A semiparametric factor model for CDO surfaces dynamics

Modelling the dynamics of credit derivatives is a challenging task in nance and economics. The recent crisis has shown that the standard market models fail to measure and forecast nancial risks and their characteristics. This work studies risk of collateralized debt obligations (CDOs) by investigating the evolution of tranche spread surfaces and base correlation surfaces using a dynamic semiparametric factor model (DSFM). The DSFM oers a combination of exible functional data analysis and dimension reduction methods, where the change in time is linear but the shape is nonparametric. The study provides an empirical analysis based on iTraxx Europe tranches and proposes an application to curve trading strategies. The DSFM allows us to describe the dynamics of all the tranches for all available maturities and series simultaneously which yields better understanding of the risk associated with trading

Implied volatility can be considered as a function of strike level and time to maturity. As it is calculated from the actual trading options, it contains dynamic, multi-dimensional information of options, modelling the implied volatility is an interesting task for researchers. Dynamic semiparametric factor models (DSFM) are used to model the implied volatility surface. It employs semiparametric factor functions and time variate loadings to reduce the dimensions of the data. This master thesis applies joint analysis with the time variate factor loadings resulted from DSFM, in order to discuss the relationship between index options and stock options. The data of DAX index option and its liquid components stock options will be applied in analysis. The result of the joint analysis shows, that the index option has long term relationship with its stock options. It is unlikely to disperse the risk by trading the stock options under the same index.

Leveraged ETF Options Implied Volatility Paradox: A Statistical Study

A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics

The aim of data transformation is to transform the original feature space of data into another space with better properties. This is typically combined with dimensionality reduction, so that the dimensionality of the transformed space is smaller. A widely used method for data transformation and dimensionality reduction is Principal Component Analysis (PCA). PCA finds a subspace that explains most of the data variance. While the new PCA feature space has interesting properties, such as removing linear correlation, PCA is an unsupervised method. Therefore, there is no guarantee that the PCA feature space will be the most appropriate for supervised tasks, such as classification or regression. On the other hand, 3-layer Multi Layer Perceptrons (MLP), which are supervised methods, can also be understood as a data transformation carried out by the hidden layer, followed by a classification/regression operation performed by the output layer. Given that the hidden layer is obtained after a supervised training process, it can be considered that it is performing a supervised data transformation. And if the number of hidden neurons is smaller than the input, also dimensionality reduction. Despite this kind of transformation being widely available (any neural network package that allows access to the hidden layer weights can be used), no extensive experimentation on the quality of 3-layer MLP data transformation has been carried out. The aim of this article is to carry out this research for classification problems. Results show that, overall, this transformation offers better results than the PCA unsupervised transformation method.

For detecting anomalies or interventions in the field of forest monitoring we propose an approach based on the spatial and temporal forecast of satellite time series data. For each pixel of the satellite image three different types of forecasts are provided, namely spatial, temporal and combined spatio-temporal forecast. Spatial forecast means that a clustering algorithm is used to group the time series data based on the features normalised difference vegetation index (NDVI) and the short-wave infrared band (SWIR). For estimation of the typical temporal trajectory of the NDVI and SWIR during the vegetation period of each spatial cluster, we apply several methods of functional data analysis including functional principal component analysis, and a novel form of random regression forests with online learning (streaming) capability. The temporal forecast is carried out by means of functional time series analysis and an autoregressive integrated moving average model. The combination of the temporal forecasts, which is based on the past of the considered pixel, and spatial forecasts, which is based on highly correlated pixels within one cluster and their past, is performed by functional data analysis, and a variant of random regression forests adapted to online learning capabilities. For evaluation of the methods, the approaches are applied to a study area in Germany for monitoring forest damages caused by wind-storm, and to a study area in Spain for monitoring forest fires.

