Control functionals for quasi-Monte Carlo integration

Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with d-dimensions and derivatives of order α, an optimal QMC rule converges at a best-possible rate O(N^-α/d). However, in applications the value of αcan be unknown and/or a rate-optimal QMC rule can be unavailable. Standard practice is to employ \alpha_L-optimal QMC where the lower bound \alpha_L ≤αis known, but in general this does not exploit the full power of QMC. One solution is to trade-off numerical integration with functional approximation. This strategy is explored herein and shown to be well-suited to modern statistical computation. A challenging application to robotic arm data demonstrates a substantial variance reduction in predictions for mechanical torques

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

A Survey on Quantum Computational Finance for Derivatives Pricing and VaR

[Abstract]: We review the state of the art and recent advances in quantum computing applied to derivative pricing and the computation of risk estimators like Value at Risk. After a brief description of the financial derivatives, we first review the main models and numerical techniques employed to assess their value and risk on classical computers. We then describe some of the most popular quantum algorithms for pricing and VaR. Finally, we discuss the main remaining challenges for the quantum algorithms to achieve their potential advantages.Xunta de Galicia; ED431G 2019/01All authors acknowledge the European Project NExt ApplicationS of Quantum Computing (NEASQC), funded by Horizon 2020 Program inside the call H2020-FETFLAG-2020-01 (Grant Agreement 951821). Á. Leitao, A. Manzano and C. Vázquez wish to acknowledge the support received from the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union (European Regional Development Fund- Galicia 2014-2020 Program), by Grant ED431G 2019/01

Effective Dimensionality Control in Quantitative Finance and Insurance

It is well-known that dimension reduction techniques such as the Brownian bridge, principal component analysis, linear transformation could increase the efficiency of Quasi-Monte Carlo (QMC) methods. Caflisch et al. (1997), who introduced two notions of effective dimension known as superposition dimension and truncation dimension, in part explain the overwhelming success of these methods for high-dimensional finance applications. By exploiting dimension reduction in QMC, we propose a new measure of effective dimension which we denote as the delta dimension. Unlike the previously proposed effective dimensions, it is easy to compute delta dimension, including its dimension distribution. We also propose a new dimension reduction technique known as the directional control (DC) method. By assigning appropriately the direction of importance of the given function, the proposed DC method optimally determines the generating matrix used to simulate the Brownian paths. Because of the flexibility of our proposed method, it can be shown that many of the existing dimension reduction methods are special cases of our proposed DC method. Furthermore, considering the functions with multiple discontinuities or differentiabilities, we propose a severity measure that allows us to identify the relative importance of the various sub-functions, which allows us to dynamically construct the optimal path generation method. By exploiting dimension reduction techniques in portfolio of insurance contracts, we propose a real-time evaluation model, i.e. Green-mesh, to select smaller number of synthetic representative points. We show that our pre-computed values could be recycled for evaluating incoming contracts. Unlike the general machine learning method, our green-mesh real-time evaluation model only takes a little computing at time 0, and achieves much higher accuracy. By exploiting dimension reduction techniques in portfolio selection, we propose an Effective Portfolio (EP) model to select smaller number of stocks in portfolio selection and uniquely determine the weights of selected stocks. We propose so called effective portfolio. We show that only certain portion of stocks dominant the whole market in which we define the number of effective stocks as EPD. Unlike randomly selected stocks, our EPD is a counting random variable with corresponding probability mass function, and it can be shown that a better portfolio alpha and beta trade-off based on a sophisticated strategy could be achieved via dimension reduction

Essays on the econometrics of option pricing

This dissertation is a collection of three essays that delve into the econometrics of option pricing. The primary objective of these essays is to develop and deploy diverse econometric techniques that enable the accurate extraction of valuable information embedded in option prices. Chapter 2 investigates jump contagion between international stock markets using options data. It introduces a multivariate option pricing model that assesses the contagious effects of market shocks. Chapter 3 tackles the challenge of estimating continuous-time option pricing models. It proposes a new filtering and estimation method for affine jump-diffusion models, enhancing computational efficiency and implementation ease. Finally, Chapter 4 develops a unified framework for non-parametric estimation of risk-neutral densities, option prices, and option sensitivities

