Halis Sak

Efficient risk simulations for linear asset portfolios in the t-copula model

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm. Numerical results for a variety of realistic portfolio examples show an impressive performance gain.

Up-regulation of TGM2 with ITGB1 and SDC4 is important in the development and metastasis of renal cell carcinoma

OBJECTIVE Tissue transglutaminase (TGM2) up-regulation is involved in the progression and dissemination of carcinomas through β1 integrin (ITGB1) association. Given that TGM2 interaction with syndecan-4 (SDC4) on the cell surface is important in the activation of ITGB1 and integrin-mediated survival signaling, we investigated the roles of TGM2, ITGB1, and SDC4 in the development and metastasis of renal cell carcinoma (RCC). MATERIAL AND METHODS Expression levels of TGM2, ITGB1, and SDC4 mRNA were analyzed in primary tumor samples (n = 95) and their healthy counterparts in addition to control and RCC epithelial cell lines. TGM2 catalytic activity in 60 randomly selected patient samples was measured by enzyme-linked sorbent plate assay. RESULTS TGM2 expression ratio showed a significant 2.9-fold decrease in 67 (70.5%) of the primary RCC tumors (P <0.0001) independent of clinical covariates, including tumor node metastasis (TNM) staging and histopathologic grading. For the remaining 28 (29.5%) tumors, a 1.95-fold increase was recorded in the TGM2 expression levels, which also showed a significant increase in ITGB1 and SDC4 expression levels in 82.6% of the overexpression cases (P <0.001). Up-regulation of TGM2 along with ITGB1 and SCD4 was associated with metastasis and a marked decrease in tumor necrosis. Consistently, RCC cell lines exhibited higher levels of TGM2 expression compared with the control epithelial cell line with a significant up-regulation of ITGB1 and SCD4 recorded for the metastatic lines. CONCLUSIONS Our findings suggest that TGM2 up-regulation along with ITGB1 and SDC4 plays an important role in the development of RCC tumors and advanced RCC with metastasis.

Original Articles: t-Copula generation for control variates

The standard method for generating multi-t vectors is simple and convenient but it has the disadvantage that the generated multi-normal and multi-t vectors are not similar. For t-copula models this destroys much of the variance reduction when using the result of the multi-normal model as external control variate. Therefore we develop a new generation method for multi-t vectors. It is based on the polar method and numerical inversion, and generates multi-normal and multi-t vectors that are very similar. Numerical experiments with simple functions of the weighted sum of t-copula vectors and with pricing European basket options with a t-copula model confirm that the obtained variance reduction factors of the new method are high; 2-100 times higher than when using the standard generation method.

Fast simulations in credit risk

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.

A copula-based simulation model for supply portfolio risk

A copula-based simulation model for supply portfolio risk in the presence of dependent breaches of contracts is introduced in this paper. We demonstrate our method for a supply-chain contract portfolio of commodity metals traded at the London Metal Exchange (LME). The analysis of spot price data on six LME com- modity metals leads us to use a t-copula dependence structure with t-marginals and generalized hyperbolic marginals for the log returns. We also provide effi- cient simulation algorithms using importance sampling for the normal and t- copula dependence structure to quantify risk measures, supply-at-risk and condi- tional supply-at-risk. Numerical examples on a portfolio of six commodity metals demonstrate that our proposed method succeeds in decreasing the variance of the simulations. A numerical sensitivity analysis for the choice of the copula function is also provided. To the best of our knowledge, this is the first paper proposing efficient simulation algorithms on a supply-chain contract portfolio that has a copula-based dependence structure with generalized hyperbolic marginals.

Efficient Numerical Inversion for Financial Simulations

Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton interpolation and Gauss-Lobatto quadrature can be utilized for financial applications. Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant.

Optimally stratified importance sampling for portfolio risk with multiple loss thresholds

Tail loss probability is an essential risk measure for linear asset portfolios. The paper presents an efficient simulation algorithm that combines importance sampling and optimal stratification to estimate tail loss probabilities for linear asset portfolios under the -copula model. Based on the combined method, an efficient procedure is developed for estimating multiple tail loss probabilities in a single simulation. For this purpose, a heuristic determines sample allocation fractions in the strata such that the maximum relative error is minimized. This idea and the heuristic can be used to minimize the maximum relative error of an arbitrary simulation associated with multiple estimates.

A copula-based model for air pollution portfolio risk and its efficient simulation

This paper introduces a portfolio approach for quantifying pollution risk in the presence of PM

Efficient simulations for a Bernoulli mixture model of portfolio credit risk

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