Accurate mapping of leaf area index (LAI) is essential for mangrove conservation and restoration. This study proposes a new approach to the retrieval of the mangrove LAI by combining a one-dimensional convolutional neural network (1D-CNN) with adaptive ensemble learning regression (AELR) and deep learning regression (DNNR) algorithms. We further evaluated the performance of OHS (Zhuhai-1) hyperspectral and GF-3 SAR images in mapping the spatial distribution of the LAI in mangroves. Finally, the outputs of the AELR and DNNR models were interpreted, and the interactions between different image features were clarified to select the sensitive spectral ranges and vegetation indexes for estimating the mangrove LAI using SHAP (Shapley additive explanation). We confirmed that 1D-CNN + DNNR provided an effective approach to estimating the mangrove LAI, as it produced a higher-accuracy inversion (R 2 = 0.8685) than that of the AELR model. It was found in this study that the 1D-CNN improved the retrieval accuracy (R 2) of the mangrove LAI from 0.097 to 0.1297 when compared with the traditional data dimension reduction (DDR) method, which demonstrated that the 1D-CNN was able to improve the inversion accuracy of the mangrove LAI. This study revealed that the synergistic use of OHS hyperspectral and GF-3 SAR images (R 2 = 0.8685, RMSE = 0.134) outperformed any of the lone datasets in the inversion of the mangrove LAI. Finally, this study provided explanations and interpretations of the outputs of the DNNR and AELR models, and it was found that the optimal spectral ranges for estimating the mangrove LAI are 637–671 nm and 802–822 nm; H19 ((NIR/Red)/Red), the NDVI, H14 (Red edge/Red), and the EMVI ((Green-SWIR 2)/(SWIR1-Green)) provided important contributions for mapping the mangrove LAI. These results provide a scientific foundation for the preservation and restoration of coastal mangroves.

Feature selection is an important method of data dimensionality reduction widely used in machine learning. In this framework, the sparse representation based feature selection methods are very attractive. This is because of the nature of these methods which try to represent a data with as less as possible non-zero coefficients. In deep neural networks, a very high dimensional feature space is usually existed. In such a situation, one can take advantages of the feature selection approaches into account. In this paper, first, three sparse feature selection methods are compared. The Sparse Group Lasso (SGL) algorithm is one of the adopted approaches. This method is theoretically very well-organized and leads to good results for man-made features. The most important property of this method is that it highly induces the sparsity to the data. A main step of the SGL method is the features grouping step. In this paper, a k-means clustering based method is applied for grouping of the features. Our experimental results show that this sparse representation based method leads to very successful results in deep neural networks.

Aiming at the features that modem industrial processes always have some characteristics of complexity and nonlinearity and the process data usually contain both Gaussion and non-Gaussion information at the same time, a new process performance monitoring and fault diagnosis method based on subsystem division and kernel entropy component analysis (Sub-KECA) is proposed in this paper. KECA as a new method for data transformation and dimensionality reduction, which chooses the best principal component vector according to the maximal Renyi entropy rather than judging by the top eigenvalue and eigenvector of the kernel matrix simply. Besides, it can be optimized and anti-disturb due to the application of subsystem division. The proposed method is applied to process monitoring of the Tennessee Eastman(TE) process. The positive simulation results indicate that this method is more feasible and efficient when comparing with KPCA method and original KECA method.

Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring.

Dimension reduction has been used to visualise the distribution of multidimensional microbiome data, but the composite variables calculated by the dimension reduction methods have not been widely used to investigate the relationship of the human gut microbiome with lifestyle and disease. In the present study, we applied several dimension reduction methods, including principal component analysis, principal coordinate analysis (PCoA), non-metric multidimensional scaling (NMDS), and non-negative matrix factorization, to a microbiome dataset from 186 subjects with symptoms of allergic rhinitis (AR) and 106 controls. All the dimension reduction methods supported that the distribution of microbial data points appeared to be continuous rather than discrete. Comparison of the composite variables calculated from the different dimension reduction methods showed that the characteristics of the composite variables differed depending on the distance matrices and the dimension reduction methods. The first composite variables calculated from PCoA and NMDS with the UniFrac distance were strongly associated with AR (FDR adjusted P = 2.4 × 10–4 for PCoA and P = 2.8 × 10–4 for NMDS), and also with the relative abundance of Bifidobacterium and Prevotella. The abundance of Bifidobacterium was also linked to intake of several nutrients, including carbohydrate, saturated fat, and alcohol via composite variables. Notably, the association between the composite variables and AR was much stronger than the association between the relative abundance of individual genera and AR. Our results highlight the usefulness of the dimension reduction methods for investigating the association of microbial composition with lifestyle and disease in clinical research.

To detect false data injection attacks (FDIAs) in power grid reconstruction and solve the problem of high data dimension and bad abnormal data processing in the power system, thereby achieving safe and stable operation of the power grid system, this study introduces machine learning methods to explore the detection of FDIAs. First, through the utilization of the standard IEEE node system and the simulation of FDIAs under the condition of non-complete topology information, the construction of the attack data set is completed, and the MatPower tool is applied to simulate and analyze the data set. Second, based on the isolated Forest (iForest) abnormal score data processing algorithm combined with the Local Linear Embedding (LLE) data dimensionality reduction method, an algorithm for data feature extraction is constructed. Finally, based on the combination of the Convolutional Neural Network (CNN) and the Gated Recurrent Unit (GRU) network, an algorithm model for FDIAs detection is constructed. The results show that in the IEEE14-bus node and IEEE118-bus node systems, the overall distribution of the state estimated before and after the attack vector injection is consistent with the initial value. In the iFores algorithm, the number of iTree and the number of samples affect the extraction of abnormal score data. When the number of iTree n is determined to be 100, and the corresponding number of samples w is determined to be 10, the algorithm has the best detection effect. The FDIAs detection algorithm model based on CNN-GRU shows good detection effects under high attack intensity, with an accuracy rate of more than 95%, and its performance is better than other traditional detection algorithms. In this study, the bad data detection model based on deep learning has an active role in the realization of the safe and stable operation of the smart grid.

