nep-rmg New Economics Papers
on Risk Management
Issue of 2015‒11‒21
twelve papers chosen by
Stan Miles
Thompson Rivers University

  1. Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Range and Realized Measures By Gerlach, Richard; Wang, Chao
  2. Fat tails and copulas: limits of diversification revisited By Ibragimov, Rustam; Prokhorov, Artem; Mo, Jingyuan
  3. The Impact of Interest Rate Risk on Bank Lending By Toni Beutler; Robert Bichsel; Adrian Bruhin; Jayson Danton
  4. Scenario generation for portfolio selection problems with tail risk measure By Jamie Fairbrother; Amanda Turner; Stein Wallace
  6. Calibration of a stock's beta using options prices By Sofiene El Aoud; Frédéric Abergel
  7. Systemic risk and insurance By Pierre-Emmanuel Darpeix
  8. Modeling Systemic Risk with Correlated Stochastic Processes By Paolo Giudici; Laura Parisi
  9. Downside Risk Neutral Probabilities By Pierre Chaigneau; Louis Eeckhoudt
  10. GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference By Hill, Jonathan B.; Prokhorov, Artem
  11. Generalized Variance: A Robust Estimator of Stock Price Volatility By Sutton, M; Vasnev, A; Gerlach, R
  12. Backtesting Value-at-Risk: A Generalized Markov Framework By Thor Pajhede

  1. By: Gerlach, Richard; Wang, Chao
    Abstract: A new framework named Realized Conditional Autoregressive Expectile (Realized- CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a framework analogous to Realized-GARCH. The Range and realized measures (Realized Variance and Realized Range) are employed as the dependent variables of the measurement equation, since they have proven more efficient than return for volatility estimation. The dependence between Range & realized measures and expectile can be modelled with this measurement equation. The grid search accuracy of the expectile level will be potentially improved with introducing this measurement equation. In addition, through employing a quadratic fitting target search, the speed of grid search is significantly improved. Bayesian adaptive Markov Chain Monte Carlo is used for estimation, and demonstrates its superiority compared to maximum likelihood in a simulation study. Furthermore, we propose an innovative sub-sampled Realized Range and also adopt an existing scaling scheme, in order to deal with the micro-structure noise of the high frequency volatility measures. Compared to the CARE, the parametric GARCH and the Realized-GARCH models, Value-at-Risk and Expected Shortfall forecasting results of 6 indices and 3 assets series favor the proposed Realized-CARE model, especially the Realized-CARE model with Realized Range and sub-sampled Realized Range.
    Keywords: Realized-CARE ; Realized Variance ; Realized Range ; Subsampling Realized Range ; Markov Chain Monte Carlo ; Target Search ; Value-at-Risk ; Expected Shortfall
    Date: 2015–09–11
  2. By: Ibragimov, Rustam; Prokhorov, Artem; Mo, Jingyuan
    Abstract: We consider the problem of portfolio risk diversification in a Value-at-Risk framework with heavy-tailed risks and arbitrary dependence captured by a copula function. We use the power law for modelling the tails and investigate whether the benefits of diversification persist when the risks in consideration are allowed to have extremely heavy tails with tail indices less than one and when their copula describes wide classes of dependence structures. We show that for asymptotically large losses with the Eyraud-Farlie-Gumbel-Morgenstern copula, the threshold value of tail indices at which diversification stops being beneficial is the same as for independent losses. We further extend this result to a wider range of dependence structures which can be approximated using power-type copulas and their approximations. This range of dependence structures includes many well known copula families, among which there are comprehensive, Archimedian, asymmetric and tail dependent copulas. In other words, diversification increases Value-at-Risk for tail indices less than one regardless of the nature of dependence between portfolio components within these classes. A wide set of simulations supports these theoretical results.
    Keywords: Value at risk ; Power law ; Diversification ; copula
    Date: 2015–09–11
  3. By: Toni Beutler (Swiss National Bank); Robert Bichsel (Swiss National Bank); Adrian Bruhin (University of Lausanne); Jayson Danton (University of Lausanne)
    Abstract: In this paper, we empirically analyze the transmission of realized interest rate risk – the gain or loss in bank economic capital due to movements in interest rates – to bank lending. We exploit a unique panel data set that contains supervisory information on the repricing maturity profiles of Swiss banks and provides us with an individual measure of interest rate risk exposure net of hedging. Our analysis yields three main results. First, our estimates indicate that a year after a permanent 1 percentage point upward shock in nominal interest rates, the average bank of 2013Q3 would ceteris paribus reduce its cumulative loan growth by approximately 170 basis points. An estimated 28% of this reduction would be the result of realized interest rate risk exposure weakening the bank’s economic capital. Second, due to the banks’ heterogeneity in interest rate risk exposure, the effect of the shock would differ across institutions and could be redistributive across regions. Finally, bank lending seems to be mainly driven by capital rather than liquidity, suggesting that a higher capitalized banking system can better shield its creditors from shocks in interest rates.
