Value-at-Risk

Hi,
Regarding the use of EVT-based VaR, I think it is dependent on the asset
class. In exchange rates, e.g., you may generally be served well with
EVT for the major currencies, but might do quite badly with emerging
market currencies. Likewise, in the credit markets, EVT may not do too
well. The assumption of a constant tail index results in misleading VaR
at the extreme tails, especially when there are several regime shifts.
Take a look at the paper "Testing for Multiple Regimes in the Tail
Behavior of Emerging Currency Returns" by B. Candelon and S. Straetmans,
LIFE Working Paper 03-035.
Cheers,
Murali

-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Debashis
Dutta
Sent: 01 July 2009 14:25
To: Wei-han Liu
Cc: R-SIG-Finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] Fw: Value-at-Risk

Dear Wei-han,

I believe EVT based VaR would provide a better solution specially in
stressed situation like the present one, modeling the extremal behaviour
in the tail. I used Peaks Over Threshold (POT) based VaR method in my
doctoral dissertation.

Back testing and comparing the new method to existing ones on real
financial events show that this POT based VaR method provides a rather
realistic model for the extremal behavior of financial processes,
enabling a precise estimation of risk measures. Through the GPD , the
model provides a way of estimating the tail behaviour of the random
variables without knowledge of the true distribution and as such it is a
good candidate for Vale at Risk computation.

Most common at this moment is the tail-fitting approach based on the
second theorem in extreme value theory (Theorem II Pickands(1975),
Balkema and de Haan(1974)). In general this conforms to the first
theorem in extreme value theory (Theorem I Fisher and Tippett(1928), and
Gnedenko (1943)).The difference between the two theorems is due to the
nature of the data generation.

 For theorem I the data are generated in full range, while in theorem II
data is only generated when it surpasses a certain threshold (POT's
models or Peak Over Threshold). The POT approach has been developed
largely in the insurance business, where only losses (pay outs) above a
certain threshold are accessible to the insurance company.

 Kind Regards,
Debashis

Value-at-Risk

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