{"title":"Estimating the Lognormal-Gamma Model of Operational Risk Using the MCMC Method","authors":"Bakhodir A. Ergashev","doi":"10.2139/ssrn.1316428","DOIUrl":"https://doi.org/10.2139/ssrn.1316428","url":null,"abstract":"The lognormal-gamma distribution, being a heavy-tailed distribution, is very attractive from the operational risk modeling perspective because historical operational losses also exhibit heavy tails. Unfortunately, fitting this model requires two severe challenges to be properly addressed. First, the density function of the lognormal-gamma distribution is expressed in the form of a Lebesgue integral. Second, if the information contained in a sample of losses is insufficient to accurately estimate the shape of the distributions tail, the capital estimates become extremely volatile. We address both challenges using the Markov chain Monte Carlo (MCMC) method and imposing prior assumptions about the models unknown parameters. As a result, we were able to reduce statistical uncertainty around capital estimates substantially. Our results also indicate that there is no need to reduce the currently accepted 99.9% quantile level for regulatory capital as suggested elsewhere in the operational risk literature.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115851121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Practical Policy Iteration: Generic Methods for Obtaining Rapid and Tight Bounds for Bermudan Exotic Derivatives Using Monte Carlo Simulation","authors":"Christopher Beveridge, M. Joshi, Rober Y. W. Tang","doi":"10.2139/ssrn.1331904","DOIUrl":"https://doi.org/10.2139/ssrn.1331904","url":null,"abstract":"We introduce a set of improvements which allow the calculation of very tight lower bounds for Bermudan derivatives using Monte Carlo simulation. These tight lower bounds can be computed quickly, and with minimal hand-crafting. Our focus is on accelerating policy iteration to the point where it can be used in similar computation times to the basic least-squares approach, but in doing so introduce a number of improvements which can be applied to both the least-squares approach and the calculation of upper bounds using the Andersen–Broadie method. The enhancements to the least-squares method improve both accuracy and efficiency.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123433958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Giuseppe Cavaliere, David I. Harvey, S. Leybourne, A. Taylor
{"title":"Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility","authors":"Giuseppe Cavaliere, David I. Harvey, S. Leybourne, A. Taylor","doi":"10.2139/ssrn.1310189","DOIUrl":"https://doi.org/10.2139/ssrn.1310189","url":null,"abstract":"In this paper we analyse the impact of non-stationary volatility on the recently developed unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2008) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T??1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T1=2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, including, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this estimator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of various models of non-stationary volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122117315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Contributions to the Estimation of Mixed-State Conditionally Heteroscedastic Latent Factor Models: A Comparative Study","authors":"Mohamed Saidane, C. Lavergne","doi":"10.2139/ssrn.1282230","DOIUrl":"https://doi.org/10.2139/ssrn.1282230","url":null,"abstract":"Mixed-State conditionally heteroscedastic latent factor models attempt to describe a complex nonlinear dynamic system with a succession of linear latent factor models indexed by a switching variable. Unfortunately, despite the framework's simplicity exact state and parameter estimation are still intractable because of the interdependency across the latent factor volatility processes. Recently, a broad class of learning and inference algorithms for time series models have been successfully cast in the framework of dynamic Bayesian networks (DBN). This paper describes a novel DBN-based switching conditionally heteroscedastic latent factor model. The key methodological contribution of this paper is the novel use of the Generalized Pseudo-Bayesian method GPB2, a structured variational learning approach and an approximated version of the Viterbi algorithm in conjunction with the EM algorithm for overcoming the intractability of exact inference in mixed-state latent factor model. The conditional EM algorithm that we have developed for the maximum likelihood estimation is based on an extended switching Kalman filter approach which yields inferences about the unobservable path of the common factors and their variances, and the latent variable of the state process. Extensive Monte Carlo simulations show promising results for tracking, interpolation, synthesis, and classification using learned models.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123128262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identifying Sources of Business Cycle Fluctuations in Germany 1975-1998","authors":"Oliver Holtemöller, Torsten Schmidt","doi":"10.2139/ssrn.1280926","DOIUrl":"https://doi.org/10.2139/ssrn.1280926","url":null,"abstract":"In this paper, we estimate a small New Keynesian dynamic stochastic general equilibrium (DSGE) model for Germany for the period from 1975 to 1998 and use it to identify the structural shocks, which have driven the business cycle. For this purpose we apply indirect inference methods, that is we specify the parameters of the theoretical model such that simulated data mimics observed data as closely as possible. In addition to the identification of structural shocks, we uncover the unobservable output gap, which is a prominent indicator in business cycle analysis. Furthermore, we show to which extent each identified shock has contributed to the business cycle fluctuations. - Business cycle accounting ; dynamic stochastic general equilibrium models ; Germany ; indirect inference ; New Keynesian macroeconomics","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130303711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Determinants of Foreign Direct Investment in Nigeria: Political Factor Effect Revisited","authors":"W. Ibrahim, Onokosi-Alliyu Saidat O.","doi":"10.2139/ssrn.1136083","DOIUrl":"https://doi.org/10.2139/ssrn.1136083","url":null,"abstract":"The paper examines the determinants of Foreign Direct Investment (FDI) in Nigeria during 1970 – 2006. cointegration techniques reveal that the major determinants of FDI are market size, real exchange rate and political factor thereby validating theoretical expectations. Furthermore, simulations using impulse response and variance decomposition analysis suggest that uncontrolled trade liberalization must be avoided.