Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)
Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)
By Philippe Jorion
McGraw-Hill (2007)
Abstract Paper

Christophe Hurlin

University of Orleans

France

Coder Page  

Christophe Perignon

HEC Paris

France

Coder Page  

This code computes the Value-at-Risk (VaR) of a portfolio under the normality assumption as explained in the chapter 7 (Portfolio Risk: Analytical Methods) of the Jorion’s book “Value-at-Risk”. The number of assets is limited to 100. From the returns time series of the N assets (TxN matrix data), the code automatically computes the (unconditional) VaR of each asset, the portfolio’s VaR, the undiversified VaR (i.e the sum of the VaR of each asset), the marginal VaR, and the component VaR for each asset. By convention, all VaRs are positive.
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Abstract
Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk, Second Edition, will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
Jorion, P., "Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)", McGraw-Hill , Second edition.
Matrix of returns
Matrix of returns
Coverage rate
Coverage rate
Portfolio's weights
Portfolio's weights
Waiting time

Please cite the publication as :

Jorion, P., "Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)", McGraw-Hill , Second edition.

Please cite the companion website as :

Jorion, P., "Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)", RunMyCode companion website, http://www.execandshare.org/CompanionSite/Site74

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Variable/Parameters Description, constraint Comments
Matrix of returns
    This (T,U) matrix includes the returns of each of the U assets (in column). The sample size T is limited to 1000 and the number of assets U is limited to 100.
    Coverage rate
      The coverage rate can be fixed at 1% (VaR99%) or at 5% (VaR95%).
      Portfolio's weights
        This vector corresponds to the weights of each asset in the portfolio. The number of weights must be identical to the number of column of the P&L’s matrix. The sum of weights must be equal to 1. The weights can be null or negative.
        Variable/Parameters Description Visualisation
        Matrix of returns The demo data corresponds to the daily returns of Bank of America (asste n°1), JP Morgan (asset n°2) and City Group (asset n°3) between 01/02/2009 and 12/31/2010.
        Coverage rate The coverage rate is fixed at 1% (VaR99%).
        Portfolio's weights Each of the 3 assets has the weight in the portfolio.
        Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)
        C. Hurlin, and C. Perignon (2012)
        Computing Date Status Actions
        Coders:

        Christophe Hurlin also created these companion sites

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        Unit Root Tests for Panel Data
        Abstract
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        Testing for Unit Roots in Heterogeneous Panels
        Abstract
        This paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics. In particular it proposes a standardized t-bar test statistic based on the (augmented) Dickey–Fuller statistics averaged across the groups. Under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension) →∞. A diagonal convergence result with T and N→∞ while N/T→k,k being a finite non-negative constant, is also conjectured. In the special case where errors in individual Dickey–Fuller (DF) regressions are serially uncorrelated a modified version of the standardized t-bar statistic is shown to be distributed as standard normal as N→∞ for a fixed T, so long as T>5 in the case of DF regressions with intercepts and T>6 in the case of DF regressions with intercepts and linear time trends. An exact fixed N and T test is also developed using the simple average of the DF statistics. Monte Carlo results show that if a large enough lag order is selected for the underlying ADF regressions, then the small sample performances of the t-bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (Unpublished manuscript, University of California, San Diego, 1993).
        Hurlin, C., "Testing for Unit Roots in Heterogeneous Panels ", Journal of Econometrics, 115, 53-74.
        Authors: Im
        Pesaran
        Shin
        Coders: Hurlin
        Last update
        10/08/2012
        Ranking
        61
        Runs
        57
        Visits
        106
        Testing for a Unit Root in Panels with Dynamic Factors
        Abstract
        This paper studies testing for a unit root for large n and T panels in which the cross-sectional units are correlated. To model this cross-sectional correlation, we assume that the data are generated by an unknown number of unobservable common factors. We propose unit root tests in this environment and derive their (Gaussian) asymptotic distribution under the null hypothesis of a unit root and local alternatives. We show that these tests have significant asymptotic power when the model has no incidental trends. However, when there are incidental trends in the model and it is necessary to remove heterogeneous deterministic components, we show that these tests have no power against the same local alternatives. Through Monte Carlo simulations, we provide evidence on the finite sample properties of these new tests.
