Across the banking book, a large bank might need to estimate several thousand default probability and loss-given-default parameters (Table 1). To turn these into regulatory capital requirements, the number of parameters increases by another order of magnitude. It is close to impossible to determine with complete precision the size of the parameter space for a large international bank’s banking book. That, by itself, is revealing. But a rough guess would put it at thousands, perhaps tens of thousands, of estimated and calibrated parameters. That is three, perhaps four, orders of magnitude greater than Basel I. If that sounds large, the parameter set for the trading book is almost certainly larger still. To give some sense of scale, consider model-based estimates of portfolio Value at Risk (VaR), a commonly-used technique for measuring risk and regulatory capital in the trading book. A large firm would typically have several thousand risk factors in its VaR model. Estimating the covariance matrix for all of the risk factors means estimating several million individual risk parameters. Multiple pricing models are then typically used to map from these risk factors to the valuation of individual instruments, each with several estimated pricing parameters. Taking all of this together, the parameter space of a large bank’s banking and trading books could easily run to several millions. These parameters are typically estimated from limited  10  Basel Committee on Banking Supervision (2004). 11  Basel Committee on Banking Supervision (2010).
13 To sum up, from a global perspective, the establishment of EMU in January 1999 represents a fundamental institutional change in the world economy, and could in part help explain the large reallocation of capital that has taken place worldwide. 11  A more sophisticated analysis based on an international portfolio choice model reaches the same conclusion (see De Santis and Gérard, 2006). EMU has enhanced regional financial integration in the euro area in both the equity and bond markets. There is evidence of active trading among euro area Member States, with euro area investors assigning a higher weight to portfolio investment in euro area countries. Over the period 1997-2001, the average increase in weights - on top of the world average portfolio weight increase in euro area assets - amounts to 12.7 percentage points for equity holdings and 22.4 percentage points for bond and note holdings. 12  See ECB (2005). 13  On international risk sharing and EMU see for example Sorensen and Yosha (1998). 6  BIS Review 43/2006  The euro area – a zone of stability Before concluding, let me emphasise that since 1999 we have experienced a number of important shocks to the global economy, such as the Y2K problem at the turn of the millennium, substantial oil price increases, the fall and the rise of the euro exchange rate, the boom and burst of the equity market bubble, global imbalances and the clouds of war and terrorism.