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on Risk Management |
| By: | Düllmann, Klaus; Puzanova, Natalia |
| Abstract: | We put forward a Merton-type multi-factor portfolio model for assessing banks' contributions to systemic risk. This model accounts for the major drivers of banks' systemic relevance: size, default risk and correlation of banks' assets as a proxy for interconnectedness. We measure systemic risk in terms of the portfolio expected shortfall (ES). Banks' (marginal) risk contributions are calculated based on partial derivatives of the ES in order to ensure a full risk allocation among institutions. We compare the performance of an importance sampling algorithm with a fast analytical approximation of the ES and the marginal risk contributions. Furthermore, we show empirically for a portfolio of large international banks how our approach could be implemented to compute bank-specific capital surcharges for systemic risk or stabilisation fees. We find that size alone is not a reliable proxy for the systemic importance of a bank in this framework. In order to smooth cyclical fluctuations of the risk measure, we explore a time-varying confidence level of the ES. -- |
| Keywords: | systemic risk contributions,systemic capital charge,expected shortfall,importance sampling,granularity adjustment |
| JEL: | C15 C63 E58 G21 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdp2:201108&r=rmg |
| By: | Ricardo Schechtman; Wagner Piazza Gaglianone |
| Abstract: | This paper investigates macro stress testing of system-wide credit risk with special focus on the tails of the credit risk distributions conditional on bad macroeconomic scenarios. These tails determine the ex-post solvency probabilities derived from the scenarios. This paper estimates the macro-credit risk link by the traditional Wilson (1997) model as well as by an alternative proposed quantile regression (QR) method (Koenker and Xiao, 2002), in which the relative importance of the macro variables can vary along the credit risk distribution, conceptually incorporating uncertainty in default correlations. Stress-testing exercises on the Brazilian household sector at the one-quarter horizon indicate that unemployment rate distress produces the most harmful effect, whereas distressed inflation and distressed interest rate show higher impacts at longer periods. Determining which of the two stress-testing approaches perceives the scenarios more severely depends on the type of comparison employed. The QR approach is revealed more conservative based on a suggested comparison of vertical distances between the tails of the conditional and unconditional credit risk cumulative distributions. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:bcb:wpaper:241&r=rmg |
| By: | Cathy W. S. Chen (Graduate Institute of Statistics and Actuarial Science, Feng Chia University); Richard Gerlach (University of Sydney Business School); Bruce B. K. Hwang (Graduate Institute of Statistics and Actuarial Science, Feng Chia University); Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, Complutense University of Madrid, and Institute of Economic Research, Kyoto University) |
| Abstract: | Value-at-Risk (VaR) is commonly used for financial risk measurement. It has recently become even more important, especially during the 2008-09 global financial crisis. We pro- pose some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models that incorporate intra-day price ranges. Model estimation and inference are performed using the Bayesian approach via the link with the Skewed-Laplace distribution. We examine how a range of risk models perform during the 2008-09 financial crisis, and evaluate how the crisis affects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices as well as two exchange rate series. We examine violation rates, back-testing criteria, market risk charges and quantile loss function values to measure and assess the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more efficiently than other models, across the series considered, which should be useful for financial practitioners. |
| Keywords: | Value-at-Risk; CAViaR model; Skewed-Laplace distribution; intra-day range; backtesting, Markov chain Monte Carlo. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:775&r=rmg |
| By: | Stoyanov, Stoyan V.; Rachev, Svetlozar T.; Fabozzi, Frank J. |
| Abstract: | We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student's t, and generalized Gaussian laws and discuss implications for the modeling of daily returns and marginal rebalancing decisions. Finally, we explore empirically the impact on the asymptotic variability of the CVaR estimator with daily returns which is a standard choice for the return frequency for risk estimation. -- |
| Keywords: | fat-tailed distributions,regularly varying tails,conditional value-at-risk,marginal rebalancing,asymptotic variability |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:29&r=rmg |
| By: | Geurdes, Han / J. F. |
| Abstract: | Credit valuation adjustment in Basel III is studied from the perspective of the mathematics involved. A bank covers mark-to-market losses for expected counterparty risk with a CVA capital charge. The CVA is known as credit valuation adjustments. In this paper it will be argued that CVA and conditioned value at risk (CVaR) have a common mathematical ancestor. The question is raised why the Basel committee, from the perspective of CVaR, has selected a specific parameterization. It is argued that a fine-tuned supervision, on the longer run, will be beneficial for counterparties with a better control over their spread. |
| Keywords: | CVA; CVaR; statistical methodology. |
| JEL: | C02 A14 C01 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30955&r=rmg |
| By: | Maarten R.C. van Oordt; Chen Zhou |
| Abstract: | The aim of this paper is to show that measures on tail dependence can be estimated in a convenient way by regression analysis. This yields the same estimates as the non-parametric method within the multivariate Extreme Value Theory framework. The advantage of the regression approach is contained by its straightforward extension to the estimation of higher dimensional tail dependence. We provide an example on international stock markets. The regression approach to tail dependence can be applied to estimate several measures of systemic importance of financial institutions in the literature. |
