A multivariate model for financial indexes and an algorithm for detection of jumps in the volatility

We study a bivariate mean reverting stochastic volatility model, finding an explicit expression for the decay of cross-asset correlations over time. We compare our result with the empirical time series of the Dow Jones Industrial Average and the Financial Times Stock Exchange 100 in the period 1984-2013, finding an excellent agreement. The main features of the model consist in the jumps in the volatilities and a nonlinear mean reversion. Based on these features, we propose an algorithm for the detection of jumps in the volatility.