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Cornish-Fisher Expansion and Value-at-Risk method in application to risk management of large portfolios
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
2011 (English)Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

One of the major problem faced by banks is how to manage the risk

exposure in large portfolios. According to Basel II regulation banks

has to measure the risk using Value-at-Risk with confidence level 99%.

However, this regulation does not specify the way to calculate Valueat-

Risk. The easiest way to calculate Value-at-Risk is to assume that

portfolio returns are normally distributed. Altough, this is the most

common way to calculate Value-at-Risk, there exists also other methods.

The previous crisis shows that the regular methods are unfortunately

not always enough to prevent bankruptcy. This paper is devoted to

compare the classical methods of estimating risk with other methods

such as Cornish-Fisher Expansion (CFVaR) and assuming generalized

hyperbolic distribution. To be able to do this study, we estimate the risk

in a large portfolio consisting of ten stocks. These stocks are chosen from

the NASDAQ 100-list in order to have highly liquid stocks (bluechips).

The stocks are chosen from different sectors to make the portfolio welldiversified.

To investigate the impact of dependence between the stocks

in the portfolio we remove the two most correlated stocks and consider

the resulting eight stock portfolio as well. In both portfolios we put equal

weight to the included stocks.

The results show that for a well-diversified large portfolio none of the

risk measures are violated. However, for a portfolio consisting of only

one highly volatile stock we prove that we have a violation in the classical

methods but not when we use the modern methods mentioned above.


Place, publisher, year, edition, pages
2011. , 94 p.
Keyword [en]
Financial Mathematics, Value-at-Risk, Expected Shortfall, Cornish-Fisher Expansion, Gaussian distribution, Generalized Hyperbolic distribution
National Category
Probability Theory and Statistics Other Mathematics
URN: urn:nbn:se:hh:diva-16274Local ID: IDE1112OAI: diva2:442078
Subject / course
Financial Mathematics
2011-05-30, Wigforssallen, Halmstad University, Halmstad, 12:27 (English)
Physics, Chemistry, Mathematics
Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2011-09-21Bibliographically approved

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