able to obtain an exact integral representation of the option price provided that we have a closed form for a Moment Generating Function of the cumulative stochastic variance or of its inverse. Using this result we derive explicit solutions in terms of two-dimensional integral for both CEV-CIR model (or power generalization of the Heston) and the SABR one. Moreover the results in this paper may be easily extended to any affine process (possibly multi-factor and including jumps) leading to numerous practical applications.
