|
on Risk Management |
| By: | Balbás, Raquel; Balbás, Beatriz; Balbás, Alejandro |
| Abstract: | The Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while super- visors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoretical point of view VaR presents some drawbacks overcome by other risk measures such as the Conditional Value at Risk (CVaR). VaR is neither differentiable nor sub-additive because it is neither continuous nor convex. On the contrary, CVaR satis es all of these properties, and this simpli es many ana- lytical studies if VaR is replaced by CVaR. In this paper several differential equations connecting both VaR and CVaR will be presented. They will allow us to address several important issues involving VaR with the help of the CVaR properties. This new methodology seems to be very efficient. In particular, a new VaR Representation Theorem may be found, and optimization problems involving VaR or probabilistic constraints always have an equivalent differentiable optimization problem. Applications in VaR, marginal VaR, CVaR and marginal CVaR estimates will be addressed as well. An illustrative actuarial numerical example will be given. |
| Keywords: | Risk and Marginal Risk Estimation; Risk Optimization and Probabilistic Constraints; VaR Representation Theorem; Differential Equations; VaR and CVaR |
| JEL: | G22 G12 G11 C65 |
| Date: | 2017–01–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:idrepe:24017&r=rmg |
| By: | Yang, Bill Huajian |
| Abstract: | Rating transition models ([8], [13]) have been widely used for multi-period scenario loss projection for CCAR stress testing and IFRS 9 expected credit loss estimation. Though the cumulative probability of default (PD) for a rating can be derived by repeatedly applying the migration matrix at each single forward scenario sequentially, divergence between the predicted and realized cumulative default rates can be significant, particularly when the predicting horizon extends to longer periods ([4]). In this paper, we propose approaches to modeling the forward PDs directly. The proposed models are structured via a credit index, representing the systematic risk for the portfolio explained by a list of macroeconomic variables, together with the risk sensitivity with respect to the credit index, for each rating and each forward term. An algorithm for parameter estimation is proposed based on maximum likelihood of observing the default frequency for each non-default rating and each forward term. The proposed models and approaches are validated on a corporate portfolio, where a forward PD model and a point-in-time rating transition model are fitted. It is observed that both models demonstrate strong strengths in predicting portfolio quarterly default rate (i.e. in one-term horizon), but the term model outperforms in general the transition model as the predicting horizon extends to longer periods (e.g., 1-year or 2-year horizons), due to the fact that the term model is calibrated over a longer horizon. We believe that the proposed models will provide practitioners a new and robust tool for modeling directly the PD term structure for multi-period scenario loss projection, for CCAR stress testing and IFRS 9 expected credit loss (ECL) estimation. |
| Keywords: | CCAR stress testing, impairment loan, IFRS 9 expected credit loss, PD term structure, forward PD, marginal PD, credit index, risk sensitivity, maximum likelihood |
| JEL: | C51 C52 C58 C6 C61 G32 G38 O3 O31 O33 O34 |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:76271&r=rmg |
| By: | Yang, Bill Huajian; Du, Zunwei |
| Abstract: | Rating transition probability models, under the asymptotic single risk factor model framework, are widely used in the industry for stress testing and multi-period scenario loss projection. For a risk-rated portfolio, it is commonly believed that borrowers with higher risk ratings are more sensitive and vulnerable to adverse shocks. This means the asset correlation is required be differentiated between ratings and fully reflected in all respects of model fitting. In this paper, we introduce a risk component, called credit index, representing the part of systematic risk for the portfolio explained by a list of macroeconomic variables. We show that the transition probability, conditional to a list of macroeconomic variables, can be formulated analytically by using the credit index and the rating level sensitivity with respect to this credit index. Approaches for parameter estimation based on maximum likelihood for observing historical rating transition frequency, in presence of rating level asset correlation, are proposed. The proposed models and approaches are validated on a commercial portfolio, where we estimate the parameters for the conditional transition probability models, and project the loss for baseline, adverse and severely adverse supervisory scenarios provided by the Federal Reserve for the period 2016Q1-2018Q1. The paper explicitly demonstrates how Miu and Ozdemir’s original methodology ([5]) on transition probability models can be structured and implemented with rating specific asset correlation. It extends Yang and Du’s earlier work on this subject ([9]).We believe that the models and approaches proposed in this paper provide an effective tool to the practitioners for the use of transition probability models. |
| Keywords: | CCAR stress testing, multi-period scenario, loss projection, credit index, risk sensitivity, asset correlation, transition frequency, transition probability, through-the-cycle, maximum likelihood |
| JEL: | C13 C5 C51 C58 G32 G38 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:76270&r=rmg |
