Artificial Neural Network Performance Boost using Probabilistic Recovery with Fast Cascade Training

Pattern Recognition and Classification is considered one of the most promising applications in the scientific field of Artificial Neural Networks (ANN). However, regardless of the vast scientific advances in almost every aspect of the technology and mathematics, neural networks still need to be fairly large and complex (i.e., deep), in order to provide robust results. In this article, we propose a novel ANN architecture approach that aims to combine two fairly small Neural Networks based on an introduced probability term of correct classification. Additionally, we present a second ANN, used to reclassify the potentially incorrect results by using the most probable error-free results as additional training data with the predicted labels. The proposed method achieves a rapid decrease in the mean square error compared to other large and complex ANN architectures with a similar execution time. Our approach demonstrates increased effectiveness when applied to various databases, related to wine, iris, the Modified National Institute of Standards and Technology (MNIST) database, the Canadian Institute for Advanced Research (Cifar32), and Fashion MNIST classification problems.

Volatility Timing: Pricing Barrier Options on DAX XETRA Index

This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

Rating Migration and Bond Valuation: Towards Ahistorical Rating Migration Matrices and Default Probability Term Structures

The study examines rating migration, and default probability term structures obtained from rating migration matrices. It expands on the use of rating migration matrices with reduced form bond valuation models, by formally delineating the probability of default according to the likely rating paths of a bond, as implied by the rating migration matrix. Further, two alternatives are also considered. First, the cost of default is stipulated as the recovery of par according to the exit rating upon default. Also, in addition to stating the value of a bond in terms of expected cash flows, when considering the probability of default, the value of a bond is alternatively stated as the present value of all likely rating paths of the bond, discounted against the market risk-bearing bond forward rates of the different rating categories. The impact of term structure volatility and rating migration uncertainty on bond valuation is also considered.It is shown that the relationship between rating migration and default probability is complex, and the default probabilities of different rating categories are time-dependent and not isolated from each other. Also, rating migration resembles a delayed default process that influences default probabilities of subsequent intervals. The implications of a rating migration matrix may perhaps only be fully understood through simulation. This form one of the first points by which to evaluate rating migration matrices. The results of the valuation model show that historical rating migration matrices may not be optimal for pricing bonds ahistorically. A principal premise of the study is the dichotomy between historical values and ahistorical estimates, particularly with regards to rating migration. It is argued that historical estimates face two key shortcomings: they must be able to accurately forecast future rating migration and rating category intensities as a result, and they must specify a method to include rating migration uncertainty. An optimization model is delineated to extract ahistorical rating migration matrices from market prices. This too has implications that should be considered. In light of the above, reduced form models may have an advantage over structural models, in their ability to portray a far more sophisticated default process.

Selectively Fine-Tuning Bayesian Network Learning Algorithm

In this work, we propose a Selective Fine-Tuning algorithm for Bayesian Networks (SFTBN). The aim is to enhance the accuracy of Bayesian Network (BN) classifiers by finding better estimations for the probability terms used by the classifiers. The algorithm augments a BN learning algorithm with a fine-tuning stage that aims to more accurately estimate the probability terms used by the BN. If the value of a probability term causes a misclassification of a training instances and falls outside its valid range then we update (fine-tune) that value. The amount of such an update is proportional to the distance between the value and its valid range. We use the algorithm to fine-tune several forms of BNs: the Naive Bayes (NB), Tree Augmented Naive Bayes (TAN), and Bayesian Augmented Naive Bayes (BAN) models. Our empirical experiments indicate that the SFTBN algorithm improves the classification accuracy of BN classifiers. We also generalized the original fine-tuning algorithm of Naive Bayesian (FTNB) for BN models. We empirically compare the two algorithms, and the empirical results show that while FTNB is more accurate than SFTBN for fine-tuning NB classifiers, SFTBN is more accurate for fine-tuning BNs than the adapted version of FTNB.

ON SOME INCONSISTENCIES IN MODELING CREDIT PORTFOLIO PRODUCTS

The survival probability term structure has become the main concept in modeling credit risk for pricing, risk management, and investment decisions. The Kth-to-default contract is not only a relatively liquid credit risk instrument but also a vehicle that credit rating agencies employ to determine the rating of more esoteric credit risky positions. In this paper, we point out some subtleties in credit risk modeling of default baskets and also identify some potential bias in the pricing formula of the Kth-to-default contract. The numerical examples suggest that this bias increases with the correlation. The results in this paper emphasize the important role of conditioning the information regarding arrival of default.