Abstracts

This document gives a brief description of the first step in our project of asset price modeling and risk prediction. Having the price evolution of 13 equity indexes from different countries for almost 20 years, the aim of our project is to suggest a suitable model describing the dynamics of these indexes. This model can be applied in price forecasting and risk prediction with a small confidence interval and relatively short calculation time. For each index, the collected dataset consists of the daily closing prices starting from 1th January 1993 until 11th January 2013, which forms 5000 daily points. First, the probability distribution of price evolution, represented by the log-returns, is studied. After data analysis, a mixture of Normal and Laplace probability distribution is associated to log-returns. Afterward, the study is focused on price dynamics modeling. Several types of asset price modeling were considered and improved over previous years. In this paper, two types of models are considered: stochastic processes and time series models (ARCH/GARCH). First, the adequacy of time series models has been tested using the Hinich portmanteau bicorrelation statistical test. Results show the inadequacy of the use of GARCH model or any of its variants for the 13 indexes under consideration. The remainder of this paper is focused on stochastic processes. Stochastic volatility (SV) models have been considered to be the most reliable models for the cases where the volatility, as in our case, has significant variations over time. Therefore, SV models where the volatility follows different types of stochastic process are considered. Furthermore, a jump-diffusion process with Log-Uniform Jump Amplitude is proposed. Comparing the volatility behavior of different indexes, the economic environment states are divided into three states (calm, normal and agitated). The transition between these three states is controlled by an external covariate following a Markov chain. The jump-diffusion model parameters calibration is carried out for each index and each covariate state to build an overall model that represents the price variation behavior. The model parameters calibration is carried out for both SV model and the jump-diffusion process. The work is in progress in order to clarify the strengths and weaknesses of each model. The comparison between these models will be based on the reliability of price and return prediction, availing the already known collected data.