Introduction

Volatility estimation is a critical aspect of risk assessment in financial markets. In this chapter, we delve into advanced topics, exploring approaches to estimate volatility over long horizons and the GARCH (1,1) model’s mean reversion process.

When assessing risk over longer timeframes, accurately estimating volatility becomes essential. Long horizon volatility and Value at Risk (VaR) calculation demand a thorough understanding of how volatility evolves and the presence of mean reversion. In this chapter, we’ll explore techniques to estimate long horizon volatility and understand the role of mean reversion within the GARCH (1,1) model.

Estimating Long Horizon Volatility

Long horizon volatility estimation involves extending volatility measurements beyond short-term periods. A common approach is to scale short-term volatility estimates to account for longer timeframes. For instance, if a stock’s daily volatility is known, the estimated long horizon volatility for a month can be calculated by scaling the daily volatility based on the square root of time.

Applying the GARCH (1,1) Model’s Mean Reversion

The GARCH (1,1) model, a widely used tool, captures volatility clustering and mean reversion patterns. Mean reversion implies that periods of high volatility are likely to be followed by periods of lower volatility and vice versa. The model estimates volatility by considering a weighted average of past squared returns and past squared volatility. This incorporates the concept of mean reversion by assigning higher weights to more recent observations.

Example: Consider a financial asset with historical volatility spikes due to market events. The GARCH (1,1) model identifies this pattern and assigns higher weight to recent volatility observations. If the asset experiences high volatility due to external factors, the model accounts for the likelihood of volatility decreasing over time, reflecting the mean reversion concept.