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131528707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian Model Selection for Structural Break Models","authors":"Andrew T. Levin, Jeremy Piger","doi":"10.2139/ssrn.1132463","DOIUrl":"https://doi.org/10.2139/ssrn.1132463","url":null,"abstract":"We take a Bayesian approach to model selection in regression models with structural breaks in conditional mean and residual variance parameters. A novel feature of our approach is that it does not assume knowledge of the parameter subset that undergoes structural breaks, but instead conducts model selection jointly over the number of structural breaks and the subset of the parameter vector that changes at each break date. Simulation experiments demonstrate that conducting this joint model selection can be quite important in practice for the detection of structural breaks. We apply the proposed model selection procedure to characterize structural breaks in the parameters of an autoregressive model for post-war U.S. inflation. We find important changes in both residual variance and conditional mean parameters, the latter of which is revealed only upon conducting the joint model selection procedure developed here.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126657044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"CHICAGO: A Fast and Accurate Method for Portfolio Risk","authors":"S. Broda, Marc S. Paolella","doi":"10.2139/ssrn.1126706","DOIUrl":"https://doi.org/10.2139/ssrn.1126706","url":null,"abstract":"The estimation of multivariate GARCH models remains a challenging task, even in modern computer environments. This manuscript shows how Independent Component Analysis can be used to estimate the Generalized Orthogonal GARCH model in a fraction of the time otherwise required. The proposed method is a two-step procedure, separating the estimation of the correlation structure from that of the univariate dynamics, thus facilitating the incorporation of non-Gaussian innovations distributions in a straightforward manner. The generalized hyperbolic distribution provides an excellent parametric description of financial returns data and is used for the univariate fits, but its convolutions, necessary for portfolio risk calculations, are intractable. This restriction is overcome by a saddlepoint approximation to the required distribution function, which is computationally cheap and extremely accurate - most notably in the tail, which is crucial for risk calculations. A simulation study and an application to stock returns demonstrate the validity of the procedure.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115290185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introduction to Multi-Agent Simulation","authors":"Peer-Olaf Siebers, U. Aickelin","doi":"10.2139/ssrn.2827970","DOIUrl":"https://doi.org/10.2139/ssrn.2827970","url":null,"abstract":"When designing systems that are complex, dynamic and stochastic in nature, simulation is generally recognised as one of the best design support technologies, and a valuable aid in the strategic and tactical decision making process. A simulation model consists of a set of rules that define how a system changes over time, given its current state. Unlike analytical models, a simulation model is not solved but is run and the changes of system states can be observed at any point in time. This provides an insight into system dynamics rather than just predicting the output of a system based on specific inputs. Simulation is not a decision making tool but a decision support tool, allowing better informed decisions to be made. Due to the complexity of the real world, a simulation model can only be an approximation of the target system. The essence of the art of simulation modelling is abstraction and simplification. Only those characteristics that are important for the study and analysis of the target system should be included in the simulation model.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131486224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Debt Sustainability in Emerging Market Countries: A 'Fan Chart' Approach","authors":"Xavier Debrun, Oya Celasun, J. Ostry","doi":"10.2139/ssrn.2005167","DOIUrl":"https://doi.org/10.2139/ssrn.2005167","url":null,"abstract":"The paper by Debrun, Celasun and Ostry focuses on the assessment of debt sustainability and stresses the need to overcome one of the main drawbacks of debt sustainability analysis, i.e. the fact that it is usually based on a deterministic approach in which uncertainty is dealt with by simulating alternative scenarios in which only one key variable at a time is hit by an adverse shock. The paper proposes a methodology that improves the understanding of the risks surrounding debt dynamics and acknowledges the probabilistic nature of debt sustainability analysis exercises. The approach, which preserves a certain degree of standardization while allowing for country-specific risk factors, uses estimates of the joint probability distributions of economic shocks to construct a large number of scenarios capturing covariances among disturbances and the dynamic response of the economy. The methodology provides for fiscal policy to adjust to shocks according to a pattern observed in emerging market economies and to be itself a source of risk. The proposed assessment of debt sustainability is probabilistic and can help policy makers to: capture country-specific features relevant for debt dynamics; have clearer signals of the risks from delaying fiscal adjustment or undertaking fiscal expansions; and improve medium-term fiscal planning given the more complete information on the debt risk profile.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123318551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}