    Date: 2015–11
  4. By: Jamie Fairbrother; Amanda Turner; Stein Wallace
    Abstract: Tail risk measures such as the conditional value-at-risk are useful in the context of portfolio selection for quantifying potential losses in worst cases. However, for scenario-based problems these are problematic: because the value of a tail risk measure only depends on a small subset of the support of the distribution of asset returns, traditional scenario based methods, which spread scenarios evenly across the whole support of the distribution, yield very unstable solutions unless we use a very large number scenarios. In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure where the the asset returns have elliptical or near-elliptical distribution. Our approach in effect prioritizes the construction of scenarios in the areas of the distribution which correspond to the tail losses of feasible portfolios. The methodology is shown to work particularly well when the distribution of assets returns are positively correlated and heavy-tailed, and the performance is shown to improve as we tighten the constraints on feasible assets.
    Date: 2015–11
  5. By: Renata Karkowska (University of Warsaw, Faculty of Management)
    Abstract: We measure a systemic risk faced by European banking sectors using the CoVaR measure. We propose the conditional value-at-risk (CoVaR) for measuring a spillover risk which demonstrates the bilateral relation between the tail risks of two financial institutions. The aim of the study is to estimate the contribution systemic risk of the bank i in the analyzed banking sector of a country in conditions of its insolvency. The study included commercial banks from 8 emerging markets from Europe, which gave a total of 40 banks, traded on the public market, which provided a market valuation of the bank's capital. The conclusions are that the CoVaR seems to be a better measure for systemic risk in the banking sector than the VaR, which is more individual. And banks in developing countries in Europe do not provide significant risk for the banking sector as a whole. But it must be taken into account that some individuals that may find objectionable. Our results hence tend to a practical use of the CoVaR for supervisory purposes.
    Keywords: Systemic Risk, Value at Risk, Risk Spillovers, Banking Sector
    JEL: G01 G10 G20 G28 G38
    Date: 2015–02
  6. By: Sofiene El Aoud (FiQuant - Chaire de finance quantitative - Ecole Centrale Paris, MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec); Frédéric Abergel (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, FiQuant - Chaire de finance quantitative - Ecole Centrale Paris)
    Abstract: We present in our work a continuous time Capital Asset Pricing Model where the volatilities of the market index and the stock are both stochastic. Using a singular perturbation technique, we provide approximations for the prices of european options on both the stock and the index. These approximations are functions of the model parameters. We show then that existing estimators of the parameter beta, proposed in the recent literature, are biased in our setting because they are all based on the assumption that the idiosyncratic volatility of the stock is constant. We provide then an unbiased estimator of the parameter beta using only implied volatility data. This estimator is a forward measure of the parameter beta in the sense that it represents the information contained in derivatives prices concerning the forward realization of this parameter, we test then its capacity of prediction of forward beta and we draw a conclusion concerning its predictive power.
    Date: 2014–03–14
  7. By: Pierre-Emmanuel Darpeix (PSE - Paris-Jourdan Sciences Economiques - CNRS - Institut national de la recherche agronomique (INRA) - EHESS - École des hautes études en sciences sociales - ENS Paris - École normale supérieure - Paris - École des Ponts ParisTech (ENPC), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)
    Abstract: The literature generally agrees that the traditional insurance sector is not a source of systemic risk, and insurers are often considered to be shock absorbers rather than shock amplifiers. Yet, the evolution of the industry both in terms of structure (concentration of the reinsurers, increased linkages with banks, especially through bancassurance conglomerates) and in terms of techniques (securitization, monolines, derivatives) increased the systemic relevance of the insurers.
    Keywords: Insurance,Systemic risk,International regulation
    Date: 2015–11
  8. By: Paolo Giudici (Department of Economics and Management, University of Pavia); Laura Parisi (Department of Economics and Management, University of Pavia)
    Abstract: In this work we propose a novel systemic risk model, based on stochastic processes and correlation networks. For each country we consider three different spread measures, one for each sector of the economy (sovereign, corporates, banks), and we model each of them as a linear combination of two stochastic processes: a country-specific idiosyncratic component and a common systematic factor. We provide an estimation model for the parameters of the processes and, for each country, we derive the aggregate default probabilities of each sector. Systemic risk is then estimated by means of a network model based on the partial correlations between the estimated processes of all sectors and countries. Our model is applied to understand the time evolution of systemic risk in the economies of the European monetary union, in the recent period. The results show that systemic risk has increased during the crisis years and that, after the crisis, a clear separation between core and peripheral economies has emerged, for all sectors of the economy.
