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# GARCH Models in R

Specify and fit GARCH models to forecast time-varying volatility and value-at-risk.

4 hours16 videos60 exercises

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## Course Description

Are you curious about the rhythm of the financial market's heartbeat? Do you want to know when a stable market becomes turbulent? In this course on GARCH models you will learn the forward looking approach to balancing risk and reward in financial decision making. The course gradually moves from the standard normal GARCH(1,1) model to more advanced volatility models with a leverage effect, GARCH-in-mean specification and the use of the skewed student t distribution for modelling asset returns. Applications on stock and exchange rate returns include portfolio optimization, rolling sample forecast evaluation, value-at-risk forecasting and studying dynamic covariances.

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1. 1

### The Standard GARCH Model as the Workhorse Model

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We start off by making our hands dirty. A rolling window analysis of daily stock returns shows that its standard deviation changes massively through time. Looking back at the past, we thus have clear evidence of time-varying volatility. Looking forward, we need to estimate the volatility of future returns. This is essentially what a GARCH model does! In this chapter, you will learn the basics of using the rugarch package for specifying and estimating the workhorse GARCH(1,1) model in R. We end by showing its usefulness in tactical asset allocation.

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Analyzing volatility
50 xp
Computing returns
100 xp
Standard deviation on subsamples
100 xp
Roll, roll, roll
100 xp
The GARCH equation for volatility prediction
50 xp
GARCH(1,1) reaction to one-off shocks
50 xp
Prediction errors
100 xp
The recursive nature of the GARCH variance
100 xp
The rugarch package
50 xp
Specify and taste the GARCH model flavors
100 xp
Out-of-sample forecasting
100 xp
Volatility targeting in tactical asset allocation
100 xp
2. 2

### Improvements of the Normal GARCH Model

Markets take the stairs up and the elevator down. This Wallstreet wisdom has important consequences for specifying a realistic volatility model. It requires to give up the assumption of normality, as well as the symmetric response of volatility to shocks. In this chapter, you will learn about GARCH models with a leverage effect and skewed student t innovations. At the end, you will be able to use GARCH models for estimating over ten thousand different GARCH model specifications.

3. 3

### Performance Evaluation

GARCH models yield volatility forecasts which serve as input for financial decision making. Their use in practice requires to first evaluate the goodness of the volatility forecast. In this chapter, you will learn about the analysis of statistical significance of the estimated GARCH parameters, the properties of standardized returns, the interpretation of information criteria and the use of rolling GARCH estimation and mean squared prediction errors to analyze the accuracy of the volatility forecast.

4. 4

### Applications

At this stage, you master the standard specification, estimation and validation of GARCH models in the rugarch package. This chapter introduces specific rugarch functionality for making value-at-risk estimates, for using the GARCH model in production and for simulating GARCH returns. You will also discover that the presence of GARCH dynamics in the variance has implications for simulating log-returns, the estimation of the beta of a stock and finding the minimum variance portfolio.

### In the following Tracks

#### Applied Finance in R

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datasets

Daily EUR/USD returnsDaily Microsoft returnsS&P 500 pricesS&P 500 returnsSimulated return data

collaborators

Kris Boudt

Professor of Finance and Econometrics at VUB and VUA

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