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on Risk Management |
| By: | Konrad Banachewicz (Vrije Universiteit Amsterdam); André Lucas (Vrije Universiteit Amsterdam) |
| Abstract: | Recent models for credit risk management make use of Hidden Markov Models (HMMs). The HMMs are used to forecast quantiles of corporate default rates. Little research has been done on the quality of such forecasts if the underlying HMM is potentially mis-specified. In this paper, we focus on mis-specification in the dynamics and the dimension of the HMM. We consider both discrete and continuous state HMMs. The differences are substantial. Underestimating the number of discrete states has an economically significant impact on forecast quality. Generally speaking, discrete models underestimate the high-quantile default rate forecasts. Continuous state HMMs, however, vastly overestimate high quantiles if the true HMM has a discrete state space. In the reverse setting, the biases are much smaller, though still substantial in economic terms. We illustrate the empirical differences using U.S. default data. |
| Keywords: | defaults; Markov switching; misspecification; quantile forecast; Expectation-Maximization; simulated maximum likelihood; importance sampling |
| JEL: | C53 C22 G32 |
| Date: | 2007–06–13 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20070046&r=rmg |
| By: | Malcolm Baker; Jeffrey Wurgler |
| Abstract: | Real investors and markets are too complicated to be neatly summarized by a few selected biases and trading frictions. The "top down" approach to behavioral finance focuses on the measurement of reduced form, aggregate sentiment and traces its effects to stock returns. It builds on the two broader and more irrefutable assumptions of behavioral finance -- sentiment and the limits to arbitrage -- to explain which stocks are likely to be most affected by sentiment. In particular, stocks of low capitalization, younger, unprofitable, high volatility, non-dividend paying, growth companies, or stocks of firms in financial distress, are likely to be disproportionately sensitive to broad waves of investor sentiment. We review the theoretical and empirical evidence for these predictions. |
| JEL: | E32 G11 G12 G14 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:13189&r=rmg |
| By: | Davide Ferrari; Sandra Paterlini |
| Abstract: | Estimating financial risk is a critical issue for banks and insurance companies. Recently, quantile estimation based on Extreme Value Theory (EVT) has found a successful domain of application in such a context, outperforming other approaches. Given a parametric model provided by EVT, a natural approach is Maximum Likelihood estimation. Although the resulting estimator is asymptotically efficient, often the number of observations available to estimate the parameters of the EVT models is too small in order to make the large sample property trustworthy. In this paper, we study a new estimator of the parameters, the Maximum Lq-Likelihood estimator (MLqE), introduced by Ferrari and Yang (2007). We show that the MLqE can outperform the standard MLE, when estimating tail probabilities and quantiles of the Generalized Extreme Value (GEV) and the Generalized Pareto (GP) distributions. First, we assess the relative efficiency between the the MLqE and the MLE for various sample sizes, using Monte Carlo simulations. Second, we analyze the performance of the MLqE for extreme quantile estimation using real-world financial data. The MLqE is characterized by a distortion parameter q and extends the traditional log-likelihood maximization procedure. When q!1, the new estimator approaches the traditional Maximum Likelihood Estimator (MLE), recovering its desirable asymptotic properties; when q 6= 1 and the sample size is moderate or small, the MLqE successfully trades bias for variance, resulting in an overall gain in terms of accuracy (Mean Squared Error). |
| Keywords: | Maximum Likelihood; Extreme Value Theory; q-Entropy; Tail-related risk measures |
| JEL: | C13 C22 C51 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:mod:wcefin:07071&r=rmg |
| By: | Loisel Stéphane (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - [Université Claude Bernard - Lyon I]) |
| Abstract: | For general risk processes, the expected time-integrated negative part of the process on a fixed time interval is introduced and studied. Differentiation theorems are stated and proved. They make it possible to derive the expected value of this risk measure, and to link it with the average total time below zero studied by Dos Reis (1993) and the probability of ruin. Differentiation of other functionals of unidimensional and multidimensional risk processes with respect to the initial reserve level are carried out. Applications to ruin theory, and to the determination of the optimal allocation of the global initial reserve which minimizes one of these risk measures, illustrate the variety of application fields and the benefits deriving from an efficient and effective use of such tools. |
| Keywords: | Ruin theory; Sample path properties; Optimal allocation; Multidimensional risk process; Risk measures |
| Date: | 2007–06–26 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:hal-00157739_v1&r=rmg |
| By: | Ravi Bansal |
| Abstract: | The recently developed long-run risks asset pricing model shows that concerns about long-run expected growth and time-varying uncertainty (i.e., volatility) about future economic prospects drive asset prices. These two channels of economic risks can account for the risk premia and asset price fluctuations. In addition, the model can empirically account for the cross-sectional differences in asset returns. Hence, the long-run risks model provides a coherent and systematic framework for analyzing financial markets. |
| JEL: | E0 E44 G0 G1 G12 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:13196&r=rmg |