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We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.

In the paper we study the stochastic process which corresponds to the random population dynamics with linear growth and uniform catastrophes, where an eliminating portion of the population is chosen uniformly. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes.

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.

An resilience optimal evaluation of financial portfolios implies having plausible hypotheses about the multiple interconnections between the macroeconomic variables and the risk parameters. In this paper, we propose a graphical model for the reconstruction of the causal structure that links the multiple macroeconomic variables and the assessed risk parameters, it is this structure that we call Stress Testing Network (STN). In this model, the relationships between the macroeconomic variables and the risk parameter define a "relational graph" among their time-series, where related time-series are connected by an edge. Our proposal is based on the temporal causal models, but unlike, we incorporate specific conditions in the structure which correspond to intrinsic characteristics this type of networks. Using the proposed model and given the high-dimensional nature of the problem, we used regularization methods to efficiently detect causality in the time-series and reconstruct the underlying causal structure. In addition, we illustrate the use of model in credit risk data of a portfolio. Finally, we discuss its uses and practical benefits in stress testing., Comment: arXiv admin note: text overlap with arXiv:1809.07401

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.