Value-at-Risk
There have been many papers that combine EVT with GARCH to give out-of-sample VaR predictions. The seminal paper on this technique McNeil, A. J., and R. Frey. (2000). ??Estimation of Tail-related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach.?? Journal of Empirical Finance 7:271?300. I have a brief description of this technique in my class slides on extreme value theory http://faculty.washington.edu/ezivot/econ512/econ512extremevalue.pdf **************************************************************** * Eric Zivot * * Professor and Gary Waterman Distinguished Scholar * * Department of Economics * * Adjunct Professor of Finance * * Adjunct Professor of Statistics * Box 353330 email: ezivot at u.washington.edu * * University of Washington phone: 206-543-6715 * * Seattle, WA 98195-3330 * * * www: http://faculty.washington.edu/ezivot * ****************************************************************
On Wed, 1 Jul 2009, Wei-han Liu wrote:
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 at burns-stat.com> To: Debashis Dutta <dutt.debashis at gmail.com> Cc: R-SIG-Finance at stat.math.ethz.ch; Murali.MENON at 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 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 Andr?? 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 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> 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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