Theory of Time Series Modeling and Risk Estimation

Abstract

Forecasting the future behavior of stock prices is an essential task in the implementation of risk management systems. In order to obtain a good forecast for the distribution of returns, prediction of future market volatility is critical. A key modeling difficulty is that market volatility cannot be observed directly. Volatility musst be inferred by looking at the past behavior of market prices or at the value of financial derivatives. Appllying the first case, one can state that if prices fluctuate a lot, volatility should be high. The ascertainment of how high is difficult. One reason is that it can not be stated whether a large shock to prices is transitory or permanent. Due to the latent character of the variable a statistical model has to be applied, making strong assumptions.