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on Risk Management |
| By: | Mabelle Sayah (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1, ISFA - Institut des Science Financière et d'Assurances - PRES Université de Lyon, Faculte des Sciences - Universite Saint Joseph - USJ - Université Saint-Joseph de Beyrouth) |
| Abstract: | A bank's capital charge computation is a widely discussed topic with new approaches emerging continuously. Each bank is computing this figure using internal methodologies in order to reflect its capital adequacy; however, a more homogeneous model is recommended by the Basel committee to enable judging the situation of these financial institutions and comparing different banks among each other. In this paper, we compare different numerical and econometric models to the sensitivity based approach (SBA) implemented by BCBS under Basel III in its February 2015 publication in order to compute the capital charge, we study the influence of having several currencies and maturities within the portfolio and try to define the time horizon and confidence level implied by Basel s III approach through an application on bonds portfolios. By implementing several approaches, we are able to find equivalent VaRs to the one computed by the SBA on a pre-defined confidence level (97.5 %). However, the time horizon differs according to the chosen methodology and ranges from 1 month up to 1 year. |
| Keywords: | Sensitivity Based approach,Capital charge,GARCH,Basel III,PCA,bonds portfolio,Dynamic Nelson Siegel,ICA,interest rate risk,trading book |
| Date: | 2015–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01217928&r=rmg |
| By: | Hale, Galina (Federal Reserve Bank of San Francisco); Krainer, John (Federal Reserve Bank of San Francisco); McCarthy, Erin |
| Abstract: | We explore the question of optimal aggregation level for stress testing models when the stress test is specified in terms of aggregate macroeconomic variables, but the underlying performance data are available at a loan level. Using standard model performance measures, we ask whether it is better to formulate models at a disaggregated level (“bottom up”) and then aggregate the predictions in order to obtain portfolio loss values or is it better to work directly with aggregated models (“top down”) for portfolio loss forecasts. We study this question for a large portfolio of home equity lines of credit. We conduct model comparisons of loan-level default probability models, county-level models, aggregate portfolio-level models, and hybrid approaches based on portfolio segments such as debt-to-income (DTI) ratios, loan-to-value (LTV) ratios, and FICO risk scores. For each of these aggregation levels we choose the model that fits the data best in terms of in-sample and out-of-sample performance. We then compare winning models across all approaches. We document two main results. First, all the models considered here are capable of fitting our data when given the benefit of using the whole sample period for estimation. Second, in out-of-sample exercises, loan-level models have large forecast errors and underpredict default probability. Average out-of-sample performance is best for portfolio and county-level models. However, for portfolio level, small perturbations in model specification may result in large forecast errors, while county-level models tend to be very robust. We conclude that aggregation level is an important factor to be considered in the stress-testing model design. |
| JEL: | C18 C52 G21 G28 |
| Date: | 2015–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedfwp:2015-14&r=rmg |
| By: | Catherine Bruneau (University Paris I Pantheon-Sorbonne and CES); Alexis Flageollet (Natixis Asset Management); Zhun Peng (University of Evry and EPEE) |
| Abstract: | In this paper we propose a flexible tool to estimate the risk sensitivity of a high- dimensional portfolio composed of different classes of assets, especially in extreme risk circumstances. We build a so-called Cvine Risk Factors Model (CRFM), which is a non-linear version of a risk factor model in a copula framework. Our tool allows us to decompose the risk of any asset and any portfolio into specific risk directions depending on the context. As an application, we compare the sensitivity of different types of portfolios to extreme risks. We also give an example of a view- type analysis as usually performed by portfolio managers who examine what their portfolio becomes under specific circumstances: here we examine the case of a low inflation context. These analyses allow us to detect changes in the diversification opportunities over time. |
| Keywords: | Regular vine copula, Factorial model, Extreme Risks, Risk Management, Portfolio Management, Diversification |
| JEL: | G11 G17 G32 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:eve:wpaper:15-03&r=rmg |
| By: | Jakob Kisiala |
| Abstract: | This thesis presents the Conditional Value-at-Risk concept and combines an analysis that covers its application as a risk measure and as a vector norm. For both areas of application the theory is revised in detail and examples are given to show how to apply the concept in practice. In the first part, CVaR as a risk measure is introduced and the analysis covers the mathematical definition of CVaR and different methods to calculate it. Then, CVaR optimization is analysed in the context of portfolio selection and how to apply CVaR optimization for hedging a portfolio consisting of options. The original contributions in this part are an alternative proof of Acerbi's Integral Formula in the continuous case and an explicit programme formulation for portfolio hedging. The second part first analyses the Scaled and Non-Scaled CVaR norm as new family of norms in $\mathbb{R}^n$ and compares this new norm family to the more widely known $L_p$ norms. Then, model (or signal) recovery problems are discussed and it is described how appropriate norms can be used to recover a signal with less observations than the dimension of the signal. The last chapter of this dissertation then shows how the Non-Scaled CVaR norm can be used in this model recovery context. The original contributions in this part are an alternative proof of the equivalence of two different characterizations of the Scaled CVaR norm, a new proposition that the Scaled CVaR norm is piecewise convex, and the entire \autoref{chapter:Recovery_using_CVaR}. Since the CVaR norm is a rather novel concept, its applications in a model recovery context have not been researched yet. Therefore, the final chapter of this thesis might lay the basis for further research in this area. |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1511.00140&r=rmg |
