Generalized Autoregressive Conditional Heteroskedasticity

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21 Aug, 2024

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Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Meaning

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) refers to a statistical model that involves making estimates concerning financial markets’ volatility. The purpose of this approach is to reduce forecasting errors by taking into account mistakes in prior estimation and improving ongoing predictions’ accuracy.

People can utilize Generalized Autoregressive Conditional Heteroskedasticity models for different types of financial information, like macroeconomic data. Moreover, financial institutions use such a model to predict the volatility of bonds, stocks, etc. Usually, financial professionals prefer this process as it offers real-world context relative to other models when predicting rates and prices of financial instruments.

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Meaning

Generalized Autoregressive Conditional Heteroskedasticity refers to a statistical autoregressive model that helps individuals predict the volatility of a financial market or asset. It enables traders to make well-formed decisions in the market and minimize losses.
GARCH models help individuals understand the riskiness associated with financial markets or securities. In contrast, ARIMA models can help predict future trends based on historical data.
GARCH models offer various benefits. For example, they help estimate VaR and option prices. Moreover, they enable one to make predictions about the risk premium.

GARCH In Finance Explained

Generalized Autoregressive Conditional Heteroskedasticity refers to a statistical model that professionals in the field of finance can use to analyze and estimate the fluctuations in financial time series data volatility. It aims to minimize errors associated with forecasting in financial markets. GARCH models can be extremely useful for financial analysts, investors, and other persons in financial markets who need to make informed decisions on the basis of future expectations concerning financial performance.

Individuals can often use the information resulting from such GARCH models to determine the assets that have the potential to generate higher returns in addition to the pricing. Moreover, they can utilize the approach to predict current investments’ returns, which in turn, helps in managing risk, optimizing portfolio decisions, allocating assets, and hedging.

This model is popular among professionals engaging in predicting the possibilities of significant asset price movements. It is an extension of the autoregressive moving average (ARMA) model. GARCH enables the variance to alter with time, which reflects that financial information or data can be subject to fluctuations or volatility.

History

Robert F. Engle, an economist, developed the term GARCH and introduced a model named Autoregressive Conditional Heteroskedasticity (ARCH) in 1982. Later, in 1986, Dr. Tim Bollerslev built on the breakthrough work of Robert F. Engle and developed the GARCH model, which assumed that financial returns’ variations are not constant over a duration. Rather, they are dependent or autocorrelated. For example, one can observe this concept in the case of security returns, where the volatility periods are clustered.

Since the introduction of GARCH, multiple variations of the model have come into existence. All such variations aim to incorporate the negative, positive, or direction of returns besides the magnitude. One can use each such variation of the original model to accommodate the particular qualities associated with industries, financial data, or stocks.

At the time of evaluating risk, financial institutions, such as banks, integrate GARCH models into the maximum expected loss and Value-at-Risk or VaR over a certain duration. These models can offer better measures of risk obtainable via monitoring only standard deviation.

Examples

Let us look at a few examples of Generalized Autoregressive Conditional Heteroskedasticity to understand the concept better.

Example #1

Suppose the price of ABC stock was not subject to much volatility and remained uniform in terms of price in comparison to the other stocks in the same industry. That said, the stock price plunged significantly because of significant changes in the economic environment. The alterations resulted from a war between two of the leading economies in the world.

To predict future volatility better, financial analysts decided to utilize the GARCH model. The model accounted for the changes in price over time and considered past and current data as inputs. Considering that the increased volatility resulting from the war was predictive of future stock price fluctuations, the tool enabled the analysts to come up with better estimates. This, in turn, helped investors make more informed decisions in the market.

Example #2

According to State Bank Of India (SBI) research, In December 2022, BSE SENSEX returns were up 4.4% year-to-date or YTD, with lower volatility compared to the other important equity markets. A granular observation of the data revealed that the Indian markets delivered the best performance when compared to the other markets. GARCH models suggest that this performance is not driven by any lag. Rather, negative news influenced the returns. This means the Indian markets are forward-looking.

The SBI research report added that utilizing the BSE SENSEX returns’ estimated volatility via the GARCH model and with the help of the Autoregressive Distributed Lag Stationarity (ARDL) model, the effects of repo rate, spread of government bond yields, and repo rate were gauged based on the BSE SENSEX returns’ volatility.

Benefits

The advantages of the Generalized Autoregressive Conditional Heteroskedasticity model are as follows:

As noted above, such a model can assist in predicting financial assets’ volatility.
The GARCH model helps in Value At Risk (VaR) estimation.
Such a model can allow people to make estimates regarding the risk premium.
The GARCH model can help estimate option prices.
As noted above, this model enables one to make informed financial decisions as they can get valuable insights concerning risk and returns associated with a financial asset.

GARCH vs ARIMA

The differences between Autoregressive Integrated Moving Average (ARIMA) and GARCH are as follows:

In finance, ARIMA refers to a statistical model describing autocorrelation in financial time series data. On the other hand, GARCH describes volatility clustering in financial time series data.
The aim of the GARCH model is to estimate the volatility associated with financial assets. That said, the ARIMA model aims to help one understand data sets and predict future trends.

Frequently Asked Questions (FAQs)

1. What are the limitations of Generalized Autoregressive Conditional Heteroskedasticity model?

The limitations of such a statistical model are as follows:
It assumes that conditional variance does not change (stationary).
Such a model is sensitive to the selection of lag length and the conditional variance’s functional form.
This model only captures volatility’s short-term dynamics.

2. What are the advantages of Generalized Autoregressive Conditional Heteroskedasticity over ARCH?

The main advantage is that GARCH involves fewer parameters, and it delivers compared to the ARCH model.

3. What are the different types of Generalized Autoregressive Conditional Heteroskedasticity models?

The different types of such a model are as follows:
Exponential GARCH (EGARCH)
Integrated GARCH (IGARCH)
Threshold GARCH (GJR-GARCH)
Standard GARCH (SGARCH)

What is the difference between Generalized Autoregressive Conditional Heteroskedasticity and stochastic volatility models?

Stochastic volatility models take into account a random variable. On the other hand, in the case of GARCH models, the conditional variance serves as the deterministic function of past data and the parameters.