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Calculation of Value-at-Risk and Expected Shortfall under model uncertainty

Böttern, Alexandra (2015) FMS820 20151
Mathematical Statistics
Abstract
This thesis studies the concept of calculation of Value-at-Risk and Ex-
pected Shortfall when the choice of model is uncertain. The method used
for solving the problem is chosen to be Bayesian Model Averaging, using
this method will reduce the model risk by taking several models into ac-
count. Monte Carlo methods are used to perform the model averaging
and the calculation of the risk measurements.
A NIG-CIR process is used to generate the data that is to be consid-
ered unknown, for which Value-at-Risk and Expected Shortfall is to be
calculated. It is chosen since it have behaviour that often occur in nan-
cial data. The model averaging is performed using six dierent processes
of varying levels of complexity. Both a weighted... (More)
This thesis studies the concept of calculation of Value-at-Risk and Ex-
pected Shortfall when the choice of model is uncertain. The method used
for solving the problem is chosen to be Bayesian Model Averaging, using
this method will reduce the model risk by taking several models into ac-
count. Monte Carlo methods are used to perform the model averaging
and the calculation of the risk measurements.
A NIG-CIR process is used to generate the data that is to be consid-
ered unknown, for which Value-at-Risk and Expected Shortfall is to be
calculated. It is chosen since it have behaviour that often occur in nan-
cial data. The model averaging is performed using six dierent processes
of varying levels of complexity. Both a weighted average based on BIC and
a equally weighted average is calculated for the two risk measurements.
The more complex models that are used in the Bayesian Model Averag-
ing is GARCH processes, an EGARCH process and a stochastic volatility
model, namely the Taylor 82 model. The methods used for parameter
estimation are Maximum likelihood estimation and Kalman ltering.
The results in this thesis clearly shows that it is advantageous to cal-
culate Value-at-Risk and Expected Shortfall using model averaging. But
there is not any clear conclusion on which weights that give the most
accurate estimate. But considering the time and eort that goes in to
calculating the weights, using equal weight seems preferable. (Less)
Please use this url to cite or link to this publication:
author
Böttern, Alexandra
supervisor
organization
course
FMS820 20151
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
7508944
date added to LUP
2015-07-01 11:49:28
date last changed
2015-07-03 08:25:00
@misc{7508944,
  abstract     = {This thesis studies the concept of calculation of Value-at-Risk and Ex-
pected Shortfall when the choice of model is uncertain. The method used
for solving the problem is chosen to be Bayesian Model Averaging, using
this method will reduce the model risk by taking several models into ac-
count. Monte Carlo methods are used to perform the model averaging
and the calculation of the risk measurements.
A NIG-CIR process is used to generate the data that is to be consid-
ered unknown, for which Value-at-Risk and Expected Shortfall is to be
calculated. It is chosen since it have behaviour that often occur in nan-
cial data. The model averaging is performed using six dierent processes
of varying levels of complexity. Both a weighted average based on BIC and
a equally weighted average is calculated for the two risk measurements.
The more complex models that are used in the Bayesian Model Averag-
ing is GARCH processes, an EGARCH process and a stochastic volatility
model, namely the Taylor 82 model. The methods used for parameter
estimation are Maximum likelihood estimation and Kalman ltering.
The results in this thesis clearly shows that it is advantageous to cal-
culate Value-at-Risk and Expected Shortfall using model averaging. But
there is not any clear conclusion on which weights that give the most
accurate estimate. But considering the time and eort that goes in to
calculating the weights, using equal weight seems preferable.},
  author       = {Böttern, Alexandra},
  language     = {eng},
  note         = {Student Paper},
  title        = {Calculation of Value-at-Risk and Expected Shortfall under model uncertainty},
  year         = {2015},
}