| By: | Eckley, Peter (Bank of England); Benetton, Matteo (LSE); Latsi, Georgia (Independent); Garbarino, Nicola (Bank of England); Kirwin, Liam (Bank of England) |
| Abstract: | Since Basel II was introduced in 2008, two approaches to calculating bank capital requirements have co-existed: lenders’ internal models, and a less risk-sensitive standardised approach. Using a unique dataset covering 7 million UK mortgages for 2005–15, and novel identification, we provide empirical evidence that the differences between these approaches cause lenders to specialise. This leads to systemic concentration of high-risk mortgages in lenders with less sophisticated risk management. Our results have broad implications for the design of the international bank capital framework. |
| Keywords: | Capital regulation; banking; mortgages; specialisation; risk-taking; Basel II |
| JEL: | G01 G21 G28 |
| Date: | 2017–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0639&r=rmg |
| By: | Muhammad, Aliyu Dahiru (Department of Economics,International Islamic University) |
| Abstract: | Increasingly corporate financial institutions are realizing the importance of risk management. This leads to innovation of financial products to mitigate the risk. Islamic banking institutions face similar risks as conventional banking institutions. However, the later has additional Shariah noncompliance risk. The objective of this study is to compare risk management practices in Islamic banking institutions between Nigeria and Malaysia. The study employs survey technique to collect data from the respondents and analyze it using various techniques. Specifically, t-test and analysis of variance as well as multiple regressions were used to analyze the data. Findings show that there is significant differences in terms of understanding risk management and risk assessment and analysis between Nigeria and Malaysia with the later taking the lead. This is due to maturity and robust legal and regulatory framework. However, the result exhibits relative competition in RMP between Nigeria and Malaysia as out of five dimensions three are not significant (RMP, RI, RCM). While Malaysia leads in some aspects of risk management, Nigeria has huge potential to change the landscape of Islamic finance in the country. This implied that risk management processes in Islamic banks require additional legal and regulatory framework to strengthen their existing condition. Further research should focus on the details of risk management techniques employed by Islamic banks in the study area. |
| Keywords: | Risk Management Practices; Islamic banking; Nigeria; Malaysia |
| JEL: | G20 G21 G28 |
| Date: | 2016–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:ris:irtiwp:2016_014&r=rmg |
| By: | Ruediger Frey; Lars Roesler; Dan Lu |
| Abstract: | The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to compute the price dynamics of traded securities one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filtering problem for a stopped diffusion process and we apply results from the filtering literature to this problem. In this way we obtain an SPDE-characterization for the filter density. Moreover, we characterize the default intensity under incomplete information and we determine the price dynamics of traded securities. Armed with these results we study derivative asset analysis in our setup: we explain how the model can be applied to the pricing of options on traded assets and we discuss dynamic hedging and model calibration. The paper closes with a small simulation study. |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1701.04780&r=rmg |
| By: | Masahiko Egami; Rusudan Kevkhishvili |
| Abstract: | This paper develops a risk management framework for companies, based on the leverage process (a ratio of company asset value over its debt) by analyzing the characteristics of general linear diffusions with killing. We approach this issue by time reversal, last passage time, and h-transform of linear diffusions. For such processes, we derive the probability density of the last passage time to a certain alarming level and the distribution of the time left until killing after the last passage time. We apply these results to the leverage process of the company. Finally, we suggest how a company should specify that abovementioned alarming level for the leverage process by solving an optimization problem. |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1701.04565&r=rmg |
| By: | Seyed Amir Hejazi; Kenneth R. Jackson; Guojun Gan |
| Abstract: | Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, forcing insurance companies to invest hundreds of thousands of dollars in computational infrastructure per year. Moreover, existing academic methodologies are focused on fair valuation of a single VA contract, exploiting ideas in option theory and regression. In most cases, the computational complexity of these methods surpasses the computational requirements of MC simulations. Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In this paper, we present a framework for valuing such portfolios based on spatial interpolation. We provide a comprehensive study of this framework and compare existing interpolation schemes. Our numerical results show superior performance, in terms of both computational efficiency and accuracy, for these methods compared to nested MC simulations. We also present insights into the challenge of finding an effective interpolation scheme in this framework, and suggest guidelines that help us build a fully automated scheme that is efficient and accurate. |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1701.04134&r=rmg |
