Keyword: CEV process

# Seminar at VU MIF: Modelling power-law distribution, 1/f noise and financial markets using stochastic differential equations

Topic: “Modelling power-law distribution, 1/f noise and financial markets using stochastic differential equations”
Speaker: habil. dr. Bronislovas Kaulakys
When? 14th of May, 17:00.
Where? VU Faculty of Mathematics and Informatics (Naugarduko g. 24, Vilnius), 400 auditorium.
Organized by: Department of the Mathematical Analysis of the VU MIF.

# Special cases of the stochastic differential equation reproducing 1/f noise

Considerable part of stochastic models available on Physics of Risk website (ex., Agent based herding model of financial markets or Long-range memory stochastic model of return) are related to the general class of stochastic differential equations derived by our group [1, 2]. The general form of this class is the following stochastic differential equation:

$$\mathrm{d} x = \left(\eta – \frac{\lambda}{2} \right) x^{2 \eta -1} \mathrm{d} t + x^\eta \mathrm{d} W . \label{sde}$$

In our talks at various scientific events and on Physics of Risk itself we frequently say that this equation also encompasses other widely known stochastic processes. Thus further in this text we will show some of the relations between this class and some widely known stochastic processes. Continue reading “Special cases of the stochastic differential equation reproducing 1/f noise” »

# Agent based herding model of financial markets

Kirman’s ant colony model, previously presented on our website as agent based (based on [1]) and stochastic (based on [2, 3]) model, has become classical example of herding modeling. Application of this model towards economic, financial or other social scenarios might seem doubtful as human society is far more complex than ant colony, but methodologically it is more useful to start from very simple and stylized model and later add complexity on top of it. Furthermore we have already shown that Kirman’s herding dynamics could be applicable in agent based marketing (see comparison of Kirman’s and Bass diffusion model). In this text we will consider financial market scenario and obtain stochastic differential equations similar to the existing stochastic models considered in [4, 5]. Continue reading “Agent based herding model of financial markets” »

# Long-range memory stochastic model of return

From the practical point of view price is the most interesting observable of the financial markets. Though modeling and analysis of price fluctuations are hindered by the fact that price itself is non-stationary process – mean price and market volatility constantly change. While price changes, at least at short time scales, behave as stationary process – mean price change is equal, or at least approximately equal, to zero. Thus it is convenient to introduce variable related to the relative price changes, which is known as return
Continue reading “Long-range memory stochastic model of return” »