Hi,

Thanks to Patrick. I think he raised the question that I had in mind. My initial idea is that if we want to do the forecasting, the distriubution change and the volatility process are the two key issues. That is part of reasons that GARCH models are the best candidates when it comes to Value-at-Risk forecasting. However, I have no idea if extreme value theory has developed in this two issues. To me, extreme value theory can do a pretty good job in in-sample fitting. What about in out-sample forecasting? I wonder.

Or what we can do is to assume the constant return distribution and the n-period ahead forecasts are calculated as the last-period estimate multiplied by the squart root of the number of periods ahead.

Please be generous enough to share your opinions, suggestion, or corrections.

Wei-han



________________________________
From: Patrick Burns <patrick@burns-stat.com>
To: Debashis Dutta <dutt.debashis@gmail.com>
Cc: R-SIG-Finance@stat.math.ethz.ch; Murali.MENON@fortisinvestments.com
Sent: Thursday, July 2, 2009 4:10:33 AM
Subject: Re: [R-SIG-Finance] Fw: Value-at-Risk

In doing the forecasting there are two
things to get right: the distribution
and the changes in volatility.  In the
research that I've done, getting the
volatility changes right appeared to be
much more important than getting the
distribution right.

I have no problem with bringing extreme
value theory in, but I don't see how the
volatility issue can be avoided.  There
is the problem of heteroskedasticity
when estimating the tails that makes
EVT tricky to apply.

The work I did was in equities, but I
suspect that the situation wouldn't
be all that different for other asset
classes.


Patrick Burns
patrick@burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of "The R Inferno" and "A Guide for the Unwilling S User")

Debashis Dutta wrote:
> Dear Murali,
> 
> I fundamentally disagree with you on your comments “…The assumption of a
> constant tail index results in misleading VaR at the extreme tails,
> especially when there are several regime shifts.” The works exhibited by
> Researchers and study made by Practitioners proved the contrary.
> 
> Please see a recent paper titled “The Extreme Value Theory Value Theory
> Performance in the event of major financial crisis" by Adrian F. Rossignolo
> Uiversity of BuenosAirs, February 2009.
> 
> 
> 
> The key outcome:
> 
> 
> 
> Extreme Value Theory (EVT) provides a method to estimate VaR at high
> quantiles of the distribution, consequently focusing on extraordinary and
> unusual circumstances. … EVT to calculate VaR for six stock market indices
> belonging to developed and emerging markets in two different ways:
> Unconditional EVT on raw returns and Conditional EVT which blends
> Quasi-Maximum-Likelihood fitting of GARCH models to estimate current dynamic
> volatility and EVT for estimating the tails of the innovation distribution
> of the GARCH residuals (both tails independently). Backtesting EVT
> representations using turmoil recorded in 2008, and comparing their
> performance with that of the most popular representations nowadays in vogue,
> it is found that EVT schemes could help institutions to avoid huge losses
> arising from market disasters. A simple exercise on the constitution of
> Regulatory Capital illustrates the advantages of EVT.
> 
> 
> 
> I being a practitioner agree with Adrain.
> 
> 
> 
> There is also a recent study on POT in GCC.
> 
> 
> 
> The paper “ The tail behavior of extreme stock returns in the Gulf emerging
> markets: An implication for financial risk management” by Aktham I.
> Maghyereh and Haitham A. Al-Zoubi , Studies in Economics and
> Finance<http://www.emeraldinsight.com/1086-7376.htm>,
> 2008, Vol. - 25, Issue 1, 21-37.
> 
> 
> 
> Findings – Not only is the heavy tail found to be a facial appearance in
> these markets, but also POT method of modelling extreme tail quantiles is
> more accurate than conventional methodologies (historical simulation and
> normal distribution models) in estimating the tail behavior of the Gulf
> markets returns. Across all return series, it is found that left and right
> tails behave very different across countries.
> 
> 
> 
> I am sorry to disagree with your comment. “Likewise, in the credit markets,
> EVT may not do too well.”
> 
> Please see the Basel Paper “Extreme tails for linear portfolio credit risk
> models” by André Lucas, Pieter Klaassen,Peter Spreij and Stefan Straetmans.
> 
> 
> 
> Concluding Remarks of the paper:
> 
> Upon comparing the analytic tail probabilities with their extreme value
> counterparts, we found that the extreme value probabilities come close to
> their true values provided one goes very far into the credit loss tail.
> 
> 
> 
> The word of caution that is also mentioned in the concluding remarks
> 
> 
> 
>  “We conclude that standard use of EVT methods as applied in, for example,
> the market risk context is inappropriate in the credit risk context.”
> Possibly you have mistaken this comment.
> 
> 
> 
> Kind Regards,
> 
> Debashis
> 
> 
> 
> 2009/7/1 <Murali.MENON@fortisinvestments.com>
> 
>> 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@stat.math.ethz.ch
>> [mailto:r-sig-finance-bounces@stat.math.ethz.ch] On Behalf Of Debashis
>> Dutta
>> Sent: 01 July 2009 14:25
>> To: Wei-han Liu
>> Cc: R-SIG-Finance@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
>>

>>> Thanks a lot, Robert.
>>>
>>> I know GARCH models has its forecasting capacity as the reference you
>>> shared indicates.
>>>
>>> I wonder if the Value-at-Risk estimated by extreme value theory can
>>> also be used for forecasting purpose. Is there some theory background
>>> in this regard?
>>>
>>> Wei-han
>>>
>>>
>>>
>>> ----- Forwarded Message ----
>>> From: Robert Iquiapaza <rbali@ufmg.br>

>>> r-sig-finance@stat.math.ethz.ch" <R-SIG-Finance@stat.math.ethz.ch>
>>> Sent: Wednesday, July 1, 2009 6:37:21 PM
>>> Subject: Re: [R-SIG-Finance] Value-at-Risk
>>>
>>> See for example "Accurate value-at-risk forecasting based on the
>>> normal-GARCH model" by C Hartz, S Mittnik, M Paolella - Computational
>>> Statistics and Data Analysis, 2006
>>>
>>> best
>>>
>>> --------------------------------------------------
>>>
>>> Sent: Tuesday, June 30, 2009 12:16 PM
>>> To: <R-SIG-Finance@stat.math.ethz.ch>
>>> Subject: [R-SIG-Finance] Value-at-Risk
>>>
>>>> Dear R-users:
>>>>
>>>> Several questions please on Value-at-Risk.
>>>>
>>>> Is Value-at-Risk designed for forecasting purpose?
>>>>
>>>> I wonder if Value-at-Risk estimated by in-sample data can be used
>>>> for
>>> out-of-sample forecasting?
>>>> If in-sample Value-at-Risk is estimated by several methods, is it
>>> appropriate to do the model comparisons based on out--of-sample
>> performance?
>>>> Wei-han Liu
>>>
>>>
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