| By: | Kristopher Gerardi; Kyle F. Herkenhoff; Lee E. Ohanian; Paul S. Willen |
| Abstract: | Previous research on mortgage default has been constrained by data limitations, including lack of data on mortgagor employment status. This paper studies mortgage default using PSID data, which includes a richer set of covariates, including employment status, equity, and other assets. In sharp contrast to prior studies, we find that unemployment and other negative financial shocks are key default predictors. Using wealth data, we find a limited scope for strategic default, as only 1/3 of underwater defaulters have enough assets to pay their mortgage. We discuss the implications of these findings for theoretical default models and for loss mitigation policies |
| JEL: | G21 G33 R3 R51 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21630&r=rmg |
| By: | Helena Chuliá (Faculty of Economics, University of Barcelona); Montserrat Guillén (Faculty of Economics, University of Barcelona); Jorge M. Uribe (Department of Economics, Universidad del Valle) |
| Abstract: | We propose a daily index of time-varying stock market uncertainty. The index is constructed after first removing the common variations in the series, based on recent advances in the literature that emphasize the difference between risk (expected variation) and uncertainty (unexpected variation). To this end, we draw on data from 25 portfolios between 1926 and 2014, sorted by size and book-to-market value. This strategy considerably reduces information requirements and modeling design costs, compared to previous proposals. We compare our index with indicators of macrouncertainty and estimate the impact of an uncertainty shock on the dynamics of variables such as production, employment, consumption, stock market prices and interest rates. Our results show that, even when the estimates can be considered as a measure of stock market uncertainty (i.e., financial uncertainty), they perform very well as indicators of the uncertainty of the economy as a whole. |
| Keywords: | Uncertainty, Risk, Factor models, Stock market. JEL classification: E00; E44; G10; G14 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:ira:wpaper:201524&r=rmg |
| By: | Ankush Agarwal (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS); Stefano De Marco (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS); Emmanuel Gobet (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS); Gang Liu (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS) |
| Abstract: | In this paper, we develop the reversible shaking transformation methods on path space of Gobet and Liu [GL15] to estimate the rare event statistics arising in different financial risk settings which are embedded within a unified framework of isonormal Gaussian process. Namely, we combine splitting methods with both Interacting Particle System (IPS) technique and ergodic transformations using Parallel-One-Path (POP) estimators. We also propose an adaptive version for the POP method and prove its convergence. We demonstrate the application of our methods in various examples which cover usual semi-martingale stochastic models (not necessarily Markovian) driven by Brownian motion and, also, models driven by fractional Brownian motion (non semi-martingale) to address various financial risks. Interestingly, owing to the Gaussian process framework, our methods are also able to efficiently handle the important problem of sensitivities of rare event statistics with respect to the model parameters. |
| Keywords: | Rare event,Monte Carlo simulation,Markov chains,ergodic properties,interacting particle systems,Malliavin calculus,sensitivity analysis,fractional Brownian motion,credit default swaps,model misspecification,deep out-of-the-money options |
| Date: | 2015–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01219616&r=rmg |
| By: | Harri Nyrhinen |
| Abstract: | We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is allowed to increase or decrease. In the latter case, the study is focused on run-off companies. Our main results give sharp asymptotic estimates for infinite time ruin probabilities. |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1511.01763&r=rmg |
| By: | Maximilian Ga{\ss}; Kathrin Glau; Maximilian Mair |
| Abstract: | We propose an interpolation method for parametric option pricing tailored to the persistently recurring task of pricing liquid financial instruments. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter risk estimation. We adapt the empirical magic point interpolation method of Barrault et al. (2004) to parametric Fourier pricing. For a large class of combinations of option types, models and free parameters the approximation converges exponentially in the degrees of freedom and moreover has explicit error bounds. Numerical experiments confirm our theoretical findings and show a significant gain in efficiency, even for examples beyond the scope of the theoretical results. This is especially promising for further applications of the method. |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1511.00884&r=rmg |