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

Explainable deep learning for arm classification during deep brain stimulation - towards digital biomarkers for closed-loop stimulation

Deep brain stimulation (DBS) is an effective technique for treating motor symptoms in neurological conditions like Parkinson’s disease and dystonic and essential tremor (DT and ET). The DBS delivery could be improved if reliable biomarkers could be found. We propose a deep learning (DL) framework based on EEGNet to search for digital biomarkers in EEG recordings for discriminating neural response from changes in DBS parameters. Here we present a proof-of-concept by distinguishing left and right arm movement in raw EEG recorded during a DBS programming session of a DT patient. Based on the classification of 1s segments from six-channel EEG, we achieve an average accuracy of up to 93.8%. In addition, we propose a simple, yet effective model-agnostic filtering strategy for explaining the network’s performance, showing which frequency band features it mostly uses to classify the EEG

Pricing Bermudan options under local Lévy models with default

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy measure. We present a pricing method for Bermudan options based on an analytical approximation of the characteristic func

Efficient computation of various valuation adjustments under local Lévy models

Various valuation adjustments (XVAs) can be written in terms of nonlinear partial integro-differential equations equivalent to forward-backward SDEs (FBSDEs). In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local Lévy model: this framework includes a local volatility function and a local jump measure. Due to the unavailability of the characteristic function for such processes, we use an asymptotic approximation based on the adjoint formulation of the problem

Bermudan option valuation under state-dependent models

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy measure. We present a pricing method for Bermudan options based on an analytical approximation of the characteristic function combined with the COS method. Due to a special form of the obtained characteristic function the price can be computed using a fast Fourier transform-based algorithm resulting in a fast and accurate calculation

Stochastic Mirror Descent for Convex Optimization with Consensus Constraints

The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed optimization problems has not been previously addressed. In this paper we study an exact distributed mirror descent algorithm in continuous-time under additive noise. We establish a linear convergence rate of the proposed dynamics for the setting of convex optimization. Our analysis draws motivation from the Augmented Lagrangian and its relation to gradient tracking. To further explore the benefits of mirror maps in a distributed setting we present a preconditioned variant of our algorithm with an additional mirror map over the Lagrangian dual variables. This allows our method to adapt to both the geometry of the primal variables, as well as to the geometry of the consensus constraint. We also propose a Gauss-Seidel type discretization scheme for the proposed method and establish its linear convergence rate. For certain classes of problems we identify mirror maps that mitigate the effect of the graph's spectral properties on the convergence rate of the algorithm. Using numerical experiments we demonstrate the efficiency of the methodology on convex models, both with and without constraints. Our findings show that the proposed method outperforms other methods, especially in scenarios where the model's geometry is not captured by the standard Euclidean nor

Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs

A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for supervised learning. The resulting model becomes a warm start for the minimization of a loss function based on the residual of the HJB PDE. The combination of supervised learning and residual minimization avoids spurious solutions and mitigate the data inefficiency of a supervised learning-only approach. Numerical tests validate the different advantages of the proposed methodology

On the performance of deep learning models for time series classification in streaming

Processing data streams arriving at high speed requires the development of models that can provide fast and accurate predictions. Although deep neural networks are the state-of-the-art for many machine learning tasks, their performance in real-time data streaming scenarios is a research area that has not yet been fully addressed. Nevertheless, there have been recent efforts to adapt complex deep learning models for streaming tasks by reducing their processing rate. The design of the asynchronous dual-pipeline deep learning framework allows to predict over incoming instances and update the model simultaneously using two separate layers. The aim of this work is to assess the performance of different types of deep architectures for data streaming classification using this framework. We evaluate models such as multi-layer perceptrons, recurrent, convolutional and temporal convolutional neural networks over several time-series datasets that are simulated as streams. The obtained results indicate that convolutional architectures achieve a higher performance in terms of accuracy and efficiency.Comment: Paper submitted to the 15th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2020

Spin polarization induced by optical and microwave resonance radiation in a Si vacancy in SiC: A promising subject for the spectroscopy of single defects

Depending on the temperature, crystal polytype, and crystal position, two opposite schemes have been observed for the optical alignment of the populations of spin sublevels in the ground state of a Si vacancy in SiC upon irradiation with unpolarized light at frequencies of zero-phonon lines. A giant change by a factor of 2-3 has been found in the luminescence intensity of zero-phonon lines in zero magnetic field upon absorption of microwave radiation with energy equal to the fine-structure splitting of spin sublevels of the vacancy ground state, which opens up possibilities for magnetic resonance detection at a single vacancy. © 2007 Pleiades Publishing, Ltd