[R-SIG-Finance] Fw: Value-at-Risk

Wed Jul 1 22:10:33 CEST 2009

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 at 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 at 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 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
>>
>> On 01/07/2009, Wei-han Liu <weihanliu2002 at yahoo.com> wrote:
>>> 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 at ufmg.br>
>>> To: Wei-han Liu <weihanliu2002 at yahoo.com>; "
>>> r-sig-finance at stat.math.ethz.ch" <R-SIG-Finance at 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 at 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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>>>
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