        Hurlin, C., "Testing for a Unit Root in Panels with Dynamic Factors", Journal of Econometrics, 122, 81-126.
        Authors: Moon
        Perron
        Coders: Hurlin
        Last update
        10/08/2012
        Ranking
        62
        Runs
        399
        Visits
        124
        Determining the Number of Factors in Approximate Factors Models
        Abstract
        In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors (r), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of r. We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice.
        Hurlin, C., "Determining the Number of Factors in Approximate Factors Models", Econometrica, 70, 191-221.
        Authors: Bai
        Ng
        Coders: Hurlin
        Last update
        01/29/2013
        Ranking
        39
        Runs
        66
        Visits
        230
        Maximum Likelihood Methods for Models of Markets in Disequilibrium
        Abstract
        For the abstract, please click on: http://www.jstor.org/discover/10.2307/1914215?uid=3738016&uid=2&uid=4&sid=56146953873
        Hurlin, C., "Maximum Likelihood Methods for Models of Markets in Disequilibrium", Econometrica, 42, 1013-1030.
        Authors: Maddala
        Nelson
        Coders: Hurlin
        Last update
        02/15/2013
        Ranking
        50
        Runs
        85
        Visits
        391
        Why don’t Banks Lend to the Private Sector in Egypt?
        Abstract
        Bank credit to the private sector fell as a share to GDP during the last decade, in spite of a successful bank recapitalization in the middle of the 2000s and high and stable growth before the recent macroeconomic turmoil. This paper explains this trend based on both bank supply factors and demand for credit from the private sector. First the paper describes the evolution of the banks’ sources and uses of funds in the period 2005-2011, characterized by two different cycles of external capital flows. Then it estimates supply and demand equations of credit to the private sector, using quarterly data for the period 1999-2011. First, the system of simultaneous equations is estimated assuming continuous market clearing. Then the system is estimated allowing for transitory disequilibrium. In general, the main results are robust to the market clearing assumption. Our main findings show that, while real industrial production and the stock market have a significant impact on credit demand, deposits and claims on government affected the supply of credit in Egypt. Finally, both models yield similar results for the most recent period of private credit contraction: the single most important factor explaining the largest share of the decline is the expansion of banking credit to the public sector. The slowdown in economic activity and the contraction of bank deposits explain the remainder of the predicted contraction in bank credit to the private sector.
        Herrera, S., C. Hurlin, and C. Zaki, "Why don’t Banks Lend to the Private Sector in Egypt? ", World Bank Working Paper Series.
        Authors: Herrera
        Hurlin
        Zaki
        Coders: Herrera
        Hurlin
        Zaki
        Last update
        10/17/2013
        Ranking
        56
        Runs
        252
        Visits
        112
        Are Public Investment Efficient in Creating Capital Stocks in Developing Countries? Estimates of Government Net Capital Stocks for 26 Developing Countries, 1970-2002
        Abstract
        In many poor countries, the problem is not that governments do not invest, but that these investments do not create productive capital. So, the cost of public investments does not correspond to the value of the capital stocks. In this paper, we propose an original non parametric approach to evaluate the efficiency function that links variations (net of depreciation) of stocks to public investments. We consider four sectors (electricity, telecommunications, roads and railways) of two Latin American countries (Mexico and Colombia). We show that there is a large discrepancy between the amount of investments and the value of increases in stocks.
        Arestoff, F., and C. Hurlin, "Are Public Investment Efficient in Creating Capital Stocks in Developing Countries? Estimates of Government Net Capital Stocks for 26 Developing Countries, 1970-2002 ", Economics Bulletin, 30, 1515-1531.
        Authors: Arestoff
        Hurlin
        Coders: Arestoff
        Hurlin
        Last update
        10/08/2012
        Ranking
        11
        Runs
        N.A.
        Visits
        26

