MULTIFRACTAL VOLATILITY THEORY FORECASTING AND PRICING FREE DOWNLOAD

Within any bounded time interval, there exists almost surely a. The multifrequency nature of volatility is consistent with the intuition that economic shocks have highly heterogeneous degrees of persistence. Multifrequency risk is easily incorporated into the drift of fundamentals, such as aggregate consumption and dividend news. Changes in the drift or volatility of fundamentals are very rare, but produce extreme asset returns in equilibrium when they do occur. The conditional discount rate moves slowly because it is dominated by the most persistent volatility components. Because it is based on a Markov chain, MSM is a highly tractable multifrequency stochastic volatility model.

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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.

Multifractal Volatility: Theory, Forecasting, and Pricing

This generates large feedback and a reasonable equity premium with moderate values of relative risk aversion. The weights are nonnegative and add up to one. An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. This suggests investigation of the tails of the data. Thus, the implied univariate volatility dynamics are smoother than standard MSM, but can still generate thick tails and long-memory volatility persistence.

The material in this chapter appeared in an earlier form in Journal of Mathematical Economics, 44, L. Part III of this book considers equilibrium valuation in greater detail.

Multifractal Volatility: Theory, Forecasting and Pricing

Panel A shows the forecasting R2 for each model. For each currency, this table reports the standard deviation of daily returns in percent over the entire subsample and over four evenly spaced subsamples. The construction of MSM is described in Chapter 3.

The conditional probability vector is computed recursively. We refer the reader to Bacry, Kozhemyak and Muzy for an excellent review of these developments.

In contrast, multifractal measures contain a continuum of local scales. Long memory in continuous time stochastic volatility models.

Journal of Financial Econometrics 4: Individual consumption coincides with individual income: Asymptotic standard errors are in parentheses. The conditional variance ht follows the autoregressive process: The estimates are obtained by maximizing the full likelihood of bivariate MSM, as described multifractall Section 4.

This result holds for both conservative and canonical measures.

Multifractal Volatility: Theory, Forecasting and Pricing

In practice, the multifractal approach is implemented as so-called Markov-Switching Multifractal model MSM in discrete time. The result is masterful and convincing, particularly for capturing return risk over multiple time horizons. If volatility increases, investors may observe a single extreme realization of the signal that is implausible under their existing beliefs. Since this requires adding only one more parameter from two to threethe increase in likelihood is large by any standard model selection criterion.

These features are consistent with the intuition that low-frequency volatility changes are infrequent but have a large price impact. Acknowledgments Our interest in fractal modeling was spurred during our graduate years at Yale by conversations with Be FisherJournal of Mathematical Economics, The smoothed conditional return in the second panel of Figure 9.

The parameter estimates in Table 9. The construction can accommodate various hypotheses about the joint distribution of the multipliers M0. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. The second and third panels of Table 4.

At short horizons, returns tend to be either close to the mean or to take large values.

In particular, for self-similar processes the scaling function has to be linear. Multifrequency News and Stock Returns Consistent with earlier research e.