
on Risk Management 
By:  Dominique Guegan (Centre d'Economie de la Sorbonne); Bertrand K Hassani (Grupo Santander et Centre d'Economie de la Sorbonne); Kehan Li (Centre d'Economie de la Sorbonne) 
Abstract:  One of the key lessons of the crisis which began in 2007 has been the need to strengthen the risk coverage of the capital framework. In response, the Basel Committee in July 2009 completed a number of critical reforms to the Basel II framework which will raise capital requirements for the trading book and complex securitisation exposures, a major source of losses for many international active banks. One of the reforms is to introduce a stressed valueatrisk (VaR) capital requirement based on a continuous 12month period of significant financial stress (Basel III (2011) [1]. However the Basel framework does not specify a model to calculate the stressed VaR and leaves it up to the banks to develop an appropriate internal model to capture material risks they face. Consequently we propose a forward stress risk measure “spectral stress VaR” (SSVaR) as an implementation model of stressed VaR, by exploiting the asymptotic normality property of the distribution of estimator of VaRp. In particular to allow SSVaR incorporating the tail structure information we perform the spectral analysis to build it. Using a data set composed of operational risk factors we fit a panel of distributions to construct the SSVaR in order to stress it. Additionally we show how the SSVaR can be an indicator regarding the inner model robustness for the bank 
Keywords:  Value at Risk; Asymptotic theory; Distribution; Spectral analysis; Stress; Risk measure; Regulation 
JEL:  C1 C6 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:15052&r=rmg 
By:  Yang, Bill Huajian; Du, Zunwei 
Abstract:  Under the Vasicek asymptotic single risk factor model, stress testing based on rating transition probability involves three components: the unconditional rating transition matrix, asset correlations, and stress testing factor models for systematic downgrade (including default) risk. Conditional transition probability for stress testing given systematic risk factors can be derived accordingly. In this paper, we extend Miu and Ozdemir’s work ([14]) on stress testing under this transition probability framework by assuming different asset correlation and different stress testing factor model for each nondefault rating. We propose two Vasicek models for each nondefault rating, one with a single latent factor for rating level asset correlation, and another multifactor Vasicek model with a latent effect for systematic downgrade risk. Both models can be fitted effectively by using, for example, the SAS nonlinear mixed procedure. Analytical formulas for conditional transition probabilities are derived. Modeling downgrade risk rather than default risk addresses the issue of low default counts for high quality ratings. As an illustration, we model the transition probabilities for a corporate portfolio. Portfolio default risk and credit loss under stress scenarios are derived accordingly. Results show, stresstesting models developed in this way demonstrate desired sensitivity to risk factors, which is generally expected. 
Keywords:  Stress testing, systematic risk, asset correlation, rating migration, Vasicek model, bootstrap aggregation 
JEL:  C1 C10 C13 C5 G3 G30 G32 G38 
Date:  2015–06–18 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:65168&r=rmg 
By:  Li, Hong (Tilburg University, School of Economics and Management) 
Abstract:  The thesis first examines the choice of sample size for mortality forecasting, and then deal with the hedging of longevity risk using longevitylinked instruments. Chapter 2 proposes a Bayesian learning approach to determine the (posterior distribution of) the sample sizes for mortality forecasting using mortality models based on linear extrapolation approaches. Chapter 3 studies the static robust management of longevity risk in the situation that the hedger does not have precise knowledge of the underlying probability distribution of the future mortality rates. Meanvariance and meanconditionalvalueatrisk objective functions are used. Chapter 4 focuses on the dynamic hedging of longevity risk in the case where the trading frequency of the longevitylinked derivatives is limited. A minimumvariance objective function is used, and timeconsistent hedging strategies are derived in both the benchmark case, where all assets can be traded continuously, and a constrained case, where the longevitylinked derivatives can only be traded at a low and deterministic frequency. 
Date:  2015 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutis:86ec7489f6d2463796cbde9beb89944d&r=rmg 
By:  Bertrand K. Hassani (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS) 
Abstract:  One of the main concern and regulatory topic financial institutions have to deal with is the model risk. Senior managers tend to consider more and more model risk as one of the highest exposure a financial institution has (as illustrated by the latest EBA paper related to Advanced Measurement Approach (AMA) for Operational Risk Capital calculation). Though, while the concept seems relatively simple, the definition of the model risk (traditional and regulatory), the origins of this one (from dogmas to misuse) and the way to manage it (from engineering conservatism into models to a proper governance process) are not necessarily well handled by practitioners, academics and regulators. Giving a clear definition and understanding the root cause of a model failure allows adopting the appropriate management style to deal with the potential issue that could lead to dramatic failures. In this paper we are proposing an analysis of the model risk trying to understand the main issues leading to the failure and the best way to address them. 
Date:  2015–03 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs01163837&r=rmg 
By:  Woohwan Kim (FR&I, Korea); Young Min Kim (Radiation Effects Research Foundation, Japan); TaeHwan Kim (Yonsei University); Seungbeom Bang (FR&I, Korea) 
Abstract:  In this paper, we propose defining the ¡®risk¡¯ of a portfolio as a multidimensional concept characterized by three components: variance, skewness and kurtosis. Unlike most previous papers studying how the first component of risk,i.e., variance, is diversified, we use both analysis and simulations to investigate how the other two components (skewness and kurtosis) are diversified when the number of stocks in a welldiversified portfolio increases. We find a couple of interesting results. When a portfolio is skewed and fattailed, then not only its variance, but also its skewness and kurtosis are simultaneously reduced as the number of risky assets in the portfolio increases. When the risky assets in a portfolio are moderately correlated, the three components tend to decrease and eventually converge to nonzero values. These nonzero limit values can be used to define the true multidimensional systematic risk of the portfolio. Hence, it can be argued that multidimensional nonsystematic risk can be diversified by constructing a wellbalanced portfolio. Another interesting result is that the skewness risk of a portfolio tends to decrease more slowly than the other two types of risk, the variance risk and the kurtosis risk, which indicates that the skewness risk is the most difficult to diversify among the three components. 
