Chapter 26 - Relevance of Volatility Forecasting in Financial Risk Management

Abstract

Market risk estimates are an evaluation of the risk incurred by a portfolio because of the price fluctuations of the portfolio's components. A risk estimate measures the risk in the future, up to a given time horizon. Therefore, risk estimates are a forecast of the forthcoming volatility. This chapter concerns the relationships among historical volatilities, the forecasts of volatility, and the risk. The key point of the chapter concerns the forecasting aspect, which is discussed in the framework of (quadratic) data-generating processes. Such processes induce a forecast by computing conditional expectations and therefore give a unique framework both for the data-generating aspect and the forecast. This point of view includes GARCH, which is a long memory process, the standard Risk Metrics, and the BIS formulas. Within this process approach, the extension to high-frequency data is straightforward. Using an hourly foreign exchange time series, the forecasts given by various processes are compared quantitatively.