Bayesian optimization in adverse scenarios

Optimization problems with expensive-to-evaluate objective functions are ubiquitous in scientific and industrial settings. Bayesian optimization has gained widespread acclaim for optimizing expensive (and often black box) functions due to its theoretical performance guarantees and empirical sample efficiency in a variety of settings. Nevertheless, many practical scenarios remain where prevailing Bayesian optimization techniques fall short. We consider four such scenarios. First, we formalize the optimization problem where the goal is to identify robust designs with respect to multiple objective functions that are subject to input noise. Such robust design problems frequently arise, for example, in manufacturing settings where fabrication can only be performed with limited precision. We propose a method that identifies a set of optimal robust designs, where each design provides probabilistic guarantees jointly on multiple objectives. Second, we consider sample-efficient high-dimensional multi-objective optimization. This line of research is motivated by the challenging task of designing optical displays for augmented reality to optimize visual quality and efficiency, where the designs are specified by high-dimensional parameterizations governing complex geometries. Our proposed trust-region based algorithm yields order-of-magnitude improvements in sample complexity on this problem. Third, we consider multi-objective optimization of expensive functions with variable-cost, decoupled, and/or multi-fidelity evaluations and propose a Bayes-optimal, non-myopic acquisition function, which significantly improves sample efficiency in scenarios with incomplete information. We apply this to hardware-aware neural architecture search where the objective, on-device latency and model accuracy, can often be evaluated independently. Fourth, we consider the setting where the search space consists of discrete (and potentially continuous) parameters. We propose a theoretically grounded technique that uses a probabilistic reparameterization to transform the discrete or mixed inner optimization problem into a continuous one leading to more effective Bayesian optimization policies. Together, this thesis provides a playbook for Bayesian optimization in several practical adverse scenarios

Valuing infrastructure investments as portfolios of interdependent real options

The value of infrastructure investments is frequently influenced by enormous uncertainty surrounding both exogenous and endogenous factors. At the same time, however, their value is generally driven by much flexibility - i.e. options - with respect to design, financing, construction and operation. Real options analysis aims to pro-actively manage risks by valuing the flexibilities inherent in uncertain investments. Although real options generally occur within portfolios whose value is affected by both exogenous and endogenous uncertainty, most existing valuation approaches focus on single (i.e. individual) options and consider only exogenous uncertainty. In this thesis, we introduce an approach for modelling and approximating the value of portfolios of interdependent real options under exogenous uncertainty, using both influence diagrams and simulation-and-regression. The key features of this approach are that it translates the interdependencies between real options into linear constraints and then integrates these in a portfolio optimisation problem, formulated as a multi-stage stochastic integer programme. To approximate the value of this optimisation problem we present a transparent valuation algorithm based on simulation and parametric regression that explicitly takes into account the state variable's multidimensional resource component. We operationalise this approach using three numerical examples of increasing complexity: an American put option in a simple single-factor setting; a natural resource investment with a switching option in a one-factor setting; and the same investment in a three-factor setting. Subsequently, we demonstrate the ability of the proposed approach to evaluate a complex natural resource investment that features both a large portfolio of interdependent real options and four underlying uncertainties. We show how our approach can be used to investigate the way in which the value of that portfolio and its individual real options are affected by the underlying operating margin and the degrees of different uncertainties. Lastly, we extend this approach to include endogenous, decision- and state-dependent uncertainties. We present an efficient valuation algorithm that is more transparent than those used in existing approaches; by exploiting the problem structure it explicitly accounts for the path dependencies of the state variables. The applicability of the extended approach to complex investment projects is illustrated by valuing an urban infrastructure investment. We show the way in which the optimal value of the portfolio and its single, well-defined options are affected by the initial operating revenues, and by the degrees of exogenous and endogenous uncertainty.Open Acces

Modeling Uncertainty in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. This study introduces a novel numerical method to solve large-scale dynamic stochastic natural resource allocation problems that cannot be addressed by conventional methods. The method is illustrated with an application focusing on the allocation of global land resource use under stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters, the range of land conversion is considerably smaller for the dynamic stochastic model as compared to deterministic scenario analysis. The scenario analysis can thus significantly overstate the magnitude of expected land conversion under uncertain crop yields