Keywords:  Diversification, Skewness, Kurtosis, Systematic Risk. 
JEL:  C10 G11 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:yon:wpaper:2015rwp81&r=rmg 
By:  Rebekka Burkholz; Matt V. Leduc; Antonios Garas; Frank Schweitzer 
Abstract:  We study cascades on a twolayer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with the case of a single layer network that is an aggregated representation of the two layers. We find that systemic risk in the twolayer network is smaller than in the aggregated one only if the coupling strength between the two layers is small. Above a critical coupling strength, systemic risk is increased because of the mutual amplification of cascades in the two layers. We even observe sharp phase transitions in the cascade size that are less pronounced on the aggregated layer. Our insights can be applied to a scenario where firms decide whether they want to split their business into a less risky core business and a more risky subsidiary business. In most cases, this may lead to a drastic increase of systemic risk, which is underestimated in an aggregated approach. 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1506.06664&r=rmg 
By:  Rahim, Yasmin Abd; Masih, Mansur 
Abstract:  This research is motivated by the desire to see the difference on interest rate risk exposure between Islamic and conventional equity across different investment horizons using wavelet analysis. Seven types of interest rates were tested with FTSE Bursa Malaysia Hijrah Shariah Index and FTSE Bursa Malaysia KLCI Index using data ranging from 1st March 2007 till 31st December 2014. The exposure to interest rate risk for both indices was highest at longer term investment horizon which is between 256 to 512 days; followed by investment horizon between 64128 days. However, short term investment horizon which is between 24 days and 48 days has the lowest exposure to interest rate risk. High correlations between indexes across investment horizons had been demonstrated empirically. Hence, the hypothesis that an application of Islamic ethical screen would ‘save’ Islamic finance from interest rate risk is not accepted. 
Keywords:  Islamic stock index, interest rate, wavelet 
JEL:  C22 C58 G11 
Date:  2015–06–25 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:65259&r=rmg 
By:  Barunik, Jozef; Barunikova, Michaela 
Abstract:  This paper revisits the fractional cointegrating relationship between exante implied volatility and expost realized volatility. Previous studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. It is argued that the concept of corridor implied volatility (CIV) should be used instead of the popular modelfree optionimplied volatility (MFIV) when assessing the relation as the latter may introduce bias to the estimation. In addition, a new tool for the estimation of fractional cointegrating relation between implied and realized volatility based on wavelets, a wavelet band least squares (WBLS) uncovers that corridor implied volatility is an unbiased forecast of future volatility in the long run. The main advantage of WBLS in comparison to other methods is that it allows us to work conveniently with potentially nonstationary volatility due to the properties of wavelets and allows us to study the relation at different investment horizons. In the estimation, we use the S&P 500 and DAX monthly and biweekly option prices covering the recent financial crisis, and we conclude that the dependence comes solely from the lower frequencies of the spectra representing long horizons. The findings enable improvement of future volatility forecasts by discarding the bias coming from the short horizons. 
Keywords:  wavelet band spectrum regression,corridor implied volatility,realized volatility,fractional cointegration 
JEL:  C14 C22 C51 C52 G14 
Date:  2015 
URL:  http://d.repec.org/n?u=RePEc:zbw:fmpwps:43&r=rmg 
By:  Lorenz Schneider; Bertrand Tavin 
Abstract:  We introduce a multifactor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding volatility factor is welldefined. These conditions appear to be rather mild. Second, we calculate the joint characteristic function of two futures prices for different maturities in the proposed model. This characteristic function is analytic. Finally, we provide numerical illustrations in terms of implied volatility and correlation produced by the proposed model with five different specifications of the seasonality pattern. The model is found to be able to produce volatility smiles at the same time as a volatility termstructure that exhibits the Samuelson effect with a seasonal component. Correlation, instantaneous or implied from calendar spread option prices via a Gaussian copula, is also found to be seasonal. 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1506.05911&r=rmg 
By:  Stefan Rass 
Abstract:  Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach of von Neumann and Morgenstern establishes the existence of suitable utility functions, and yields to gametheory as the most prominent materialization of a theory to determine optimal behavior. Although this appears to be a most natural approach to risk management too, applications in critical infrastructures often violate the implicit assumption of actions leading to deterministic consequences. In that sense, the gameplay in a critical infrastructure risk control competition is intrinsically random in the sense of actions having uncertain consequences. Mathematically, this takes us to utility functions that are probabilitydistributionvalued, in which case we loose the canonic (in fact every possible) ordering on the space of payoffs, and the original techniques of von Neumann and Morgenstern no longer apply. This work introduces a new kind of game in which uncertainty applies to the payoff functions rather than the player's actions (a setting that has been widely studied in the literature, yielding to celebrated notions like the trembling hands equilibrium or the purification theorem). In detail, we show how to fix the nonexistence of a (canonic) ordering on the space of probability distributions by only mildly restricting the full set to a subset that can be totally ordered. Our vehicle to define the ordering and establish basic gametheory is nonstandard analysis and hyperreal numbers. 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1506.07368&r=rmg 