| 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 et Labex ReFi) |
| Abstract: | Contrary to the current regulatory trend concerning extreme risks, the purpose of this paper is to emphasize the necessity of considering the Value-at-Risk (VaR) with extreme confidence levels like 99.9%, as an alternative way to measure risks in the “extreme tail”. Although the mathematical definition of the extreme VaR is trivial, its computation is challenging in practice, because the uncertainty of the extreme VaR may not be negligible for a finite amount of data. We begin to build confidence intervals around the unknown VaR. We build them using two different approaches, the first using Smirnov's result (Smirnov, 1949 [24]) and the second Zhu and Zhou's result (Zhu and Zhou, 2009 [25]), showing that this last one is robust when we use finite samples. We compare our approach with other methodologies which are based on bootstrapping techniques, Christoffersen et al. (2005) [7], focusing on the estimation of the extreme quantiles of a distribution. Finally, we apply these confidence intervals to perform a stress testing exercice with historical stock returns during financial crisis, for identifying potential violations of the VaR during turmoil periods on financial markets |
| Keywords: | Regulation; Extreme risk; Extreme Value-at-Risk; Confidence interval; Asymptotic theory; Stress testing |
| JEL: | C14 D81 G28 G32 |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16034rr&r=rmg |
| By: | Anulekha Dhara; Bikramjit Das; Karthik Natarajan |
| Abstract: | Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert information is available in terms of bivariate marginals. Such expert information allows for one to choose from among the many possible parametric families of bivariate copulas. By considering a neighborhood of distance $\rho$ around the bivariate marginals with the Kullback-Leibler divergence measure, we model the trade-off between conservatism in the worst-case risk measure and confidence in the expert information. Our bound is developed when the only information available on the bivariate marginals forms a tree structure in which case it is efficiently computable using convex optimization. For consistent marginals, as $\rho$ approaches $\infty$, the bound reduces to the comonotonic upper bound and as $\rho$ approaches $0$, the bound reduces to the worst-case bound with bivariates known exactly. We also discuss extensions to inconsistent marginals and instances where the expert information which might be captured using other parameters such as correlations. |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1701.04167&r=rmg |
| By: | Antoine Jacquier; Claude Martini; Aitor Muguruza |
| Abstract: | The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve generated by this model, and develop efficient pricing algorithms for VIX futures and options. We further analyse the validity of the rough Bergomi model to jointly describe the VIX and the SPX, and present a joint calibration algorithm based on the hybrid scheme by Bennedsen, Lunde and Pakkanen. |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1701.04260&r=rmg |
| By: | Benedetta Frassi (IMT School for advanced studies); Fabio Pammolli (Politecnico di Milano, Dipartimento di ingegneria gestionale); Luca Regis (University of Siena, Department of economics and statistics) |
| Abstract: | In this article, we assess, through an empirical investigation based on Italian data, how uncertainty regarding future mortality may affect public pension expenditure. Based on a representative sample of Italian pensioners from 1985 to 2011, we find a consistent underestimation of improvements seen in mortality and life expectancy when forecasts are based on expectations. The pension expenditure estimated using realized mortality rates is shown to be consistently higher than that obtained by using average forecasted scenarios, produced with well-known stochastic mortality models. The paper highlights the importance of considering the uncertainty regarding future pension benfits, i.e. of evaluating and managing the longevity risk in public pension plans. |
| Keywords: | longevity risk, mortality model, pension, retirement |
| JEL: | C15 C32 J11 J26 |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:ial:wpaper:1/2017&r=rmg |
| By: | Reyes, Celia M.; Mina, Christian D.; Agbon, Adrian D.; Gloria, Reneli Ann B. |
| Abstract: | While agricultural insurance has long been considered a risk management tool for farmers in both developing and developed economies, policy directions toward sustainability vary across countries. Reviewing the literature provides a comprehensive view of relevant issues, such as objectives of the program, credit access by farmers, program costs, and premium subsidies provided by the national and local governments. This paper provides insights on how agricultural insurance programs from selected developed and developing economies were implemented. Learning from different country experiences, agricultural insurance is important yet costly to implement. Private insurance companies complement with the government-run insurance company to improve coverage rates. Targeting eligible beneficiaries is crucial in the success of a highly subsidized agricultural insurance, especially in developing economies. |
| Keywords: | Philippines, crop insurance, agricultural insurance, developed economies, developing economies |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:phd:dpaper:dp_2017-02&r=rmg |