GARCH(1,1) Model Overview and Specification

This question focuses on a basic yet central time-series model for financial volatility, asking the candidate to explain how a simple autoregressive volatility process works in intuitive terms and then to formalize it. The setup is a single financial return series with volatility that changes over time, and the candidate must articulate how today's risk depends on past shocks and past levels of risk. This style of question is common in quant research, risk, and derivatives roles where modeling and forecasting volatility is a core task, especially in banks, hedge funds, and volatility-focused trading teams.

Answering it well requires fluency with conditional variance, shocks or innovations in a return process, and the distinction between the mean and volatility equations in time-series models. The interviewer is looking for correct model specification, clear identification and interpretation of each parameter, and an understanding of conditions like positivity and stability. They will also watch for awareness of volatility clustering, persistence, and mean reversion, and whether the candidate connects the formal recursion to practical behavior observed in financial return data.

What it tests

Time-varying volatility models like GARCH(1,1) are built on the principle that the variance of a time series is not constant but evolves based on its own past behavior. Specifically, these models capture the empirical fact that large shocks (high volatility) tend to be followed by more large shocks, and small shocks by more small shocks—a phenomenon known as volatility clustering. The model achieves this by making the conditional variance at time $t$ a function of both the previous period's squared innovation (shock) and the previous period's variance. This recursive structure allows the model to adapt to changing market conditions, reflecting the persistence and mean-reverting nature of volatility. The reason this pattern holds is that financial markets often experience periods of turbulence and calm, and the best predictor of current risk is often recent risk, not a long-run average.