A hybrid quantum Wasserstein GAN with applications to option pricing

This paper conducts an in-depth exploration of harnessing Machine Learning techniques in the context of Quantum methods for Option Pricing. We develop and implement a novel Hybrid Quantum Wasserstein GAN for loading arbitrary distributions from a classical state into a quantum state, which is of interest beyond its financial applications. In particular, our hybrid methodology eliminates several potential sources of instability and has superior performance compared to fully quantum generative models if the target distribution is classical. Our qWGAN can be used to capture the probability distribution of an asset at maturity, and transmute it into a quantum state as demonstrated on synthetic as well as real data experiments. In an Option Pricing context we present a full pipeline using this methodology and leverage the Iterative Quantum Amplitude Estimation algorithm to derive the expected option payoff, ensuring a quadratic enhancement in error scaling compared to traditional methods

Evolving Ensemble Fuzzy Classifier

The concept of ensemble learning offers a promising avenue in learning from data streams under complex environments because it addresses the bias and variance dilemma better than its single model counterpart and features a reconfigurable structure, which is well suited to the given context. While various extensions of ensemble learning for mining non-stationary data streams can be found in the literature, most of them are crafted under a static base classifier and revisits preceding samples in the sliding window for a retraining step. This feature causes computationally prohibitive complexity and is not flexible enough to cope with rapidly changing environments. Their complexities are often demanding because it involves a large collection of offline classifiers due to the absence of structural complexities reduction mechanisms and lack of an online feature selection mechanism. A novel evolving ensemble classifier, namely Parsimonious Ensemble pENsemble, is proposed in this paper. pENsemble differs from existing architectures in the fact that it is built upon an evolving classifier from data streams, termed Parsimonious Classifier pClass. pENsemble is equipped by an ensemble pruning mechanism, which estimates a localized generalization error of a base classifier. A dynamic online feature selection scenario is integrated into the pENsemble. This method allows for dynamic selection and deselection of input features on the fly. pENsemble adopts a dynamic ensemble structure to output a final classification decision where it features a novel drift detection scenario to grow the ensemble structure. The efficacy of the pENsemble has been numerically demonstrated through rigorous numerical studies with dynamic and evolving data streams where it delivers the most encouraging performance in attaining a tradeoff between accuracy and complexity.Comment: this paper has been published by IEEE Transactions on Fuzzy System

Conformal prediction of option prices

The uncertainty associated with option price predictions has largely been overlooked in the literature. This paper aims to fill this gap by quantifying such uncertainty using conformal prediction. Conformal prediction is a model-agnostic procedure that constructs prediction intervals, ensuring valid coverage in finite samples without relying on distributional assumptions. Through the simulation of synthetic option prices, we find that conformal prediction generates prediction intervals for gradient boosting machines with an empirical coverage close to the nominal level. Conversely, non-conformal prediction intervals exhibit empirical coverage levels that fall short of the nominal target. In other words, they fail to contain the actual option price more frequently than expected for a given coverage level. As anticipated, we also observe a decrease in the width of prediction intervals as the size of the training data increases. However, we uncover significant variations in the width of these intervals across different options. Specifically, out-of-the-money options and those with a short time-to-maturity exhibit relatively wider prediction intervals. Then, we perform an empirical study using American call and put options on individual stocks. We find that the empirical results replicate those obtained in the simulation experiment.info:eu-repo/semantics/publishedVersio

Option Pricing using Quantum Computers

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu

EISim: A Platform for Simulating Intelligent Edge Orchestration Solutions

To support the stringent requirements of the future intelligent and interactive applications, intelligence needs to become an essential part of the resource management in the edge environment. Developing intelligent orchestration solutions is a challenging and arduous task, where the evaluation and comparison of the proposed solution is a focal point. Simulation is commonly used to evaluate and compare proposed solutions. However, the currently existing, openly available simulators are lacking in terms of supporting the research on intelligent edge orchestration methods. To address this need, this article presents a simulation platform called Edge Intelligence Simulator (EISim), the purpose of which is to facilitate the research on intelligent edge orchestration solutions. EISim is extended from an existing fog simulator called PureEdgeSim. In its current form, EISim supports simulating deep reinforcement learning based solutions and different orchestration control topologies in scenarios related to task offloading and resource pricing on edge. The platform also includes additional tools for creating simulation environments, running simulations for agent training and evaluation, and plotting results