The times change: multivariate subordination. Empirical facts

The management of correlation risk is of the utmost importance in several areas of investment banking: multi-asset derivatives pricing and hedging, optimal asset allocation, risk management, statistical arbitrage and many others.§ However, the modeling of correlation as a time-dependent quantity—as opposed to that of the volatility, say—is still in its infancy. In this article, we present a mechanism for the presence of a stochastic covariance matrix in financial markets, and provide an explanation for the returns' heavy tailed joint distribution. This mechanism relies on sampling returns according to an appropriate event time. Using CAC 40 high-frequency data, we compare the predictions of our model with real-world statistics and find very good agreement. <fn id="FN0001"> §Even single asset derivatives desks are sensitive to shifts in correlation if, for instance, they are focused on a specific sectorial or geographic exposure. </fn>