        Christophe Perignon also created these companion sites

        The Risk Map: A New Tool for Validating Risk Models
        Abstract
        This paper presents a new tool for validating risk models. This tool, called the Risk Map, jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of Value-at-Risk (VaR) super exception, which is defined as a situation in which the loss exceeds both the standard VaR and a VaR defined at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions is rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic (e.g. CoVaR) risk estimates or to assess the performance of the margin system of a clearing house.
        Colletaz, G., C. Hurlin, and C. Perignon, "The Risk Map: A New Tool for Validating Risk Models", SSRN.
        Authors: Colletaz
        Hurlin
        Perignon
        Coders: Colletaz
        Hurlin
        Perignon
        Last update
        07/25/2013
        Ranking
        51
        Runs
        146
        Visits
        431
        A New Approach to Comparing VaR Estimation Methods
        Abstract
        We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
        Perignon, C., and D. Smith, C. Hurlin, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives , 15, 54-66.
        Authors: Perignon
        Smith
        Coders: Perignon
        Smith
        Hurlin
        Last update
        07/16/2012
        Ranking
        54
        Runs
        11
        Visits
        270
        Backtesting Value-at-Risk: A Duration-Based Approach
        Abstract
        Financial risk model evaluation or backtesting is a key part of the internal model’s approach to market risk management as laid out by the Basle Committee on Banking Supervision. However, existing backtesting methods have relatively low power in realistic small sample settings. Our contribution is the exploration of new tools for backtesting based on the duration of days between the violations of the Value-at-Risk. Our Monte Carlo results show that in realistic situations, the new duration-based tests have considerably better power properties than the previously suggested tests.
        Hurlin, C., and C. Perignon, "Backtesting Value-at-Risk: A Duration-Based Approach", Journal of Financial Econometrics, 2, 84-108.
        Authors: Pelletier
        Christoffersen
        Coders: Hurlin
        Perignon
        Last update
        07/23/2012
        Ranking
        26
        Runs
        17
        Visits
        207
        Evaluating Interval Forecasts
        Abstract
        A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage. Consequently, the author sets out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.
        Hurlin, C., C. Perignon, "Evaluating Interval Forecasts", International Economic Review, 39, 841-862.
        Authors: Christoffersen
        Coders: Hurlin
        Perignon
        Last update
        03/09/2012
        Ranking
        32
        Runs
        57
        Visits
        167
        The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk
        Abstract
        The hybrid approach combines the two most popular approaches to VaR estimation: RiskMetrics and Historical Simulation. It estimates the VaR of a portfolio by applying exponentially declining weights to past returns and then finding the appropriate percentile of this time-weighted empirical distribution. This new approach is very simple to implement. Empirical tests show a significant improvement in the precision of VaR forecasts using the hybrid approach relative to these popular approaches.
        Hurlin, C., C. Perignon, "The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk", Risk, 1, 64-67.
        Authors: Boudoukh
        Richardson
        Whitelaw
        Coders: Hurlin
        Perignon
        Last update
        07/17/2012
        Ranking
        52
        Runs
        4
        Visits
        67
        Diversification and Value-at-Risk
        Abstract
        A pervasive and puzzling feature of banks’ Value-at-Risk (VaR) is its abnormally high level, which leads to excessive regulatory capital. A possible explanation for the tendency of commercial banks to overstate their VaR is that they incompletely account for the diversification effect among broad risk categories (e.g., equity, interest rate, commodity, credit spread, and foreign exchange). By underestimating the diversification effect, bank’s proprietary VaR models produce overly prudent market risk assessments. In this paper, we examine empirically the validity of this hypothesis using actual VaR data from major US commercial banks. In contrast to the VaR diversification hypothesis, we find that US banks show no sign of systematic underestimation of the diversification effect. In particular, diversification effects used by banks is very close to (and quite often larger than) our empirical diversification estimates. A direct implication of this finding is that individual VaRs for each broad risk category, just like aggregate VaRs, are biased risk assessments.
        Perignon, C., and D. Smith, "Diversification and Value-at-Risk", Journal of Banking and Finance, 34.
        Authors: Perignon
        Smith
        Coders: Perignon
        Smith
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        45
        A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR
        Abstract
        In this paper, we propose a theoretical and empirical comparison of two popular systemic risk measures - Marginal Expected Shortfall (MES) and Delta Conditional Value at Risk (ΔCoVaR) - that can be estimated using publicly available data. First, we assume that the time-varying correlation completely captures the dependence between firm and market returns. Under this assumption, we derive three analytical results: (i) we show that the MES corresponds to the product of the conditional ES of market returns and the time-varying beta of this institution, (ii) we give an analytical expression of the ΔCoVaR and show that the CoVaR corresponds to the product of the VaR of the firm's returns and the time-varying linear projection coefficient of the market returns on the firm's returns and (iii) we derive the ratio of the MES to the ΔCoVaR. Second, we relax this assumption and propose an empirical comparison for a panel of 61 US financial institutions over the period from January 2000 to December 2010. For each measure, we propose a cross-sectional analysis, a time-series comparison and rankings analysis of these institutions based on the two measures.
