Trade Volatility Using GARCH Model | Quantra Classroom

Welcome to?Quantra?Classroom, where we delve into the exciting world of?trading?with?GARCH?forecasted?volatility! In our previous email, we explored the importance and learning how to estimate?volatility?using?the Parkinson estimator.?

Towards the end of our discussion, we touched upon the idea of using estimated volatility as an input for volatility forecasting models like GARCH. Today, let's continue this fascinating conversation and explore how we can trade based on these forecasted volatility values.

All the concepts covered in this tutorial are taken from this?Quantra?course on?Options?Volatility?Trading: Concepts and Strategies. You can take a Free Preview of the course by clicking on the green-coloured Free Preview button on the right corner of the screen next to the FAQs tab and learn all these concepts in detail.

What are the characteristics of?volatility?

The characteristics of?volatility?describe its properties and behaviour in the financial markets.

Some key characteristics of?volatility?are:

• Volatility?Clustering:?Volatility?exhibits a tendency to cluster, meaning that periods of high?volatility?are often followed by more high?volatility?and periods of low?volatility?tend to be followed by more low?volatility. This characteristic suggests that?volatility?persists over time and tends to occur in clusters or groups.

• Volatility-Return relationship: When there are big changes in returns, whether positive or negative, it usually leads to higher?volatility. This is because significant price movements indicate increased uncertainty and the possibility of more price fluctuations. To measure the impact of these large returns on?volatility, we square the latest return, which emphasises their influence.
• Mean Reversion: Although?volatility?can exhibit clustering behaviour, it also has a mean-reverting nature. This means that periods of high?volatility?are typically followed by periods of lower?volatility?and vice versa.?Volatility?tends to revert to its long-term average or equilibrium level over time.

In the above graph of CBOE VIX, you can see that?volatility?reverts around its mean (red line) over time.

You might be wondering why we are suddenly interested in the characteristics of?volatility. It is because the?volatility?forecasting?models?like?GARCH?use the weighted sums of these characteristics of?volatility?to predict the?volatility.?

GARCH?Model

The?GARCH?(Generalized Autoregressive Conditional Heteroskedasticity)?model?is a widely used econometric?model?for estimating and forecasting?volatility?in financial markets. It assumes that the conditional variance of a financial asset's returns follows an autoregressive process, where the current conditional variance depends on the past conditional variances and the past squared returns.?

The key idea behind the?GARCH?model?is to capture the?volatility?clustering phenomenon observed in financial markets, where periods of high?volatility?tend to be followed by more high?volatility, and periods of low?volatility?tend to be followed by more low?volatility.

For the sake of simplicity, we will be focusing on the?GARCH(1,1)?model?for our?volatility?prediction purpose. The equation for?GARCH(1,1) is shown below:

where?

* V is the long-term variance of the time series, which is the historical?volatility?estimated by the Parkinson estimator.?

* γ is the weight given to the long-term variance V.

* rt-12 i.e. squared return at time t-1 is calculated?using?monthly returns?

* α is the weight given to the squared return at time t-1

* σt-12 i.e. variance of the time series (volatility) at time t-1

* β is the weight given to the variance of the time series (volatility) at time t-1

To estimate the?GARCH?parameters ( ??,??,??) we will maximise the log-likelihood function.

The Python code for estimating the?GARCH?parameters and forecasting the?volatility?using?the?GARCH(1,1)?model?is covered in?this?unit of the?Options?Volatility?Trading: Concepts and Strategies?course. You need to take a Free Preview of the course by clicking on the green-coloured Free Preview button on the right corner of the screen next to the FAQs tab and go to Section 15 and Unit 12 of the course.

Trading?with?GARCH?forecast

Once you have forecasted the?volatility?using?the?GARCH(1,1)?model, you can create a?trading?strategy based on?volatility?forecasts.

Let’s devise a sample?trading?strategy based on the?volatility?forecast. The strategy can be as follows:

• Entry:?If the forecasted?volatility?is greater than the implied?volatility?of at-the-money(ATM) call and put options, buy a straddle. On the other hand, if the forecasted?volatility?is less than the implied?volatility?of ATM call and put options, sell a straddle.
• Exit:?Once a long or short position is opened, close it after a week.
• Re-entry:?Once the position is closed, re-estimate the?model, forecast?volatility?again for one month and generate the?trading?signals.

• signal = 1?a long straddle position is to be opened
• signal = -1?a short straddle position is to be opened
• signal = 0?any open?position is to be closed.

The backtesting and strategy analysis for the above strategy has been covered in detail along with the Python code in the?Options?Volatility?Trading: Concepts and Strategies?course.

What to do next?

• Go to?this?course?
• Click on Free Preview
• Go through 10-15% of course content?
• Drop us your comments, queries on?community?

IMPORTANT DISCLAIMER: This email is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset.