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Rで学ぶGARCHモデル

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更新日 2024/08

GARCHモデルを指定・適合し、時変ボラティリティとバリュー・アット・リスクを予測します。

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RApplied Finance

4時間

16 ビデオ

60 演習

4,550 XP

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コース説明

金融市場の鼓動のリズムに興味はありませんか？安定した市場がいつ乱高下に変わるのか知りたいと思いませんか？このGARCHモデルのコースでは、金融意思決定でリスクとリターンのバランスをとるための先を見据えたアプローチを学びます。コースは、標準的な正規分布のGARCH(1,1)モデルから始めて、レバレッジ効果を持つ高度なボラティリティモデル、平均へのGARCHの組み込み、資産リターンのモデリングにおける歪んだスチューデントt分布の活用へと段階的に進みます。株式や為替リターンへの応用として、ポートフォリオ最適化、ロールングサンプルでの予測評価、バリュー・アット・リスクの予測、動学的共分散の分析を扱います。

前提条件

Time Series Analysis in R Manipulating Time Series Data in R

1

The Standard GARCH Model as the Workhorse Model

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.

Analyzing volatility

Computing returns

Standard deviation on subsamples

Roll, roll, roll

The GARCH equation for volatility prediction

GARCH(1,1) reaction to one-off shocks

Prediction errors

The recursive nature of the GARCH variance

The rugarch package

Specify and taste the GARCH model flavors

Out-of-sample forecasting

Volatility targeting in tactical asset allocation

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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.

Non-normality of standardized returns

Skewed student t distribution parameters

Estimation of non-normal GARCH model

Standardized returns

Leverage effect

News impact curve

Estimation of GJR garch model

Predicting returns

The AR(1)-GJR GARCH dynamics of MSFT returns

Effect of mean model on volatility predictions

Avoid unnecessary complexity

Modeling choices

Fixing GARCH parameters

Parameter bounds and impact on forecasts

Variance targeting

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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.

Statistical significance

Significance testing

Analyzing estimation output

A better model for EUR/USD returns

Goodness of fit

Mean squared prediction errors

Comparing likelihood and information criteria

Diagnosing absolute standardized returns

Validation of GARCH model assumptions

Correlogram and Ljung-Box test

Change estimation sample

Backtesting using ugarchroll

ugarchroll arguments

In-sample versus rolling sample vol

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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.

Value-at-risk

Comovement between predicted vol and VaR

Sensitivity of coverage to distribution model

For production and simulation

Actual versus simulated returns

Use in production

Use in simulation

Starting values

GARCH covariance

Estimation of beta

Minimum variance portfolio weights

Congratulations

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