The purpose of this thesis is to provide an insight into quantitative risk management through the introduction of the two risk measures, Value at Risk and Expected Shortfall by estimating these with GARCH, Semi-GARCH, and Volatility Weighted Historical Simulation.
The theoretical background gives a basic understanding of risk management and risk measures for financial institutions. The development of Basel Accords can be regarded as a standard for bank’s trading portfolios by determining capital requirements. To effectively manage the market risks, it is extremely important to estimate the risk measures. The most commonly reported risk measure is Value at Risk, which is defined as the maximum expected loss of a portfolio over a defined time horizon with a given confidence level. However, VaR fails to capture tail risk and is not a coherent measure of risk due to its non-sub-additive character. The Expected Shortfall, on the other hand, satisfies this property and thus is a coherent risk measure. It is now widely used in quantitative risk management. Besides, the ES provides an average of the losses that exceed the VaR, that means it indicates a better property than VaR with respect to tail risk.
Moreover, this thesis compares the forecasting ability of different models in estimating VaR and ES, whereby modelling of GARCH, Semi-GARCH and VWHS are investigated. These models represent the most important tools in the quantitative risk management for financial institutions. With the advancement of quantitative risk models for the analysis of financial time series, the risk managers could get potential opportunities to understand and study the structure as well as the behaviour of financial markets. The progress of each model and the procedure to estimate risk measures were introduced and then applied in the empirical section.
In terms of forecasting risk measures, an accurate model should be evaluated by Backtesting. This is a method of testing risk models by providing probabilities about the extent to which the calculated forecasts match the actual losses. The results of Backtesting therefore might indicate possible problems and support risk managers in making decision as well as planning strategies.
In conclusion, after presenting the different ways modeling risks and empirical analysis using various financial datasets, it is important to highlight that the Semi-GARCH model generates the best predictive performance in comparison, with GARCH and VWHS models also performing well.

The purpose of this thesis is to provide an insight into

quantitative

risk

management

through the introduction of the two

risk

measures

, Value at

Risk

and

Expected

Shortfall by estimating these with

GARCH

,

Semi-GARCH

, and Volatility Weighted Historical Simulation.

The theoretical background gives a basic understanding of

risk

management

and

risk

measures

for

financial

institutions.

The

development of Basel Accords can

be regarded

as a standard for bank’s trading portfolios by determining capital requirements. To

effectively

manage the market

risks

, it is

extremely

important

to estimate the

risk

measures

. The most

commonly

reported

risk

measure

is Value at

Risk

, which

is defined

as the maximum

expected

loss of a portfolio over a defined time horizon with a

given

confidence level.

However

,

VaR

fails to capture tail

risk

and is not a coherent

measure

of

risk

due to its non-sub-additive character. The

Expected

Shortfall,

on the other hand

, satisfies this property and

thus

is a coherent

risk

measure

. It is

now

widely

used

in

quantitative

risk

management

.

Besides

, the ES provides an average of the losses that exceed the

VaR

, that means it indicates a better property than

VaR

with respect to tail

risk

.

Moreover

, this thesis compares the forecasting ability of

different

models

in estimating

VaR

and ES, whereby modelling of

GARCH

,

Semi-GARCH

and

VWHS

are investigated

. These

models

represent the most

important

tools in the

quantitative

risk

management

for

financial

institutions. With the advancement of

quantitative

risk

models

for the analysis of

financial

time series, the

risk

managers could

get

potential opportunities to understand and study the structure

as well

as the

behaviour

of

financial

markets. The progress of each

model

and the procedure to estimate

risk

measures

were introduced

and then applied in the empirical section.

In terms of forecasting

risk

measures

, an accurate

model

should

be evaluated

by

Backtesting

. This is a method of testing

risk

models

by providing probabilities about the extent to which the calculated forecasts match the actual losses. The results of

Backtesting

therefore

might indicate possible problems and support

risk

managers in making decision

as well

as planning strategies.

In conclusion

, after presenting the

different

ways modeling

risks

and empirical analysis using various

financial

datasets, it is

important

to highlight that the

Semi-GARCH

model

generates the best predictive performance

in comparison

, with

GARCH

and

VWHS

models

also

performing well.

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