A neural network-based framework for financial model calibration

A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial option prices. The framework consists of two parts: a forward pass in which we train the weights of the ANN off-line, valuing options under many different asset model parameter settings; and a backward pass, in which we evaluate the trained ANN-solver on-line, aiming to find the weights of the neurons in the input layer. The rapid on-line learning of implied volatility by ANNs, in combination with the use of an adapted parallel global optimization method, tackles the computation bottleneck and provides a fast and reliable technique for calibrating model parameters while avoiding, as much as possible, getting stuck in local minima. Numerical experiments confirm that this machine-learning framework can be employed to calibrate parameters of high-dimensional stochastic volatility models efficiently and accurately.Comment: 34 pages, 9 figures, 11 table

The IPAC Image Subtraction and Discovery Pipeline for the intermediate Palomar Transient Factory

We describe the near real-time transient-source discovery engine for the intermediate Palomar Transient Factory (iPTF), currently in operations at the Infrared Processing and Analysis Center (IPAC), Caltech. We coin this system the IPAC/iPTF Discovery Engine (or IDE). We review the algorithms used for PSF-matching, image subtraction, detection, photometry, and machine-learned (ML) vetting of extracted transient candidates. We also review the performance of our ML classifier. For a limiting signal-to-noise ratio of 4 in relatively unconfused regions, "bogus" candidates from processing artifacts and imperfect image subtractions outnumber real transients by ~ 10:1. This can be considerably higher for image data with inaccurate astrometric and/or PSF-matching solutions. Despite this occasionally high contamination rate, the ML classifier is able to identify real transients with an efficiency (or completeness) of ~ 97% for a maximum tolerable false-positive rate of 1% when classifying raw candidates. All subtraction-image metrics, source features, ML probability-based real-bogus scores, contextual metadata from other surveys, and possible associations with known Solar System objects are stored in a relational database for retrieval by the various science working groups. We review our efforts in mitigating false-positives and our experience in optimizing the overall system in response to the multitude of science projects underway with iPTF.Comment: 66 pages, 21 figures, 7 tables, accepted by PAS

Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixed-point arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of Ordinary Differential Equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single precision floating-point and fixed-point arithmetic with round-to-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit (LSB) in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by Partial Differential Equations (PDEs).Comment: Submitted to Philosophical Transactions of the Royal Society