Barrier options and Greeks: Modeling with neural networks

This paper proposes a non-parametric technique of option valuation and hedging. Here, we replicate the extended Black–Scholes pricing model for the exotic barrier options and their corresponding Greeks using the fully connected feed-forward neural network. Our methodology involves some benchmarking experiments, which result in an optimal neural network hyperparameter that effectively prices the barrier options and facilitates their option Greeks extraction. We compare the results from the optimal NN model to those produced by other machine learning models, such as the random forest and the polynomial regression; the output highlights the accuracy and the efficiency of our proposed methodology in this option pricing problem. The results equally show that the artificial neural network can effectively and accurately learn the extended Black–Scholes model from a given simulated dataset, and this concept can similarly be applied in the valuation of complex financial derivatives without analytical solutions

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Numerical simulations of die casting with uncertainty quantification and optimization using neural networks

Die casting is one type of metal casting in which liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters is difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, uncertainty quantification and design optimization is proposed. This framework includes high-speed numerical simulations of solidification, micro-structure and mechanical properties prediction models along with experimental inputs for calibration and validation. In order to have a better prediction of product quality, both experimental data and stochastic variations in process parameters with numerical modeling are employed. This enhances the utility of traditional numerical simulations used in die casting. OpenCast, a novel and comprehensive computational framework to simulate solidification problems in materials processing is developed. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. Multiple case studies are presented by coupling surrogate models such as polynomial chaos expansion (PCE) and neural network with OpenCast for uncertainty quantification and optimization. The effects of stochasticity in the alloy composition, boundary and initial conditions on the product quality of die casting are analyzed using PCE. Further, a high dimensional stochastic analysis of the natural convection problem is presented to model uncertainty in the material properties and boundary conditions using neural networks. In die casting, heat extraction from molten metal is achieved by cooling lines in the die which impose nonuniform boundary temperatures on the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. Thus, a multi-objective optimization problem is solved to demonstrate a procedure for improvement of product quality and process efficiency

Text Similarity Between Concepts Extracted from Source Code and Documentation

Context: Constant evolution in software systems often results in its documentation losing sync with the content of the source code. The traceability research field has often helped in the past with the aim to recover links between code and documentation, when the two fell out of sync. Objective: The aim of this paper is to compare the concepts contained within the source code of a system with those extracted from its documentation, in order to detect how similar these two sets are. If vastly different, the difference between the two sets might indicate a considerable ageing of the documentation, and a need to update it. Methods: In this paper we reduce the source code of 50 software systems to a set of key terms, each containing the concepts of one of the systems sampled. At the same time, we reduce the documentation of each system to another set of key terms. We then use four different approaches for set comparison to detect how the sets are similar. Results: Using the well known Jaccard index as the benchmark for the comparisons, we have discovered that the cosine distance has excellent comparative powers, and depending on the pre-training of the machine learning model. In particular, the SpaCy and the FastText embeddings offer up to 80% and 90% similarity scores. Conclusion: For most of the sampled systems, the source code and the documentation tend to contain very similar concepts. Given the accuracy for one pre-trained model (e.g., FastText), it becomes also evident that a few systems show a measurable drift between the concepts contained in the documentation and in the source code.</p

