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A Comparison of Some Value-at-Risk Validation Methods

Pålsson, John LU (2019) In LUTFMS-3381-2019 FMSM01 20182
Mathematical Statistics
Abstract
This report examines the concept of validating financial risk models, specifically Value-at-Risk, and compares the required regulatory tests with more advanced validation methods based on testing different martingale characteristics. The validation methods are considered in a classic backtesting scenario on a real custom portfolio, a Monte Carlo experiment to compare the empirical power on different data generation processes and finally simulated in an online scenario for a long time period on real data. The results suggests that the chosen validation methods perform better than the required regulatory tests. The tests that perform best are a multivariate independence test and a regression test.
Popular Abstract
Comparing the regulation required risk model validation methods to alternative methods using a Monte Carlo experiment and an online test indicates a possibility to create a better validation model

In light of the current Fundamental Review of the Trading Book, which suggests many changes to regulation concerning risk management, we have focused on specifically evaluating the suggested model validation method. The required methods was compared to a selection of alternative validation methods to evaluate different desired properties of the results, by comparing a Value-at-Risk measure to actual returns. Results indicate that the alternative methods has better empirical power, probability to reject an incorrect model, than the required... (More)
Comparing the regulation required risk model validation methods to alternative methods using a Monte Carlo experiment and an online test indicates a possibility to create a better validation model

In light of the current Fundamental Review of the Trading Book, which suggests many changes to regulation concerning risk management, we have focused on specifically evaluating the suggested model validation method. The required methods was compared to a selection of alternative validation methods to evaluate different desired properties of the results, by comparing a Value-at-Risk measure to actual returns. Results indicate that the alternative methods has better empirical power, probability to reject an incorrect model, than the required method in most cases. Comparing the validation results over a long period of time indicates that there may be an advantage in using multiple different validation methods to be able to gather more information on how a model performs and how to improve the model.

The subject of risk model validation is important to ensure that the risk estimates is reliable. Financial risk can be explained as how large the loss can be with some probability. This is related to the profit, as an increased possible profit will also increase the risk. Thus, it is important to know the risk, but there is no universal way to measure it. The most important risk measure is the Value-at-Risk, which is used for regulation in risk management. The Value-at-Risk results is tested through a violation sequence which should have the correct amount of violations as well as being the violations being independent.

The required validation method only tests the amount while ignoring the independence. This project evaluates the difference between only testing the number of violations, only testing the independence and combining both hypotheses in one test. This consists of the following tests, Kupiec's, Perignon and Smith's, Ljung-Box, Hurlin and Tokpavi's, Christoffersens CC and Duration tests as well as Engle and Manganellis' Dynamic Quantile test. To compare these tests a Monte Carlo experiment was used to avoid the problem of small sample sizes and simulations was done from Bernoulli distributions and different GARCH-models to simulate realistic settings. The validation tests were also used on VaR-results from a custom portfolio of stocks between 2000-2018 and simulated an online validation model.

The aim for this project was to evaluate different validation methods and test them in an online setting to advise a company in developing a financial risk system. In this case it is important to not only validate according to regulations but also validate to find a good model to avoid unnecessary capital requirements. It is also important that the user is able to rely on the risk estimates and thus be able to assess the model in a robust way. (Less)
Please use this url to cite or link to this publication:
author
Pålsson, John LU
supervisor
organization
course
FMSM01 20182
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Value-at-Risk, Monte Carlo simulation, Model Validation, Backtesting
publication/series
LUTFMS-3381-2019
report number
2019:E52
ISSN
1404-6342
language
English
id
8991215
date added to LUP
2020-10-05 14:52:02
date last changed
2020-10-05 14:53:13
@misc{8991215,
  abstract     = {{This report examines the concept of validating financial risk models, specifically Value-at-Risk, and compares the required regulatory tests with more advanced validation methods based on testing different martingale characteristics. The validation methods are considered in a classic backtesting scenario on a real custom portfolio, a Monte Carlo experiment to compare the empirical power on different data generation processes and finally simulated in an online scenario for a long time period on real data. The results suggests that the chosen validation methods perform better than the required regulatory tests. The tests that perform best are a multivariate independence test and a regression test.}},
  author       = {{Pålsson, John}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{LUTFMS-3381-2019}},
  title        = {{A Comparison of Some Value-at-Risk Validation Methods}},
  year         = {{2019}},
}