        Benoit, S., G. Colletaz, C. Hurlin, and C. Perignon, "A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR", SSRN.
        Authors: Benoit
        Colletaz
        Hurlin
        Perignon
        Coders: Benoit
        Colletaz
        Hurlin
        Perignon
        Last update
        10/25/2012
        Ranking
        53
        Runs
        181
        Visits
        398
        Techniques for Verifying the Accuracy of Risk Management Models
        Abstract
        Risk exposures are typically quantified in terms of a "Value at Risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss probability distribution. Given their function both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to quantify the accuracy of an institution's VaR estimates. This study shows that the formal statistical procedures that would typically be used in performance-based VaR verification tests require large samples to produce a reliable assessment of a model's accuracy in predicting the size and likelihood of very low probability events. Verification test statistics based on historical trading profits and losses have very poor power in small samples, so it does not appear possible for a bank or its supervisor to verify the accuracy of a VaR estimate unless many years of performance data are available. Historical simulation-based verification test statistics also require long samples to generate accurate results: Estimates of 0.01 critical values exhibit substantial errors even in samples as large as ten years of daily data.
        Hurlin, C., C. Perignon, "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives, 3, 73-84.
        Authors: Kupiec
        Coders: Hurlin
        Perignon
        Last update
        04/17/2012
        Ranking
        57
        Runs
        26
        Visits
        339
        The pernicious effects of contaminated data in risk management
        Abstract
        Banks hold capital to guard against unexpected surges in losses and long freezes in financial markets. The minimum level of capital is set by banking regulators as a function of the banks’ own estimates of their risk exposures. As a result, a great challenge for both banks and regulators is to validate internal risk models. We show that a large fraction of US and international banks uses contaminated data when testing their models. In particular, most banks validate their market risk model using profit-and-loss (P/L) data that include fees and commissions and intraday trading revenues. This practice is inconsistent with the definition of the employed market risk measure. Using both bank data and simulations, we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models. Moreover, our estimates suggest that the use of contaminated data can significantly reduce (market-risk induced) regulatory capital.
        Fresard, L., C. Perignon, and A. Wilhelmsson, "The pernicious effects of contaminated data in risk management", Journal of Banking and Finance, 35.
        Authors: Fresard
        Perignon
        Wilhelmsson
        Coders: Fresard
        Perignon
        Wilhelmsson
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        42
        The level and quality of Value-at-Risk disclosure by commercial banks
        Abstract
        In this paper we study both the level of Value-at-Risk (VaR) disclosure and the accuracy of the disclosed VaR figures for a sample of US and international commercial banks. To measure the level of VaR disclosures, we develop a VaR Disclosure Index that captures many different facets of market risk disclosure. Using panel data over the period 1996–2005, we find an overall upward trend in the quantity of information released to the public. We also find that Historical Simulation is by far the most popular VaR method. We assess the accuracy of VaR figures by studying the number of VaR exceedances and whether actual daily VaRs contain information about the volatility of subsequent trading revenues. Unlike the level of VaR disclosure, the quality of VaR disclosure shows no sign of improvement over time. We find that VaR computed using Historical Simulation contains very little information about future volatility.
        Perignon, C., and D. Smith, "The level and quality of Value-at-Risk disclosure by commercial banks", Journal of Banking and Finance, 34.
        Authors: Perignon
        Smith
        Coders: Perignon
        Smith
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        25
        A New Approach to Comparing VaR Estimation Methods
        Abstract
        We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
        Perignon, C., and D. Smith, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives, Winter.
        Authors: Smith
        Perignon
        Coders: Perignon
        Smith
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        43
        Margin Backtesting
        Abstract
        This paper presents a validation framework for collateral requirements or margins on a derivatives exchange. It can be used by investors, risk managers, and regulators to check the accuracy of a margining system. The statistical tests presented in this study are based either on the number, frequency, magnitude, or timing of margin exceedances, which are de…ned as situations in which the trading loss of a market participant exceeds his or her margin. We also propose an original way to validate globally the margining system by aggregating individual backtesting statistics ob- tained for each market participant.
        Hurlin, C., and C. Perignon, "Margin Backtesting", University of Orleans, HEC Paris.
        Authors: Hurlin
        Perignon
        Coders: Hurlin
        Perignon
        Last update
        07/23/2014
        Ranking
        36
        Runs
        377
        Visits
        433
        Value-at-Risk (Chapter 5: Computing VaR)
        Abstract
        Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
        Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 5: Computing VaR)", MacGraw-Hill, Third Edition.
        Authors: Jorion
        Coders: Hurlin
        Perignon
        Last update
        03/19/2012
        Ranking
        44
        Runs
        63
        Visits
        328

