Multiple Time Scales In Volatility And Leverage Correlations PDF Download
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| Author | : Josep Perelló |
| Publisher | : |
| Total Pages | : 19 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
Download Multiple Time Scales in Volatility and Leverage Correlations Book in PDF, ePub and Kindle
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 | : Eric T. Hillebrand |
| Publisher | : |
| Total Pages | : 40 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
Download Overlaying Time Scales in Financial Volatility Data Book in PDF, ePub and Kindle
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 | : Jaume Masoliver |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 2005 |
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| ISBN | : |
Download Multiple Time Scales and the Exponential Ornstein-Uhlenbeck Stochastic Volatility Model Book in PDF, ePub and Kindle
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 | : Tim Bollerslev |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 2008 |
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| ISBN | : |
Download Leverage and Volatility Feedback Effects in High-Frequency Data Book in PDF, ePub and Kindle
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 | : Lan Zhang |
| Publisher | : |
| Total Pages | : |
| Release | : 2003 |
| Genre | : Economics |
| ISBN | : |
Download A Time of Two Time Scales Book in PDF, ePub and Kindle
| Author | : Amaan Mehrabian |
| Publisher | : |
| Total Pages | : |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
Download The Leverage Effect in Stochastic Volatility Book in PDF, ePub and Kindle
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 | : Lan Zhang |
| Publisher | : |
| Total Pages | : 29 |
| Release | : 2003 |
| Genre | : Rate of return |
| ISBN | : |
Download A Tale of Two Time Scales Book in PDF, ePub and Kindle
It is a common practice in finance to estimate volatility from the sum of frequently-sampled squared returns. However market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. This work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the usual' volatility estimator fails when the returns are sampled at the highest frequency.
| Author | : Roger Lee |
| Publisher | : |
| Total Pages | : 15 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Download How Leverage Shifts and Scales a Volatility Skew Book in PDF, ePub and Kindle
To model leveraged investments such as leveraged ETFs, define the beta-leveraged product on a positive semimartingale S to be the stochastic exponential of beta times the stochastic logarithm of S.In various asymptotic regimes, we relate rigorously the implied volatility surfaces of the beta-leveraged product and the underlying S, via explicit shifting/scaling transformations. In particular, a family of regimes with jump risk admit a shift coefficient of -3/2, unlike the previously conjectured 1/2 shift. The 1/2, we prove, holds in a family of continuous (including fBm-driven) stochastic volatility regimes at short expiry and at small volatility-of-volatility. In another regime, which does not admit a simple spatial shifting/scaling rule, we find an expiry scaling together with a spatial transformation.
| Author | : Feiyue Di |
| Publisher | : |
| Total Pages | : 123 |
| Release | : 2011 |
| Genre | : |
| ISBN | : 9781124773117 |
Download Multiple Time Scales Stochastic Volatility Modeling Method in Heath-jarrow-morton Model of Interest Rate Market Book in PDF, ePub and Kindle
We utilize multiple time scales processes in consistent dynamic modeling to capture main time scales and heterogeneity features of the volatility process of Heath-Jarrow-Moton models in the fixed income market. The Black-Scholes type HJM models are prevailing in both industry and academy. However since these models assume that the volatility process of the underlying financial contract is constant during the term period, they are not able to incorporate some implied volatility phenomenons emerging after the Crash of 1987. Stochastic volatility modeling is one of the main approach to overcome the above defects of the Black-Scholes type models. By applying the time scale separation, that is, the singular perturbation method, we show that the stochastic volatility HJM model we proposed are parsimonious and robust effective models. In fact, we carry out this framework on the linear finite dimensional realizable HJM models, derive the explicit pricing formulas of floorlet contracts under this stochastic volatility HJM models and estimate the accuracy of the result. Meanwhile, as a specific example, we studied the stochastic volatility Hull-White model explicitly. Besides the pricing function of the floorlet contracts, we also obtain the explicit form of the pricing function of the swaption. Following the calibration procedures we proposed, we calibrated this model by a group of daily swaption data from PIMCO. The calibration result shows that the mutliple time scales stochastic volatility Hull-White model is able to capture the implied volatility smile and this model is stable statically.
| Author | : Ramazan Gencay |
| Publisher | : |
| Total Pages | : 40 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
Download Asymmetry of Information Flow between Volatilities Across Time Scales Book in PDF, ePub and Kindle
Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and consequently, the calculation of risk at different time scales.
