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Author: Josep Perelló
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.
Author: Josep Perelló
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.
Author: Jaume Masoliver
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.
Author: Eric T. Hillebrand
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find this short correlation time scale in six different daily financial time series and use it to improve the short-term forecasts from GARCH models. We study different generalizations of GARCH that allow for several time scales. On our holding sample, none of the considered models can fully exploit the information contained in the short scale. Wavelet analysis shows a correlation between fluctuations on long and on short scales. Models accounting for this correlation as well as long memory models for absolute returns appear to be promising.
Author: Jean-Philippe Bouchaud
Publisher: Cambridge University Press
ISBN: 9780521819169
Category : Business & Economics
Languages : en
Pages : 410
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Book Description
Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.
Author: Alireza Javaheri
Publisher: John Wiley & Sons
ISBN: 111894397X
Category : Business & Economics
Languages : en
Pages : 325
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Book Description
A new, more accurate take on the classical approach to volatility evaluation Inside Volatility Filtering presents a new approach to volatility estimation, using financial econometrics based on a more accurate estimation of the hidden state. Based on the idea of "filtering", this book lays out a two-step framework involving a Chapman-Kolmogorov prior distribution followed by Bayesian posterior distribution to develop a robust estimation based on all available information. This new second edition includes guidance toward basing estimations on historic option prices instead of stocks, as well as Wiener Chaos Expansions and other spectral approaches. The author's statistical trading strategy has been expanded with more in-depth discussion, and the companion website offers new topical insight, additional models, and extra charts that delve into the profitability of applied model calibration. You'll find a more precise approach to the classical time series and financial econometrics evaluation, with expert advice on turning data into profit. Financial markets do not always behave according to a normal bell curve. Skewness creates uncertainty and surprises, and tarnishes trading performance, but it's not going away. This book shows traders how to work with skewness: how to predict it, estimate its impact, and determine whether the data is presenting a warning to stay away or an opportunity for profit. Base volatility estimations on more accurate data Integrate past observation with Bayesian probability Exploit posterior distribution of the hidden state for optimal estimation Boost trade profitability by utilizing "skewness" opportunities Wall Street is constantly searching for volatility assessment methods that will make their models more accurate, but precise handling of skewness is the key to true accuracy. Inside Volatility Filtering shows you a better way to approach non-normal distributions for more accurate volatility estimation.
Author: Tim Bollerslev
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
We examine the relationship between volatility and past and future returns in high-frequency equity market data. Consistent with a prolonged leverage effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be significantly negative for several days, while the reverse cross-correlations between absolute returns and future returns are generally negligible. Based on a simple aggregation formula, we demonstrate how the high-frequency data may similarly be used in more effectively assessing volatility asymmetries over longer daily return horizons. Motivated by the striking cross-correlation patterns uncovered in the high-frequency data, we investigate the ability of some popular continuous-time stochastic volatility models for explaining the observed asymmetries. Our results clearly highlight the importance of allowing for multiple latent volatility factors at very fine time scales in order to adequately describe and understand the patterns in the data.
Author: Riccardo Rebonato
Publisher: John Wiley & Sons
ISBN: 0470091401
Category : Business & Economics
Languages : en
Pages : 864
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Book Description
In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School
Author: Gilles Zumbach
Publisher: Springer Science & Business Media
ISBN: 3642317413
Category : Business & Economics
Languages : en
Pages : 326
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Book Description
This book surveys empirical properties of financial time series, discusses their mathematical basis, and describes uses in risk evaluation, option pricing or portfolio construction. The author introduces and assesses a range of processes against the benchmark.
Author: Amaan Mehrabian
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
A striking empirical feature of many financial time series is that when the price drops, the future volatility increases. This negative correlation between the financial return and future volatility processes was initially addressed in Black 76 and explained based on financial leverage, or a firm's debt-to-equity ratio: when the price drops, financial leverage increases, the firm becomes riskier, and hence, the future expected volatility increases. The phenomenon is, therefore, traditionally been named the leverage effect. In a discrete time Stochastic Volatility (SV) model framework, the leverage effect is often modelled by a negative correlation between the innovation processes of return and volatility equations. These models can be represented as state space models in which the returns and the volatilities are considered as the observed and the latent state variables respectively. Including the leverage effect in the SV model not only results in a better fit ...
Author: Johannes Voit
Publisher: Springer Science & Business Media
ISBN: 3662051257
Category : Mathematics
Languages : en
Pages : 298
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Book Description
This textbook describes parallels between statistical physics and finance - both those established in the 100-year-long interaction between these disciplines, as well as new research results on capital markets. The random walk, well known in physics, is also the basic model in finance, upon which are built, for example, the Black--Scholes theory of option pricing and hedging, or methods of risk control using diversification. Here the underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated. Computer simulations of interacting agent models of financial markets provide insights into the origins of asset price fluctuations. Stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes. These models allow for predictions. This study edition has been updated with a presentation of several new and significant developments, e.g. the dynamics of volatility smiles and implied volatility surfaces, path integral approaches to option pricing, a new and accurate simulation scheme for options, multifractals, the application of nonextensive statistical mechanics to financial markets, and the minority game. Moreover, the book was scanned for and corrected from errors, both typographical and in presentation.
