1,720,988 research outputs found
Fast Simulation of Multifactor Portfolio Credit Risk in the t-Copula Model
No full textWe present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the t-copula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and a scaled chi-square random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and apply a change of measure to the chi-square random variable. Then, conditional on the chi-square random variable, we apply the importance sampling procedure developed for the Gaussian copula model in Glasserman, Kang, Shahabuddin (2005b). We support our importance sampling procedure by numerical examples
Inverse conic programming with applications
No full textLinear programming duality yields efficient algorithms for solving inverse linear programs. We show that special classes of conic programs admit a similar duality and, as a consequence, establish that the corresponding inverse programs are efficiently solvable. We discuss applications of inverse conic programming in portfolio optimization and utility function identification. (C) 2004 Elsevier B.V. All rights reserved.The authors would like to thank the anonymous referees and Donald Goldfarb for valuable comments.
Fast Simulation of Multifactor Portfolio Credit Risk
No full textThis paper develops rare-event simulation methods for the estimation of portfolio credit risk-the risk of losses to a portfolio resulting from defaults of assets in the portfolio. Portfolio credit risk is measured through probabilities of large losses, which are typically due to defaults of many obligors (sources of credit risk) to which a portfolio is exposed. An essential element of a portfolio view of credit risk is a model of dependence between these sources of credit risk: large losses occur rarely and are most likely to result from systematic risk factors that affect multiple obligors. As a consequence, estimating portfolio credit risk poses a challenge both because of the rare-event property of large losses and the dependence between defaults. To address this problem, we develop an importance sampling technique within the widely used Gaussian copula model of dependence. We focus on difficulties arising in multifactor models-that is, models in which multiple factors may be common to multiple obligors, resulting in complex dependence between defaults. Our importance sampling procedure shifts the mean of the common factor to increase the frequency of large losses. In multifactor models, different combinations of factor outcomes and defaults can produce large losses, so our method combines multiple importance sampling distributions, each associated with a shift in the mean of common factors. We characterize "optimal" mean shifts. Finding these points is both a combinatorial problem and a convex optimization problem, so we address computational aspects of this step as well. We establish asymptotic optimality results for our method, showing that-unlike standard simulation-it remains efficient as the event of interest becomes rarer.The ¯rst two authors dedicate this work to the memory of Perwez Shahabuddin, who died after
the original submission of the paper. They thank the reviewers for their careful reading of the
paper and many constructive comments. The second author thanks Dr. Kyungsik Lee for a
discussion on the subset sum problem. This research was partially supported by National Science
Foundation grant DMI 03-00044.
Fairing the gamma: an engineering approach to sensitivity estimation
No full textIn the finance industry, obtaining stable estimates for sensitivities of derivatives to price changes in an underlying asset is very important from a practical point of view. However, this aim is often hindered by the absence of closed-form expressions for Greeks or the requirement of an excessive computational workload due to the complexities of various exotic derivative structures. However, ad hoc numerical schemes to produce stable Greeks such as nonlinear regression can result in nonsensical values. This article proposes a fairing algorithm designed for the computation of gamma values of exotic derivatives. Examples are presented at exotic derivatives to which the algorithm is applied and some analytical and numerical results are provided that show its usefulness in reducing the mean square error of gamma estimates.
Large deviations in multifactor portfolio credit risk
No full textThe measurement of portfolio credit risk focuses on rare but significant large-loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabilities decrease toward zero. Both limits are also based on letting the size of the portfolio increase. Our analysis reveals a qualitative distinction between the two cases: in the rare-default regime, the tail of the loss distribution decreases exponentially, but in the large-threshold regime the decay is consistent with a power law. This indicates that the dependence between defaults imposed by the Gaussian copula is qualitatively different for portfolios of high-quality and lower-quality credits.
Mixout: Effective Regularization to Finetune Large-scale Pretrained Language Models
No full textIn natural language processing, it has been observed recently that generalization could be greatly improved by finetuning a large-scale language model pretrained on a large unlabeled corpus. Despite its recent success and wide adoption, finetuning a large pretrained language model on a downstream task is prone to degenerate performance when there are only a small number of training instances available. In this paper, we introduce a new regularization technique, to which we refer as “mixout”, motivated by dropout. Mixout stochastically mixes the parameters of two models. We show that our mixout technique regularizes learning to minimize the deviation from one of the two models and that the strength of regularization adapts along the optimization trajectory. We empirically evaluate the proposed mixout and its variants on finetuning a pretrained language model on downstream tasks. More specifically, we demonstrate that the stability of finetuning and the average accuracy greatly increase when we use the proposed approach to regularize finetuning of BERT on downstream tasks in GLUE
Exploiting regenerative structure to estimate finite time averages via simulation
No full textWe propose nonstandard simulation estimators of expected time averages over finite intervals [0, t], seeking to enhance estimation efficiency. We make three key assumptions: (i) the underlying stochastic process has regenerative structure, (ii) the time average approaches a known limit as time t increases and (iii) time 0 is a regeneration time. To exploit those properties, we propose a residual-cycle estimator, based on data from the regenerative cycle in progress at time t, using only the data after time t. We prove that the residual-cycle estimator is unbiased and more efficient than the standard estimator for all sufficiently large t. Since the relative efficiency increases in t, the method is ideally suited to use when applying simulation to study the rate of convergence to the known limit. We also consider two other simulation techniques to be used with the residual-cycle estimator. The first involves overlapping cycles, paralleling the technique of overlapping batch means in steady-state estimation; multiple observations are taken from each replication, starting a new observation each time the initial regenerative state is revisited. The other technique is splitting, which involves independent replications of the terminal period after time t, for each simulation up to time t. We demonstrate that these alternative estimators provide efficiency improvement by conducting simulations of queueing models.
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