    Date: 2015–11
  9. By: Pierre Chaigneau; Louis Eeckhoudt
    Abstract: The price of any asset can be expressed with risk neutral probabilities, which are adjusted to incorporate risk preferences. This paper introduces the concepts of downside (respectively outer) risk neutral probabilities, which are adjusted to incorporate the preferences for downside (resp. outer) risk and higher degree risks. We derive new asset pricing formulas that rely on these probability measures. Downside risk neutral probabilities allow to value assets in a simple mean-variance framework. The associated pricing kernel is linear in wealth, as in the CAPM. With outer risk neutral probabilities, the pricing kernel is quadratic in wealth, and can be U-shaped.
    Keywords: Asset pricing, downside risk, quadratic pricing kernel, linear pricing kernel, prudence, risk neutral probabilities.
    Date: 2015
  10. By: Hill, Jonathan B.; Prokhorov, Artem
    Abstract: We construct a Generalized Empirical Likelihood estimator for a GARCH(1,1) model with a possibly heavy tailed error. The estimator imbeds tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality, efficiency and empirical likelihood based confidence regions for very heavy-tailed random volatility data. We show the implied probabilities from the tail-trimmed Continuously Updated Estimator elevate weight for usable large values, assign large but not maximum weight to extreme observations, and give the lowest weight to non-leverage points. We derive a higher order expansion for GEL with imbedded tail-trimming (GELITT), which reveals higher order bias and efficiency properties, available when the GARCH error has a finite second moment. Higher order asymptotics for GEL without tail-trimming requires the error to have moments of substantially higher order. We use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample. We also present robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation. Finally, we present a broad simulation study for GEL and GELITT, and demonstrate profile weighted expected shortfall for the Russian Ruble - US Dollar exchange rate. We show that tail-trimmed CUE-GMM dominates other estimators in terms of bias, mse and approximate normality. AMS classifications : 62M10 , 62F35.
    Keywords: GEL ; GARCH ; tail trimming ; heavy tails ; robust inference ; efficient moment estimation ; expected shortfall ; Russian Ruble
    JEL: C13 C49
    Date: 2015–09–11
  11. By: Sutton, M; Vasnev, A; Gerlach, R
    Abstract: This paper proposes an ex-post volatility estimator, called generalized variance, that uses high frequency data to provide measurements robust to the idiosyncratic noise of stock markets caused by market microstructures. The new volatility estimator is analyzed theoretically, examined in a simulation study and evaluated empirically against the two currently dominant measures of daily volatility: realized volatility and realized range. The main finding is that generalized variance is robust to the presence of microstructures while delivering accuracy superior to realized volatility and realized range in several circumstances. The empirical study features Australian stocks from the ASX 20.
    Keywords: Volatility ; Robust estimator
    Date: 2015–04–30
  12. By: Thor Pajhede (Department of Economics, University of Copenhagen)
    Abstract: Testing the validity of Value-at-Risk (VaR) forecasts, or backtesting, is an integral part of modern market risk management and regulation. This is often done by applying independence and coverage tests developed in Christoffersen (1998) to so-called hit-sequences derived from VaR forecasts and realized losses. However, as pointed out in the literature, see Christoffersen (2004), these aforementioned tests suffer from low rejection frequencies, or (empirical) power, when applied to hit-sequences derived from simulations matching empirical stylized characteristics of return data. One key observation of the studies is that non-Markovian behavior in the hit-sequences may cause the observed lower power performance. To allow for non-Markovian behavior, we propose to generalize the backtest framework for Value-at-Risk forecasts, by extending the original first order dependence of Christoffersen (1998) to allow for a higher, or k’th, order dependence. We provide closed form expressions for the tests as well as asymptotic theory. Not only do the generalized tests have power against k’th order dependence by definition, but also included simulations indicate improved power performance when replicating the aforementioned studies.
    Keywords: Value-at-Risk, Backtesting, Risk Management, Markov Chain, Duration-based test, quantile, likelihood ratio, maximum likelihood.
    JEL: C12 C15 C52 C32
    Date: 2015–11–18

This nep-rmg issue is ©2015 by Stan Miles. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.