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Copula-GARCH模型下的两资产期权定价

Garchmodels unlocks univariate and multivariate GARCH models in one framework.

karjamatti/Copula-GARCH

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README.md

This app simulates daily returns of a portfolio that consists of 4 asset class indices. The simulation is based on the GARCH-Copula framework.

The App Copula-GARCH模型下的两资产期权定价 is currently written so that it runs on MacOS. If you wish to run it on other systems, please check that the path to the data file works.

A lot of the packages used Copula-GARCH模型下的两资产期权定价 in the script require compiling. This can get dicey, but some tips and tricks I can give are:

  • Install homebrew (availble from https://brew.sh/)
  • Install the required compilers (an easy way is to run the command: $ brew install gcc)
  • Check the "Makevars" -file in ~/.R/

The "Makevars" -file should be something along the lines of:

where the number 9 etc. corresponds to your gcc version. (run the command "$ which gcc" to find out.)

APP USER INSTRUCTIONS

An easy way to run the app, is to open the script in RStudio, and run all of the code. This should eventually open a pop up window with the user interface. Do not attempt to alter the code while the pop-up is open!

The script should automatically load, or install and load and Copula-GARCH模型下的两资产期权定价 load any required packages. however, do keep in mind that the packages might require compiling, which usually asks for a simple user-input (y/n). These inputs might mess up sourcing/running the code, so maybe try installing the required packages in the console first.

Typically, the user should only need to adjust or specify parameters that are accessible through the user interface of the app. However, if the application shows an error messages, this might be due to incorrectly specified parameters in the script. (e.g. number of index return vectors per asset class)

The parameters most likely needing adjustment are at the beginning of the script for convenience.

DEFAULT DATA SET

On Github, the original default dataset is not provided due to licensing reasons. However, a pseudo-dataset based on the original with randomization is provided.

To ensure the functionality of the app, the data should be called 'dailydata.csv', and contain trading dates in the first column (header 'Date'), and the returns of the following 7 indices/instruments:

PROVIDING CUSTOM INDEX RETURNS AND UPDATING THE DEFAULT DATA SET

In order to yield accurate condtional forecasts, the return data should be updated daily. (Ironically enough, this is not the case for me, since I do not have access Copula-GARCH模型下的两资产期权定价 to the original data source any longer. )

When/if updating data, please Copula-GARCH模型下的两资产期权定价 remember to keep in mind:

SPECIFYING PARAMETERS IN THE SCRIPT

The most likely cause for adjusting parameters in the script is in case the user wants to provide their own return data. In this case, the number of return indices in the adjusted data file should be specified, so that the user interface recognizes which asset classes the indices belong to.

Also, the number of simulated variates can be changed by adjusting the parameters at the beginning of the script. Keep in mind, that while this speeds up the simulations, it reduces Copula-GARCH模型下的两资产期权定价 the convergence of the model fitting, and might yield surprisingly inaccurate forecasts.

It is very well possible that some index returns do not fit the GARCH-specfications that well. It is also possible that Copula-GARCH模型下的两资产期权定价 the GARCH-fit might not be sufficient for parameter convergence! In case of no convergence, you can try to specify a tolerance parameter in the garch fit, for example:

on line 167 of the application script

The correctness of the script is also not guaranteed! If you see something weird and cath a bug, please shoot me an email at [email protected]!

The script is likely to contain errors, bad practices and other mishaps. If you have any questions, please contact Copula-GARCH模型下的两资产期权定价 the email address found in this document.

About

This is a portfolio risk visualization tool, based on a Copula-GARCH framework and a Shiny UI.

Copula-GARCH模型下的两资产期权定价

Classes (S4) of commonly used elliptical, Archimedean, extreme-value and other copula families, as well as their rotations, mixtures and asymmetrizations. Nested Archimedean copulas, related tools and special functions. Methods for density, distribution, random number generation, bivariate dependence measures, Rosenblatt transform, Kendall distribution function, perspective and contour plots. Fitting of copula models with potentially partly fixed parameters, including standard errors. Serial independence tests, copula specification tests (independence, exchangeability, radial symmetry, extreme-value dependence, goodness-of-fit) and model selection based on cross-validation. Empirical copula, smoothed versions, and non-parametric estimators of the Pickands dependence function.

garchmodels

A parsnip backend for GARCH models in the tidymodels framework.

Tutorials

Getting Started with Garchmodels: A walkthrough of the tidy modeling approach with the package.

Tuning Univariate Garch Models: Learn how to tune parameters of univariate garch models.

Installation

Why Garchmodels?

Garchmodels unlocks univariate and multivariate GARCH models in one framework.

In a single framework you will be able to find what you need:

Univariate Methods: garchmodels connects to the rugarch package.

Multivariate Methods: garchmodels connects to the rugarch and rmgarch packages. Available methods include DCC-Garch (Dynamic Conditional Correlation Garch), Copula-GARCH模型下的两资产期权定价 Copula Garch and GO-Garch models.

Copula-GARCH模型下的两资产期权定价

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Abstract

This paper minimizes the risk of Brent oil in a multivariate portfolio, with three risk-minimizing goals: variance, parametric value-at-risk (VaR), and semiparametric value-at-risk. Brent oil is combined with five emerging ASEAN (Association of Southeast Asian Nations) stock indexes and five more developed non-ASEAN indexes. The preliminary dynamic equiciorrelation estimates indicate that the ASEAN stock indexes are less integrated and thus potentially better for diversification purposes. The portfolio results Copula-GARCH模型下的两资产期权定价 show that the ASEAN indexes are better hedges for oil in terms of minimum variance and minimum VaR. However, although the ASEAN indexes have higher extreme risk, we find that a portfolio with these indexes has slightly lower modified VaR than a portfolio with the non-ASEAN indexes. The reason is probably the higher variance and higher equicorrelation of the non-ASEAN indexes, because these inputs affect the value of the modified downside risk of a portfolio. As a complementary analysis, we put a 50 percent constraint on Brent in the portfolios, and then the portfolios with the non-ASEAN indexes have better risk-minimizing results.