
11:47 PM (0 minutes ago)



Let v(t) be a univariate volatility series. Then we calculate phi(v(t)) which I have seen appears as a some parametric function of t which is not quite a power law. We optimize an excess(v,alpha,beta) function by some Lp norm
excess(v,alpha,beta) = (d/dt)^alpha v + (Laplacian)^beta v
If the minimum is achieved for alpha0 and beta0, then we have the candidate for the NavierStokes type term. It may simply be not significant but it would be a surprise to me obviously. If it is expressible as a function of say like the NavierStokes term which is not even sensible of course without a ‘space’ variable. This simple test can begin the foray into this project of seeking thresholds for phase transition to turbulence in volatility now here Laplacian needs interpretation. We have the market graph. This is where we can begin seeking some laws for volatility. I am serious sir because it is impossible that volatility follows diffusion and calm water effects. Otherwise the financial volatility cascading etc published in Nature since 19956 or earlier would make little sense. Onsager’s vortex formation model is my inspiration here and for the actual 2D pointvertex model he was able to explain formation of new vortices from the NavierStokes PDE directly.
Leave a Reply