Chemical process modeling is the basis for research and applications in related fields. With the development of industrial informatization, data-driven process modeling techniques are increasingly applied in chemical processes, helping to obtain more accurate results with less model development costs. However, due to the high-dimensional nonlinear characteristics of most chemical processes, problems such as the “curse of dimensionality” and information redundancy will render the models more prone to overfitting with reduced accuracies and weaker generalization abilities. Many data dimensionality reduction methods are adopted to mitigate the above problems, but most are limited by inaccurate association measurements and weak redundancy exclusion. In this paper, the extensive existence of data associations and information redundancies is first revealed through the analysis from an information-theoretic perspective. Then, a feature selection method based on conditional refined maximal information coefficient maximization (CRMICM) is proposed to improve the consistency of association measurement and the accuracy of redundancy estimation with limited samples. The final prediction modeling test for an actual fluidized catalytic cracking (FCC) process proves the extensive association between the variables and targets. Only a few variables are essential for the modeling, while the rest are redundant. Compared with other methods, CRMICM achieves the best dimensionality reduction effects on the FCC process data regarding the number of features and model prediction accuracy, showing its good applicability for chemical processes.

In vielen Anwendungen ist es notwendig, die stochastische Schwankungen der maximalen Abweichungen der nichtparametrischen Schätzer von Quantil zu wissen, zB um die verschiedene parametrische Modelle zu überprüfen. Einheitliche Konfidenzbänder sind daher für nichtparametrische Quantil Schätzungen der Regressionsfunktionen gebaut. Die erste Methode basiert auf der starken Approximation der empirischen Verfahren und Extremwert-Theorie. Die starke gleichmäßige Konsistenz liegt auch unter allgemeinen Bedingungen etabliert. Die zweite Methode beruht auf der Bootstrap Resampling-Verfahren. Es ist bewiesen, dass die Bootstrap-Approximation eine wesentliche Verbesserung ergibt. Der Fall von mehrdimensionalen und diskrete Regressorvariablen wird mit Hilfe einer partiellen linearen Modell behandelt. Das Verfahren wird mithilfe der Arbeitsmarktanalysebeispiel erklärt. Hoch-dimensionale Zeitreihen, die nichtstationäre und eventuell periodische Verhalten zeigen, sind häufig in vielen Bereichen der Wissenschaft, zB Makroökonomie, Meteorologie, Medizin und Financial Engineering, getroffen. Der typische Modelierungsansatz ist die Modellierung von hochdimensionalen Zeitreihen in Zeit Ausbreitung der niedrig dimensionalen Zeitreihen und hoch-dimensionale zeitinvarianten Funktionen über dynamische Faktorenanalyse zu teilen. Wir schlagen ein zweistufiges Schätzverfahren. Im ersten Schritt entfernen wir den Langzeittrend der Zeitreihen durch Einbeziehung Zeitbasis von der Gruppe Lasso-Technik und wählen den Raumbasis mithilfe der funktionalen Hauptkomponentenanalyse aus. Wir zeigen die Eigenschaften dieser Schätzer unter den abhängigen Szenario. Im zweiten Schritt erhalten wir den trendbereinigten niedrig-dimensionalen stochastischen Prozess (stationär).

Equity basket correlation can be estimated both using the physical measure from stock prices, and also using the risk neutral measure from option prices. The difference between the two estimates motivates a so-called “dispersion strategy”. We study the performance of this strategy on the German market and propose several profitability improvement schemes based on implied correlation (IC) forecasts. Modelling IC conceals several challenges. Firstly the number of correlation coefficients would grow with the size of the basket. Secondly, IC is not constant over maturities and strikes. Finally, IC changes over time. We reduce the dimensionality of the problem by assuming equicorrelation. The IC surface (ICS) is then approximated from the implied volatilities of stocks and the implied volatility of the basket. To analyze the dynamics of the ICS we employ a dynamic semiparametric factor model.