        Other Companion Sites on same paper

        Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)

        Other Companion Sites relative to similar papers

        Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests
        Abstract
        In this paper we propose a new tool for backtesting that examines the quality of Value-at-Risk (VaR) forecasts. To date, the most distinguished regression-based backtest, proposed by Engle and Manganelli (2004), relies on a linear model. However, in view of the dichotomic character of the series of violations, a non-linear model seems more appropriate. In this paper we thus propose a new tool for backtesting (denoted DB) based on a dynamic binary regression model. Our discrete-choice model, e.g. Probit, Logit, links the sequence of violations to a set of explanatory variables including the lagged VaR and thelagged violations in particular. It allows us to separately test the unconditional coverage, the independence and the conditional coverage hypotheses and it is easy to implement. Monte-Carlo experiments show that the DB test exhibits good small sample properties in realistic sample settings (5% coverage rate with estimation risk). An application on a portfolio composed of three assets included in the CAC40 market index is finally proposed.
        Hurlin, C., and E. Dumitrescu, "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests", Finance, 33.
        Authors: Hurlin
        Pham
        Coders: Hurlin
        Dumitrescu
        Last update
        07/05/2012
        Ranking
        20
        Runs
        46
        Visits
        168
        The Risk Map: A New Tool for Validating Risk Models
        Abstract
        This paper presents a new tool for validating risk models. This tool, called the Risk Map, jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of Value-at-Risk (VaR) super exception, which is defined as a situation in which the loss exceeds both the standard VaR and a VaR defined at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions is rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic (e.g. CoVaR) risk estimates or to assess the performance of the margin system of a clearing house.
        Colletaz, G., C. Hurlin, and C. Perignon, "The Risk Map: A New Tool for Validating Risk Models", SSRN.
        Authors: Colletaz
        Hurlin
        Perignon
        Coders: Colletaz
        Hurlin
        Perignon
        Last update
        07/25/2013
        Ranking
        51
        Runs
        146
        Visits
        431
        Backtesting Value-at-Risk: A GMM Duration-based Test
        Abstract
        This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e. the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple J-statistic based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christoffersen, 1998). Third, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. Besides, we study the consequences of the estimation risk on the duration-based backtesting tests and propose a sub-sampling approach for robust inference derived from Escanciano and Olmo (2009). An empirical application for Nasdaq returns confirms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities.
        Colletaz, G., B. Candelon, C. Hurlin, and S. Tokpavi, "Backtesting Value-at-Risk: A GMM Duration-based Test", Journal of Financial Econometrics, 9(2), 314-343 .
        Authors: Candelon
        Colletaz
        Hurlin
        Tokpavi
        Coders: Colletaz
        Candelon
        Hurlin
        Tokpavi
        Last update
        06/28/2012
        Ranking
        55
        Runs
        23
        Visits
        291
        Prices and Asymptotics for Discrete Variance Swaps
        Abstract
        We derive closed-form expressions for the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston and Hull-White stochastic volatility models we give simple explicit expressions (improving Broadie and Jain (2008a) for the Heston case). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than the continuous variance swap. Interest rates and correlation between underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a), Jarrow et al. (2012) and Keller-Ressel (2011).
        Bernard, C., and Z. Cui, "Prices and Asymptotics for Discrete Variance Swaps", SSRN.
        Authors: Bernard
        Cui
        Coders: Bernard
        Cui
        Last update
        11/22/2012
        Ranking
        N.A.
        Runs
        10
        Visits
        302
        A New Approach to Comparing VaR Estimation Methods
        Abstract
        We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
        Perignon, C., and D. Smith, C. Hurlin, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives , 15, 54-66.
        Authors: Perignon
        Smith
        Coders: Perignon
        Smith
        Hurlin
        Last update
        07/16/2012
        Ranking
        54
        Runs
        11
        Visits
        270
        Volatility Forecast Comparison Using Imperfect Volatility Proxies
        Abstract
        The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We motivate our study with analytical results on the distortions caused by some widely used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. We then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of “robust” loss functions. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.
        Patton, J. A., "Volatility Forecast Comparison Using Imperfect Volatility Proxies", Journal of Econometrics, 160, 246-256.
        Authors: Patton
        Coders: Patton
        Last update
        11/17/2012
        Ranking
        1
        Runs
        90
        Visits
        993
        The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk
        Abstract
        The hybrid approach combines the two most popular approaches to VaR estimation: RiskMetrics and Historical Simulation. It estimates the VaR of a portfolio by applying exponentially declining weights to past returns and then finding the appropriate percentile of this time-weighted empirical distribution. This new approach is very simple to implement. Empirical tests show a significant improvement in the precision of VaR forecasts using the hybrid approach relative to these popular approaches.
        Hurlin, C., C. Perignon, "The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk", Risk, 1, 64-67.
        Authors: Boudoukh
        Richardson
        Whitelaw
        Coders: Hurlin
        Perignon
        Last update
        07/17/2012
        Ranking
        52
        Runs
        4
        Visits
        67
        Competition and the Cost of Debt
        Abstract
        This paper empirically shows that the cost of bank debt is systematically higher for firms that operate in competitive product markets. Using various proxies for product market competition, and reductions of import tariff rates to capture exogenous changes to a firm's competitive environment, I find that competition has a significantly positive effect on the cost of bank debt. Moreover, the analysis reveals that the effect of competition is greater in industries in which small firms face financially strong rivals, in industries with intense strategic interactions between firms, and in illiquid industries. Overall, these findings suggest that banks price financial contracts by taking into account the risk that arises from product market competition.
        Valta, P., "Competition and the Cost of Debt", Journal of Financial Economics, 105.
        Authors: Valta
