Risk indicators in equity markets

The distribution of securities prices in financial markets is known to exhibit heavy tails, and furthermore the time trajectory has occasional extreme swings or reversals in direction. The modelling of heavy tails has been achieved with the addition of a homogeneous point process to a diffusive process. However, the timing of the jumps in the point process should capture the price reversals. In this paper a non-homogeneous point process is introduced, so that the intensity and size of jumps are state dependent. The state is characterized by stress measures, which are composed from combinations of risk factors. The factors considered are the bond-stock yield differential and the volatility index. The parameters in the model are estimated from data on the US market from 1990 - 2007. An out-of-sample test is performed for 2008 - 2009. The model captures the swings in equities prices and provides a basis for anticipating reversals from risk factors.