We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are validated against real data. Our empirical studies of order flow uncover several interesting regularities in the way trading orders are placed and cancelled. The resulting simple model of order flow is used to simulate price formation under a continuous double auction, and the statistical properties of the resulting simulated sequence of prices are compared to those of real data. The model is constructed using one stock (AZN) and tested on 24 other stocks. For low volatility, small tick size stocks (called Group I) the predictions are very good, but for stocks outside Group I they are not good. For Group I, the model predicts the correct magnitude and functional form of the distribution of the volatility and the bid-ask spread, without adjusting any parameters based on prices. This suggests that at least for Group I stocks, the volatility and heavy tails of prices are related to market microstructure effects, and supports the hypothesis that, at least on short time scales, the large fluctuations of absolute returns are well described by a power law with an exponent that varies from stock to stock.

An empirical behavioral model of liquidity and volatility

The linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach 2:5, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average ?17% faster than the most unstable sinuous mode and ?30 times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growthrates registered in the presence of the roughness element, an amplification factor of N D 9 is reached within ?50 roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

/pdf/laminar-turbulent-transition-induced-by-a-discrete-roughness-4bgyslh1ak.pdf

Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer

Advances in switchable and highly insulating autonomous (self-powered) glazing systems for adaptive low energy buildings

Optical and thermal performance of glazing units containing PCM in buildings: A review

We investigate the nonlinear patterns of volatility in seven Bitcoin markets. In particular, we explore the fractional long-range dependence in conjunction with the potential inherent stochasticity of volatility time series under four diverse distributional assumptions, i.e., Normal, Student-t, Generalized Error (GED), and t-Skewed distribution. Our empirical findings signify the existence of long-range memory in Bitcoin market volatility, irrespectively of distributional inference. The same applies to entropy measurement, which indicates a high degree of randomness in the estimated series. As Bitcoin markets are highly disordered and risky, they cannot be considered suitable for hedging purposes. Our results provide strong evidence against the efficient market hypothesis.

Long-range memory, distributional variation and randomness of bitcoin volatility

It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundstrom theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resulting finite-difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree.

By following the philosophy behind the Chebyshev polynomials, a non-uniform grid for piecewise polynomial interpolations of degree q⩽N is introduced in this paper, where N + 1 is the total number of grid nodes. It is shown that when q=N, this polynomial interpolation coincides with the Chebyshev interpolation, and the resulting finite-difference schemes are equivalent to Chebyshev collocation methods. Finally, test cases are run showing how stability and correct transient behaviours are achieved for any degree q<N through the use of the proposed non-uniform grids. Discussions are complemented by spectra and pseudospectra of the finite-difference operators. Copyright © 2007 John Wiley & Sons, Ltd.

/pdf/stable-high-order-finite-difference-methods-based-on-non-264krktp1a.pdf

Juan A. Hernández

Papers

Stable high‐order finite‐difference methods based on non‐uniform grid point distributions

Solar heat gain coefficient of water flow glazings

Analytical solution to the one-dimensional non-uniform absorption of solar radiation in uncoated and coated single glass panes

Analytical solutions to evaluate solar radiation overheating in simplified glazed rooms

Spectral problem for water flow glazings