        Coders: Valta
        Last update
        08/16/2013
        Ranking
        27
        Runs
        N.A.
        Visits
        81
        How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes
        Abstract
        We propose a discrete-time stochastic volatility model in which regime switching serves three purposes. First, changes in regimes capture low-frequency variations. Second, they specify intermediate-frequency dynamics usually assigned to smooth autoregressive transitions. Finally, high-frequency switches generate substantial outliers. Thus a single mechanism captures three features that are typically viewed as distinct in the literature. Maximum-likelihood estimation is developed and performs well in finite samples. Using exchange rates, we estimate a version of the process with four parameters and more than a thousand states. The multifractal outperforms GARCH, MS-GARCH, and FIGARCH in- and out-of-sample. Considerable gains in forecasting accuracy are obtained at horizons of 10 to 50 days.
        Calvet, E. L., and A. J. Fisher, "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes", Journal of Financial Econometrics, 2, 49-83.
        Authors: Calvet
        Fisher
        Coders: Calvet
        Fisher
        Last update
        07/23/2012
        Ranking
        6
        Runs
        118
        Visits
        470
        Does Corporate Governance Predict Firms' Market Values? Evidence from Korea
        Abstract
        We report strong OLS and instrumental variable evidence that an overall corporate governance index is an important and likely causal factor in explaining the market value of Korean public companies. We construct a corporate governance index (KCGI, 0~100) for 515 Korean companies based on a 2001 Korea Stock Exchange survey. In OLS, a worst-to-best change in KCGIpredicts a 0.47 increase in Tobin's q (about a 160% increase in share price). This effect is statistically strong (t = 6.12) and robust to choice of market value variable (Tobin's q, market/book, and market/sales), specification of the governance index, and inclusion of extensive control variables. We rely on unique features of Korean legal rules to construct an instrument for KCGI. Good instruments are not available in other comparable studies. Two-stage and three-stage least squares coefficients are larger than OLS coefficients and are highly significant. Thus, this paper offers evidence consistent with a causal relationship between an overall governance index and higher share prices in emerging markets. We also find that Korean firms with 50% outside directors have 0.13 higher Tobin's q (roughly 40% higher share price), after controlling for the rest of KCGI. This effect, too, is likely causal. Thus, we report the first evidence consistent with greater board independence causally predicting higher share prices in emerging markets.
        Kim, W., B. S. Black , and H. Jang, "Does Corporate Governance Predict Firms' Market Values? Evidence from Korea", The Journal of Law, Economics, & Organization, 22, 366-413.
        Authors: Kim
        Black
        Jang
        Coders: Kim
        Black
        Jang
        Last update
        10/08/2012
        Ranking
        5
        Runs
        39
        Visits
        150
        Forcasting Expected Shortfall with a Generalized Asymetric Student-t Distribution
        Abstract
        Financial returns typically display heavy tails and some skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be espe- cially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using a recent generalization of the asymmetric Student-t distribution to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial returns and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distribution is used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide empirical evidence for the usefulness of the generalized distribution in improving prediction of downside market risk of financial assets.
        Galbraith, W. J., and D. Zhu, "Forcasting Expected Shortfall with a Generalized Asymetric Student-t Distribution", Centre interuniversitaire de recherche en analyse des organisations.
        Authors: Galbraith
        Zhu
        Coders: Galbraith
        Zhu
        Last update
        07/27/2012
        Ranking
        41
        Runs
        9
        Visits
        143
        Margin Backtesting
        Abstract
        This paper presents a validation framework for collateral requirements or margins on a derivatives exchange. It can be used by investors, risk managers, and regulators to check the accuracy of a margining system. The statistical tests presented in this study are based either on the number, frequency, magnitude, or timing of margin exceedances, which are de…ned as situations in which the trading loss of a market participant exceeds his or her margin. We also propose an original way to validate globally the margining system by aggregating individual backtesting statistics ob- tained for each market participant.
        Hurlin, C., and C. Perignon, "Margin Backtesting", University of Orleans, HEC Paris.
        Authors: Hurlin
        Perignon
        Coders: Hurlin
        Perignon
        Last update
        07/23/2014
        Ranking
        36
        Runs
        377
        Visits
        433
        A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR
        Abstract
        In this paper, we propose a theoretical and empirical comparison of two popular systemic risk measures - Marginal Expected Shortfall (MES) and Delta Conditional Value at Risk (ΔCoVaR) - that can be estimated using publicly available data. First, we assume that the time-varying correlation completely captures the dependence between firm and market returns. Under this assumption, we derive three analytical results: (i) we show that the MES corresponds to the product of the conditional ES of market returns and the time-varying beta of this institution, (ii) we give an analytical expression of the ΔCoVaR and show that the CoVaR corresponds to the product of the VaR of the firm's returns and the time-varying linear projection coefficient of the market returns on the firm's returns and (iii) we derive the ratio of the MES to the ΔCoVaR. Second, we relax this assumption and propose an empirical comparison for a panel of 61 US financial institutions over the period from January 2000 to December 2010. For each measure, we propose a cross-sectional analysis, a time-series comparison and rankings analysis of these institutions based on the two measures.
        Benoit, S., G. Colletaz, C. Hurlin, and C. Perignon, "A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR", SSRN.
        Authors: Benoit
        Colletaz
        Hurlin
        Perignon
        Coders: Benoit
        Colletaz
        Hurlin
        Perignon
        Last update
        10/25/2012
        Ranking
        53
        Runs
        181
        Visits
        398
        Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts
        Abstract
        Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model(CAPM)implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.
        Patton, J. A., and A. Timmermann, "Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts", Journal of Financial Economics, 98, 605-625.
        Authors: Patton
        Timmermann
        Coders: Patton
        Timmermann
        Last update
        11/17/2012
        Ranking
        63
        Runs
        19
        Visits
        116
        Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach
        Abstract
        When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observation is not explicitely computable. Using Hermite polynomials, I construct an explicit sequences of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.
        Aït-Sahalia, Y., "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach", Econometrica, 70, 223-262.
        Authors: Aït-Sahalia
        Coders: Aït-Sahalia
        Last update
        10/29/2014
        Ranking
        2
        Runs
        119
        Visits
        621
        Evaluating Interval Forecasts
        Abstract
        A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage. Consequently, the author sets out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.
        Hurlin, C., C. Perignon, "Evaluating Interval Forecasts", International Economic Review, 39, 841-862.
        Authors: Christoffersen
        Coders: Hurlin
        Perignon
        Last update
        03/09/2012
        Ranking
        32
        Runs
        57
        Visits
        167
        Backtesting Value-at-Risk: A Duration-Based Approach
        Abstract
        Financial risk model evaluation or backtesting is a key part of the internal model’s approach to market risk management as laid out by the Basle Committee on Banking Supervision. However, existing backtesting methods have relatively low power in realistic small sample settings. Our contribution is the exploration of new tools for backtesting based on the duration of days between the violations of the Value-at-Risk. Our Monte Carlo results show that in realistic situations, the new duration-based tests have considerably better power properties than the previously suggested tests.
        Hurlin, C., and C. Perignon, "Backtesting Value-at-Risk: A Duration-Based Approach", Journal of Financial Econometrics, 2, 84-108.
        Authors: Pelletier
        Christoffersen
        Coders: Hurlin
        Perignon
        Last update
        07/23/2012
        Ranking
        26
        Runs
        17
        Visits
        207
        Backtesting Value-at-Risk Accuracy: A Simple New Test
        Abstract
        This paper proposes a new test of value-at-risk (VAR) validation. Our test exploits the idea that the sequence of VAR violations (hit function) – taking value 1 - α if there is a violation, and -α otherwise – for a nominal coverage rate α verifies the properties of a martingale difference if the model used to quantify risk is adequate (Berkowitz et al., 2005). More precisely, we use the multivariate portmanteau statistic of Li and McLeod (1981), an extension to the multivariate framework of the test of Box and Pierce (1970), to jointly test the absence of autocorrelation in the vector of hit sequences for various coverage rates considered relevant for the management of extreme risks. We show that this shift to a multivariate dimension appreciably improves the power properties of the VAR validation test for reasonable sample sizes.
        Hurlin, C., and S. Tokpavi, "Backtesting Value-at-Risk Accuracy: A Simple New Test", Journal of Risk, 9, 19-37.
        Authors: Hurlin
        Tokpavi
        Coders: Hurlin
        Tokpavi
        Last update
        03/13/2012
        Ranking
        49
        Runs
        2
        Visits
        240
        Forecasting Realized Volatility Using a Nonnegative Semiparametric Model
        Abstract
        This paper introduces a parsimonious and yet exible nonnegative semi-parametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndor-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the distributional form of its error component is left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Asymptotic properties are established for the new estimation method. Simulation studies validate the new estimation method. The out-of-sample performance of the proposed model is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential smoothing method, a linear AR(1) model, a log-linear AR(1) model, and two long-memory ARFIMA models. Various loss functions are utilized to evaluate the predictive accuracy of the alternative methods. It is found that the new model generally produces highly competitive forecasts.
        Preve, D., J. Yu, "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model", Uppsala University.
        Authors: Eriksson
        Preve
        Yu
        Coders: Preve
        Yu
        Last update
        06/06/2012
        Ranking
        64
        Runs
        19
        Visits
        114
        Value-at-Risk (Chapter 5: Computing VaR)
        Abstract
        Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
        Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 5: Computing VaR)", MacGraw-Hill, Third Edition.
        Authors: Jorion
        Coders: Hurlin
        Perignon
        Last update
        03/19/2012
        Ranking
        44
        Runs
        63
        Visits
        328
        The pernicious effects of contaminated data in risk management
        Abstract
        Banks hold capital to guard against unexpected surges in losses and long freezes in financial markets. The minimum level of capital is set by banking regulators as a function of the banks’ own estimates of their risk exposures. As a result, a great challenge for both banks and regulators is to validate internal risk models. We show that a large fraction of US and international banks uses contaminated data when testing their models. In particular, most banks validate their market risk model using profit-and-loss (P/L) data that include fees and commissions and intraday trading revenues. This practice is inconsistent with the definition of the employed market risk measure. Using both bank data and simulations, we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models. Moreover, our estimates suggest that the use of contaminated data can significantly reduce (market-risk induced) regulatory capital.
        Fresard, L., C. Perignon, and A. Wilhelmsson, "The pernicious effects of contaminated data in risk management", Journal of Banking and Finance, 35.
        Authors: Fresard
        Perignon
        Wilhelmsson
        Coders: Fresard
        Perignon
        Wilhelmsson
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        42
        Techniques for Verifying the Accuracy of Risk Management Models
        Abstract
        Risk exposures are typically quantified in terms of a "Value at Risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss probability distribution. Given their function both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to quantify the accuracy of an institution's VaR estimates. This study shows that the formal statistical procedures that would typically be used in performance-based VaR verification tests require large samples to produce a reliable assessment of a model's accuracy in predicting the size and likelihood of very low probability events. Verification test statistics based on historical trading profits and losses have very poor power in small samples, so it does not appear possible for a bank or its supervisor to verify the accuracy of a VaR estimate unless many years of performance data are available. Historical simulation-based verification test statistics also require long samples to generate accurate results: Estimates of 0.01 critical values exhibit substantial errors even in samples as large as ten years of daily data.
        Hurlin, C., C. Perignon, "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives, 3, 73-84.