| Keywords: | Tail dependence; Regression analysis; Extreme Value Theory; Systemic risk |
| JEL: | C14 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:dnb:dnbwpp:296&r=rmg |
| By: | Basak, Suleyman; Chabakauri, Georgy |
| Abstract: | Despite much work on hedging in incomplete markets, the literature still lacks tractable dynamic hedges in plausible environments. In this article, we provide a simple solution to this problem in a general incomplete-market economy in which a hedger, guided by the traditional minimum-variance criterion, aims at reducing the risk of a non-tradable asset or a contingent claim. We derive fully analytical optimal hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks," familiar in risk management applications, as well as retaining the intuitive features of their static counterparts. We obtain our time-consistent hedges by dynamic programming, while the extant literature characterizes either static or myopic hedges, or dynamic ones that minimize the variance criterion at an initial date and from which the hedger may deviate unless she can pre-commit to follow them. We apply our results to the discrete hedging problem of derivatives when trading occurs infrequently. We determine the corresponding optimal hedge and replicating portfolio value, and show that they have structure similar to their complete-market counterparts and reduce to generalized Black-Scholes expressions when specialized to the Black-Scholes setting. We also generalize our results to richer settings to study dynamic hedging with Poisson jumps, stochastic correlation and portfolio management with benchmarking. |
| Keywords: | benchmarking; correlation risk; derivatives; discrete hedging; hedging; incomplete markets, minimum-variance criterion; Poisson jumps; risk management; time-consistency |
| JEL: | C61 D81 G11 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:8402&r=rmg |
| By: | Stoyanov, Stoyan V.; Rachev, Svetlozar T.; Racheva-Iotova, Boryana; Fabozzi, Frank J. |
| Abstract: | In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we address the common criticism and discuss three popular methods for extreme risk modeling based on full distribution modeling and and extreme value theory. -- |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:30&r=rmg |
| By: | Helder Ferreira de Mendonça; Delio Jose Cordeiro Galvao; Renato Falci Villela Loures |
| Abstract: | This paper analyzes the impact of the changes in capital requirements on bank’s risk and the trade-off between economic activity and the risk of financial institutions in the Brazilian economy. Hence, an analysis based on dynamic panel data taking into account 73 banks and a vector autoregression analysis for the period from 2001 to 2008 is made. The findings underscore that banks which adopt riskier strategies reach higher profitability. Moreover, the results suggest that the banking regulation is an important instrument for reaching the balance between the economic growth and the low exposition to the risk of banking firms in markets such as the Brazilian one. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:bcb:wpaper:243&r=rmg |
| By: | Francesco Cesarone; Andrea Scozzari; Fabio Tardella |
| Abstract: | Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1105.3594&r=rmg |
| By: | Xiaohong Chen (Cowles Foundation, Yale University) |
| Abstract: | In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results. |
| Keywords: | Nonlinear time series, Temporal dependence, Tail dependence, Penalized sieve M estimation, Penalized sieve minimum distance, Semiparametric two-step, Nonlinear ill-posed inverse, Mixtures, Conditional moment restrictions, Nonparametric endogeneity, Dynamic asset pricing, Varying coefficient VAR, GARCH, Copulas, Value-at-risk |
| JEL: | C13 C14 C20 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1804&r=rmg |
| By: | Gaurab Aryal; Isabelle Perrigne; Quang Vuong |
| Abstract: | We study the identification of an insurance model with multidimensional screening, where insurees are characterized by risk and risk aversion. The model is solved using the concept of certainty equivalence under constant absolute risk aversion and an unspecified joint distribution of risk and risk aversion. The paper then analyzes how data availability constraints identification under four data scenarios from the ideal situation to a more realistic one. The observed number of accidents for each insuree plays a key role to identify the model. In a first part, we consider the case of a continuum of coverages offered to each insuree whether the damage distribution is fully observed or truncated. Truncation arises from that an insuree files a claim only when the accident involves a damage above the deductible. Despite bunching due to multidimensional screening, we show that the joint distribution of risk and risk aversion is identified. In a second part, we consider the case of a finite number of coverages offered to each insuree. When the full damage distribution is observed, we show that despite additional pooling due to the finite number of contracts, the joint distribution of risk and risk aversion is identified under a full support assumption and a conditional independence assumption involving the car characteristics. When the damage distribution is truncated, the joint distribution is identified up to the probability that the damage is above the deductible. In a third part, we derive the restrictions imposed by the model on observables for the fourth scenario. We also propose several identification strategies for the damage probability at the deductible. These identification results are further exploited in a companion paper developing an estimation method with an application to insurance data |
| JEL: | C14 L62 D82 D86 |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2011-538&r=rmg |