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on Risk Management |
| By: | Bernardi, Mauro |
| Abstract: | Finite mixtures of Skew distributions have become increasingly popular in the last few years as a flexible tool for handling data displaying several different characteristics such as multimodality, asymmetry and fat-tails. Examples of such data can be found in financial and actuarial applications as well as biological and epidemiological analysis. In this paper we will show that a convex linear combination of multivariate Skew Normal mixtures can be represented as finite mixtures of univariate Skew Normal distributions. This result can be useful in modeling portfolio returns where the evaluation of extremal events is of great interest. We provide analytical formula for different risk measures like the Value-at-Risk and the Expected Shortfall probability. |
| Keywords: | Finite mixtures; Skew Normal distributions; Value-at-Risk; Expected Shortfall probability |
| JEL: | C16 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39828&r=rmg |
| By: | Bernardi, Mauro; Maruotti, Antonello; Lea, Petrella |
| Abstract: | The derivation of loss distribution from insurance data is a very interesting research topic but at the same time not an easy task. To find an analytic solution to the loss distribution may be mislading although this approach is frequently adopted in the actuarial literature. Moreover, it is well recognized that the loss distribution is strongly skewed with heavy tails and present small, medium and large size claims which hardly can be fitted by a single analytic and parametric distribution. Here we propose a finite mixture of Skew Normal distributions that provides a better characterization of insurance data. We adopt a Bayesian approach to estimate the model, providing the likelihood and the priors for the all unknow parameters; we implement an adaptive Markov Chain Monte Carlo algorithm to approximate the posterior distribution. We apply our approach to a well known Danish fire loss data and relevant risk measures, as Value-at-Risk and Expected Shortfall probability, are evaluated as well. |
| Keywords: | Markov chain Monte Carlo; Bayesian analysis; mixture model; Skew-Normal distributions; Loss distribution; Danish data |
| JEL: | C52 C11 C01 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39826&r=rmg |
| By: | Krieger, Kevin; Fodor, Andy; Mauck, Nathan; Stevenson, Greg |
| Abstract: | We consider which readily observable characteristics of individual stocks (e.g., option implied volatility, accounting data, analyst data) may be used to forecast subsequent extreme price movements. We are the first to explicitly consider the predictive influence of option implied volatility in such a framework, which we unsurprisingly find to be an important indicator of future extreme price movements. However, after controlling for implied volatility levels, other factors, particularly firm age and size, still have additional predictive power of extreme future returns. Furthermore, excluding predicted extreme return stocks leads to a portfolio that has lower risk (standard deviation of returns) without sacrificing performance. |
| Keywords: | Implied volatility; portfolio management |
| JEL: | G11 G00 |
| Date: | 2012–05–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39845&r=rmg |
| By: | Rodrigo Mariscal; Andrew Powell |
| Abstract: | There are many sources of inflation forecasts for Latin America. The International Monetary Fund, Latin Focus, the Economist Intelligence Unit and other consulting companies all offer inflation forecasts. However, these sources do not provide any probability measures regarding the risk of inflation. In some cases, Central Banks offer forecast and probability analyses but typically their models are not fully transparent. This technical note attempts to develop a relatively homogeneous set of methodologies and employs them to estimate inflation forecasts, probability distributions for those forecasts and hence probability measures of high inflation. The methodologies are based on both parametric and non-parametric estimation. Results are given for five countries in the region that have inflation targeting regimes. |
| JEL: | C53 E37 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:idb:wpaper:4785&r=rmg |
| By: | Delatte, Anne-Laure; Lopez, Claude |
| Abstract: | In this paper, we propose to identify the dependence structure existing between the returns of equity and commodity futures and its evolution through the past 20 years. The key point is that we do not do not impose the dependence structure but let the data select it. To do so, we model the dependence between commodity (metal, agriculture and energy) and stock markets using a flexible approach that allows us to investigate whether the co-movement is : (i) symmetric and occurring most of the time, (ii) symmetric and occurring mostly during extreme events and (iii) asymmetric and occurring mostly during extreme events. We also allow for this dependence to be time-varying from January 1990 to February 2012. Our analysis uncovers three major stylized facts. First, we find that the dependence between commodity and stock markets is time varying, symmetric and occurs most of the time (as opposed to mostly in extreme events). Second, not allowing for time-varying parameters in the dependence distribution generates a bias toward evidence of tail dependence. Similarly, considering only tail dependence may lead to wrong evidence of asymmetry. Third, a growing comovement between industrial metals and equity markets is identified as early as in 2003, a comovement that spreads to all commodity classes and becomes unambiguously stronger with the global financial crisis after Fall 2008. |
| Keywords: | copula; commodity market; time varying; tail-dependence; comovement; equity market |
| JEL: | F30 C20 Q0 G10 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39860&r=rmg |
| By: | Tanya Ara\'ujo; Jo\~ao Dias; Samuel Eleut\'erio; Francisco Lou\c{c}\~a |
| Abstract: | This paper investigates the common intuition suggesting that during crises the shape of the financial market clearly differentiates from that of random walk processes. In this sense, it challenges the analysis of the nature of financial markets proposed by Fama and his associates. For this, a geometric approach is proposed in order to define the patterns of change of the market and a measure of multivariate kurtosis is used in order to test deviations from multinormality. The emergence of crises can be measured in this framework, using all the available information about the returns of the stocks under consideration and not only the index representing the market. |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1207.1202&r=rmg |
| By: | Kelly, Bryan; Lustig, Hanno; van Nieuwerburgh, Stijn |
| Abstract: | We examine the pricing of financial crash insurance during the 2007-2009 financial crisis in U.S. option markets. A large amount of aggregate tail risk is missing from the price of financial sector crash insurance during the financial crisis. The difference in costs of out-of-the-money put options for individual banks, and puts on the financial sector index, increases fourfold from its pre-crisis 2003-2007 level. We provide evidence that a collective government guarantee for the financial sector, which lowers index put prices far more than those of individual banks, explains the divergence in the basket-index put spread. |
| Keywords: | financial crisis; government bailout; option pricing models; systemic risk; too-big-to-fail |
| JEL: | E44 E60 G12 G13 G18 G21 G28 H23 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9023&r=rmg |