        Authors: Kupiec
        Coders: Hurlin
        Perignon
        Last update
        04/17/2012
        Ranking
        57
        Runs
        26
        Visits
        339
        Diversification and Value-at-Risk
        Abstract
        A pervasive and puzzling feature of banks’ Value-at-Risk (VaR) is its abnormally high level, which leads to excessive regulatory capital. A possible explanation for the tendency of commercial banks to overstate their VaR is that they incompletely account for the diversification effect among broad risk categories (e.g., equity, interest rate, commodity, credit spread, and foreign exchange). By underestimating the diversification effect, bank’s proprietary VaR models produce overly prudent market risk assessments. In this paper, we examine empirically the validity of this hypothesis using actual VaR data from major US commercial banks. In contrast to the VaR diversification hypothesis, we find that US banks show no sign of systematic underestimation of the diversification effect. In particular, diversification effects used by banks is very close to (and quite often larger than) our empirical diversification estimates. A direct implication of this finding is that individual VaRs for each broad risk category, just like aggregate VaRs, are biased risk assessments.
        Perignon, C., and D. Smith, "Diversification and Value-at-Risk", Journal of Banking and Finance, 34.
        Authors: Perignon
        Smith
        Coders: Perignon
        Smith
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        45
        Outliers and GARCH Models in Financial Data
        Abstract
        We propose to extend the additive outlier (AO) identification procedure developed by Franses and Ghijsels(Franses, P.H., Ghijsels, H., 1999. Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15, 1–9) to take into account the innovative outliers (IOs) in a GARCH model. We apply it to three daily stock market indexes and examine the effects of outliers on the diagnostics of normality.
        Charles, A., and O. Darné, D. Banulescu, E. Dumitrescu, "Outliers and GARCH Models in Financial Data", Economics Letters, 86, 347-352.
        Authors: Charles
        Darné
        Coders: Charles
        Darné
        Banulescu
        Dumitrescu
        Last update
        06/22/2012
        Ranking
        15
        Runs
        61
        Visits
        238
        The level and quality of Value-at-Risk disclosure by commercial banks
        Abstract
        In this paper we study both the level of Value-at-Risk (VaR) disclosure and the accuracy of the disclosed VaR figures for a sample of US and international commercial banks. To measure the level of VaR disclosures, we develop a VaR Disclosure Index that captures many different facets of market risk disclosure. Using panel data over the period 1996–2005, we find an overall upward trend in the quantity of information released to the public. We also find that Historical Simulation is by far the most popular VaR method. We assess the accuracy of VaR figures by studying the number of VaR exceedances and whether actual daily VaRs contain information about the volatility of subsequent trading revenues. Unlike the level of VaR disclosure, the quality of VaR disclosure shows no sign of improvement over time. We find that VaR computed using Historical Simulation contains very little information about future volatility.
        Perignon, C., and D. Smith, "The level and quality of Value-at-Risk disclosure by commercial banks", Journal of Banking and Finance, 34.
        Authors: Perignon
        Smith
        Coders: Perignon
        Smith
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        25
        Extracting Factors from Heteroskedastic Asset Returns
        Abstract
        This paper proposes an alternative to the asymptotic principal components procedure of Connor and Korajczyk (Journal of Financial Economics, 1986) that is robust to time series heteroskedasticity in the factor model residuals. The new method is simple to use and requires no assumptions stronger than those made by Connor and Korajczyk. It is demonstrated through simulations and analysis of actual stock market data that allowing heteroskedasticity sometimes improves the quality of the extracted factors quite dramatically. Over the period from 1989 to 1993, for example, a single factor extracted using the Connor and Korajczyk method explains only 8.2% of the variation of the CRSP value-weighted index, while the factor extracted allowing heteroskedasticity explains 57.3%. Accounting for heteroskedasticity is also important for tests of the APT, with p-values sometimes depending strongly on the factor extraction method used.
        Jones, S. C., "Extracting Factors from Heteroskedastic Asset Returns", Journal of Financial Economics, 62, 293-325.
        Authors: Jones
        Coders: Jones
        Last update
        11/17/2012
        Ranking
        30
        Runs
        17
        Visits
        81
        A New Approach to Comparing VaR Estimation Methods
        Abstract
        We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
        Perignon, C., and D. Smith, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives, Winter.
        Authors: Smith
        Perignon
        Coders: Perignon
        Smith
        Last update
        11/23/2012
        Ranking
        9999
        Runs
        N.A.
        Visits
        43
        Pitfalls in backtesting Historical Simulation VaR models
        Abstract
        Abstract Historical Simulation (HS) and its variant, the Filtered Historical Simulation (FHS), are the most popular Value-at-Risk forecast methods at commercial banks. These forecast methods are traditionally evaluated by means of the unconditional backtest. This paper formally shows that the unconditional backtest is always inconsistent for backtesting HS and FHS models, with a power function that can be even smaller than the nominal level in large samples. Our findings have fundamental implications in the determination of market risk capital requirements, and also explain Monte Carlo and empirical findings in previous studies. We also propose a data-driven weighted backtest with good power properties to evaluate HS and FHS forecasts. A Monte Carlo study and an empirical application with three US stocks confirm our theoretical findings. The empirical application shows that multiplication factors computed under the current regulatory framework are downward biased, as they inherit the inconsistency of the unconditional backtest.
        Escanciano, J., and P. Pei, "Pitfalls in backtesting Historical Simulation VaR models", Journal of Banking and Finance, 36, 2233-2244.
        Authors: Escanciano
        Pei
        Coders: Escanciano
        Pei
        Last update
        02/22/2013
        Ranking
        9999
        Runs
        N.A.
        Visits
        32
        A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics
        Abstract
        This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the Expected Shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.
        Colletaz, G., "A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics", Journal of Econometrics, 157, 297-305.
        Authors: Zhu
        Galbraith
        Coders: Colletaz
        Last update
        05/05/2012
        Ranking
        38
        Runs
        6
        Visits
        95
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