|
 7:39 PM (1 minute ago)
|
|
||
|
||||
Dear Professor Donoho,
Sir, the attached article describes the modern (post scale-free) network theory with basic material and then they fully focus on theory for scale-free networks. Given such attention to these, it is perhaps worthwhile to explain what makes our market graph of interest for a scientific study of global volatility. There is no natural ‘space’ between assets in the financial market. One has some obvious options to create edges between asset nodes. The most obvious to the professional financial practitioner will be the correlation not of volatilities but returns. This is certainly a good approach to create a complex network for financial assets but I believe that it is more natural to use the correlations between stochastic volatility. This is because these correlations give us an indication of any volatility spillover effects. For N assets the correlation of volatilities is NxN and we have just thresholded the off-diagonal elements by three standard deviations of the empirical correlation matrix entries. This is a perfectly natural way to define a market graph/network. This is a dense graph with no power law distribution but a visible spectrum of degree clustering at multiple sites.In standard courses on social network analysis several other metrics are used to characterize the network structure. Generally missing from this list seems to be the Laplace spectrum of the graph. The Chatterjee-Diaconis paper addresses other issues of the statistical foundations and results for specified degree structure and prove that for the so-called beta model with is just an implicit log-linear model for the Bernoulli probabilities for edge-existence by normalized products of weights put on vertices. It is shown by Olhede-Wolfe that from the point of view of maximum likelihood estimation of these parameters the model of using degree weights on vertices is similar statistically. The Chatterjee-Diaconis result guarantees that there is a surjection of beta-parameter space and all possible degree distributions on the graph.
The reason I believe that the Laplace spectrum and its statistics are probably fundamental is because they clearly affect the differential equations on the graph of the form
(d/dt – Laplacian)u = F(u)
which are our primary models for volatility, perhaps to be modified based on bad residuals.
2 Attachments
Preview attachment Screenshot from 2015-06-06 19:32:23.png
Screenshot from 2015-06-06 19:32:23.png
Preview attachment evolution_of_networks.pdf
|
7:43 PM (1 hour ago)
|
|
||
|
||||
|
9:20 PM (5 minutes ago)
|
|
||
|
||||
Sir the degree distributions of the complex networks of Barbasi-Albert are plotted in the snapshot attached. This conclusively shows that our market network do not fall into the paradigm that Barbasi-Albert et. al. has established late 1990s onward. This complex network of financial markets is important enough to deserve careful theory, and this is something I believe I can work on successfully in a reasonable span of time in academic detail.
Attachments area
evolution_of_networks.pdf
Advertisements
Reader
Leave a Reply