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

LEVERAGING MACHINE LEARNING TO IDENTIFY QUALITY ISSUES IN THE MEDICAID CLAIM ADJUDICATION PROCESS

Medicaid is the largest health insurance in the U.S. It provides health coverage to over 68 million individuals, costs the nation over $600 billion a year, and subject to improper payments (fraud, waste, and abuse) or inaccurate payments (claim processed erroneously). Medicaid programs partially use Fee-For-Services (FFS) to provide coverage to beneficiaries by adjudicating claims and leveraging traditional inferential statistics to verify the quality of adjudicated claims. These quality methods only provide an interval estimate of the quality errors and are incapable of detecting most claim adjudication errors, potentially millions of dollar opportunity costs. This dissertation studied a method of applying supervised learning to detect erroneous payment in the entire population of adjudicated claims in each Medicaid Management Information System (MMIS), focusing on two specific claim types: inpatient and outpatient. A synthesized source of adjudicated claims generated by the Centers for Medicare & Medicaid Services (CMS) was used to create the original dataset. Quality reports from California FFS Medicaid were used to extract the underlying statistical pattern of claim adjudication errors in each Medicaid FFS and data labeling utilizing the goodness of fit and Anderson-Darling tests. Principle Component Analysis (PCA) and business knowledge were applied for dimensionality reduction resulting in the selection of sixteen (16) features for the outpatient and nineteen (19) features for the inpatient claims models. Ten (10) supervised learning algorithms were trained and tested on the labeled data: Decision tree with two configurations - Entropy and Gini, Random forests with two configurations - Entropy and Gini, Naïve Bayes, K Nearest Neighbor, Logistic Regression, Neural Network, Discriminant Analysis, and Gradient Boosting. Five (5) cross-validation and event-based sampling were applied during the training process (with oversampling using SMOTE method and stratification within oversampling). The prediction power (Gini importance) for the selected features were measured using the Mean Decrease in Impurity (MDI) method across three algorithms. A one-way ANOVA and Tukey and Fisher LSD pairwise comparisons were conducted. Results show that the Claim Payment Amount significantly outperforms the rest of the prediction power (highest Mean F-value for Gini importance at the α = 0.05 significance) for both claim types. Finally, all algorithms' recall and F1-score were measured for both claim types (inpatient and outpatient) and with and without oversampling. A one-way ANOVA and Tukey and Fisher LSD pairwise comparisons were conducted. The results show a statistically significant difference in the algorithm's performance in detecting quality issues in the outpatient and inpatient claims. Gradient Boosting, Decision Tree (with various configurations and sampling strategies) outperform the rest of the algorithms in recall and F1-measure on both datasets. Logistic Regression showing better recall on the outpatient than inpatient data, and Naïve Bays performs considerably better from recall and F1- score on outpatient data. Medicaid FFS programs and consultants, Medicaid administrators, and researchers could use this study to develop machine learning models to detect quality issues in the Medicaid FFS claim datasets at scale, saving potentially millions of dollars

Front propagation in random media.

244 p.This PhD thesis deals with the problem of the propagation of fronts under random circumstances. Astatistical model to represent the motion of fronts when are evolving in a media characterized bymicroscopical randomness is discussed and expanded, in order to cope with three distinctapplications: wild-land fire simulation, turbulent premixed combustion, biofilm modeling. In thestudied formalism, the position of the average front is computed by making use of a sharp-frontevolution method, such as the level set method. The microscopical spread of particles which takesplace around the average front is given by the probability density function linked to the underlyingdiffusive process, that is supposedly known in advance. The adopted statistical front propagationframework allowed a deeper understanding of any studied field of application. The application ofthis model introduced eventually parameters whose impact on the physical observables of the frontspread have been studied with Uncertainty Quantification and Sensitivity Analysis tools. Inparticular, metamodels for the front propagation system have been constructed in a non intrusiveway, by making use of generalized Polynomial Chaos expansions and Gaussian Processes.bcam:basque center for applied mathematic

Front Propagation in Random Media

This PhD thesis deals with the problem of the propagation of fronts under random circumstances. A statistical model to represent the motion of fronts when are evolving in a media characterized by microscopical randomness is discussed and expanded, in order to cope with three distinct applications: wild-land fire simulation, turbulent premixed combustion, biofilm modeling. In the studied formalism, the position of the average front is computed by making use of a sharp-front evolution method, such as the level set method. The microscopical spread of particles which takes place around the average front is given by the probability density function linked to the underlying diffusive process, that is supposedly known in advance. The adopted statistical front propagation framework allowed a deeper understanding of any studied field of application. The application of this model introduced eventually parameters whose impact on the physical observables of the front spread have been studied with Uncertainty Quantification and Sensitivity Analysis tools. In particular, metamodels for the front propagation system have been constructed in a non intrusive way, by making use of generalized Polynomial Chaos expansions and Gaussian Processes.The Thesis received funding from Basque Government through the BERC 2014-2017 program. It was also funded by the Spanish Ministry of Economy and Competitiveness MINECO via the BCAM Severo Ochoa SEV-2013-0323 accreditation. The PhD is fundend by La Caixa Foundation through the PhD grant “La Caixa 2014”. Funding from “Programma Operativo Nazionale Ricerca e Innovazione” (PONRI 2014-2020) , “Innotavive PhDs with Industrial Characterization” is kindly acknowledged for a research visit at the department of Mathematics and Applications “Renato Caccioppoli” of University “Federico II” of Naples