30 research outputs found
Clearing price distributions in call auctions
We propose a model for price formation in financial markets based on clearing
of a standard call auction with random orders, and verify its validity for
prediction of the daily closing price distribution statistically. The model
considers random buy and sell orders, placed following demand- and supply-side
valuation distributions; an equilibrium equation then leads to a distribution
for clearing price and transacted volume. Bid and ask volumes are left as free
parameters, permitting possibly heavy-tailed or very skewed order flow
conditions. In highly liquid auctions, the clearing price distribution
converges to an asymptotically normal central limit, with mean and variance in
terms of supply/demand-valuation distributions and order flow imbalance. By
means of simulations, we illustrate the influence of variations in order flow
and valuation distributions on price/volume, noting a distinction between high-
and low-volume auction price variance. To verify the validity of the model
statistically, we predict a year's worth of daily closing price distributions
for 5 constituents of the Eurostoxx 50 index; Kolmogorov-Smirnov statistics and
QQ-plots demonstrate with ample statistical significance that the model
predicts closing price distributions accurately, and compares favourably with
alternative methods of prediction
Forward and Backward Dynamics in implicitly defined Overlapping Generations Models
In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely defined, while the backward dynamics is well defined. We derive properties of the global forward equilibrium paths based on properties of the backward dynamics. We propose the framework of iterated function systems (IFS) to describe the set of forward equilibria, and apply the IFS framework to a one- and a two-dimensional version of the overlapping generations (OLG)-model. We show that, if the backward dynamics is chaotic and has a homoclinic orbit (a “snap-back repellerâ€) the set of forward equilibrium paths converges to a fractal attractor. Forward equilibria may be interpreted as sunspot equilibria, where a random sunspot sequence determines equilibrium selection at each date.
Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes
Clearing price distributions in call auctions
We propose a model for price formation in financial markets based on the clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed employing demand- and supply-side valuation distributions; an equilibrium equation then leads to a distribution for clearing price and transacted volume. Bid and ask volumes are left as free parameters, permitting possibly heavy-tailed or very skewed order flow conditions. In highly liquid auctions, the clearing price distribution converges to an asymptotically normal central limit, with mean and variance in terms of supply/demand-valuation distributions and order flow imbalance. By means of simulations, we illustrate the influence of variations in order flow and valuation distributions on price/volume, noting a distinction between high- and low-volume auction price variance. To verify the validity of the model statistically, we predict a year's worth of daily closing price distributions for five constituents of the Eurostoxx 50 index; Kolmogorov–Smirnov statistics and QQ-plots demonstrate with ample statistical significance that the model predicts closing price distributions accurately, and compares favourably with alternative methods of prediction
Heavy tailed distributions in closing auctions
We study the tails of closing auction return distributions for a sample of liquid European stocks. We use the stochastic call auction model of Derksen et al. [1] to derive a relation between tail exponents of limit order placement distributions and tail exponents of the resulting closing auction return distribution and we verify this relation empirically. Counter-intuitively, large closing price fluctuations are typically not caused by large market orders, instead tails become heavier when market orders are removed. The model explains this by the observation that limit orders are submitted so as to counter existing market order imbalance
Capital-labor substitution and competitive non-linear endogenous business cycles
We develop simple geometrical methods to study local indeterminacy, bifurcations, and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models. We present in particular a simple, constructive, geometrical characterization of the support of stochastic sunspot equilibria, not only arbitrarily near a steady state, but also along local bifurcations. These methods are applied to a simple aggregative model to study in particular the influence of capital-labor substitution and of the aggregate labor supply wage elasticity on the occurrence of competitive endogenous deterministic or stochastic fluctuations
Heavy tailed distributions in closing auctions
We study the tails of closing auction return distributions for a sample of liquid European stocks. We use the stochastic call auction model of Derksen et al. [1] to derive a relation between tail exponents of limit order placement distributions and tail exponents of the resulting closing auction return distribution and we verify this relation empirically. Counter-intuitively, large closing price fluctuations are typically not caused by large market orders, instead tails become heavier when market orders are removed. The model explains this by the observation that limit orders are submitted so as to counter existing market order imbalance