Value at risk and selfsimilarity
Menkens, Olaf (2007) Value at risk and selfsimilarity. In: Miller, John and Edelman, David and Appleby, John A.D., (eds.) Numerical methods for finance. Chapman & Hall/CRC Financial Mathematics Series, 8 . CRC Press, pp. 225253. ISBN 9781584889250 Full text available as: AbstractThe concept of Value at Risk measures the "risk" of a portfolio and is a statement of the following form: With probability q the potential loss will not exceed the Value at Risk figure. It is in widespread use within the banking industry.
It is common to derive the Value at Risk figure of d days from the one of one–day by multiplying with √d. Obviously, this formula is right, if the changes in the value of the portfolio are normally distributed with stationary and independent increments. However, this formula is no longer valid, if arbitrary distributions are assumed. For example, if the distributions of the changes in the value of the portfolio are self–similar with Hurst coefficient H,
the Value at Risk figure of one–day has to be multiplied by dH in order to get the Value at Risk figure for d days.
This paper investigates to which extent this formula (of multiplying by √d) can be applied for all financial time series. Moreover, it will be studied how much the risk can be over– or underestimated, if the above formula is used. The scaling law coefficient and the Hurst exponent are calculated for various financial time series for several quantiles. Item Type:  Book Section 

Refereed:  Yes 

Uncontrolled Keywords:  Square–root–of–time rule; time–scaling of risk; scaling law; Value at Risk; self–similarity; order statistics; Hurst exponent estimation in the quantiles; 

Subjects:  Mathematics 

DCU Faculties and Centres:  DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences 

Publisher:  CRC Press 

Copyright Information:  Copyright © 2007 Taylor and Francis 

Use License:  This item is licensed under a Creative Commons AttributionNonCommercialShare Alike 3.0 License. View License 

ID Code:  537 

Deposited On:  02 Sep 2008 15:38 by DORAS Administrator. Last Modified 01 Mar 2009 04:02 

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