arXiv subjects

Carlos Vázquez

Publications and source records attributed to Carlos Vázquez.

12 recordsLinked to original sources

arXiv2026

Numerical methods for Langevin-type SPDE: an implicit Milstein approach and multilevel Monte Carlo techniques

In this work, we investigate the numerical approximation of degenerate Langevin-type stochastic partial differential equations (SPDEs) in two spatial dimensions. These SPDEs arise in stochastic dynamics and mathematical finance, among other applications. In order to handle the mixed deterministic-stochastic structure of the equation and the degeneracy of the differential operator, we propose a semi-implicit Milstein finite difference scheme for the numerical solution. Through the Fourier analysis of the mean-square stability and convergence, we derive explicit conditions on the coefficients under which the scheme is stable, jointly with explicit convergence rates in terms of the discretization parameters. We further embed the proposed scheme within a Multilevel Monte Carlo (MLMC) framework to reduce the computational cost associated with SPDE simulations, and we derive its theoretical computational complexity. Numerical experiments confirm theoretical convergence rates and show that the MLMC strategy achieves an accuracy comparable to standard Monte Carlo at a fraction of the computational cost, reducing the complexity from $\mathcal{O}(\varepsilon^{-5})$ to $\mathcal{O}(\varepsilon^{-3})$ for a target root-mean-square error $\varepsilon$. These results show that combining semi-implicit Milstein schemes with MLMC techniques provides an effective approach for the numerical simulation of Langevin-type SPDEs.

math.NA↗

arXiv2026

Rough volatility dynamics in commodity markets

In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the theoretical analysis of this general model, we focus on the rBergomi and rHeston models and their calibration to market data of vanilla futures options on WTI Crude Oil. Finally, numerical results illustrate the performance of the proposed rough volatility models for commodities pricing.

q-fin.PR↗

arXiv2025

Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing

The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of financial derivatives-traditionally addressed through Monte Carlo integration techniques. In this work, we introduce two hybrid classical-quantum methods to address the option pricing problem. These approaches rely on reconstructing Fourier series representations of statistical distributions from the outputs of Quantum Machine Learning (QML) models based on Parametrized Quantum Circuits (PQCs). We analyze the impact of data size and PQC dimensionality on performance. Quantum Accelerated Monte Carlo (QAMC) is employed as a benchmark to quantitatively assess the proposed models in terms of computational cost and accuracy in the extraction of Fourier coefficients. Through the numerical experiments, we show that the proposed methods achieve remarkable accuracy, becoming a competitive quantum alternative for derivatives valuation.

quant-ph↗

arXiv2024

Real Option Pricing using Quantum Computers

In this work we present an alternative methodology to the standard Quantum Accelerated Monte Carlo (QAMC) applied to derivatives pricing. Our pipeline benefits from the combination of a new encoding protocol, referred to as the direct encoding, and a amplitude estimation algorithm, the modified Real Quantum Amplitude Estimation (mRQAE) algorithm. On the one hand, the direct encoding prepares a quantum state which contains the information about the sign of the expected payoff. On the other hand, the mRQAE is able to read all the information contained in the quantum state. Although the procedure we describe is different from the standard one, the main building blocks are almost the same. Thus, all the extensive research that has been performed is still applicable. Moreover, we experimentally compare the performance of the proposed methodology against the standard QAMC employing a quantum emulator and show that we retain the speedups.

quant-ph↗

arXiv2024

Evaluating Microscopic and Macroscopic Models for Derivative Contracts on Commodity Indices

In this article, we analyze two modeling approaches for the pricing of derivative contracts on a commodity index. The first one is a microscopic approach, where the components of the index are modeled individually, and the index price is derived from their combination. The second one is a macroscopic approach, where the index is modeled directly. While the microscopic approach offers greater flexibility, its calibration results to be more challenging, thus leading practitioners to favor the macroscopic approach. However, in the macroscopic model, the lack of explicit futures curve dynamics raises questions about its ability to accurately capture the behavior of the index and its sensitivities. In order to investigate this, we calibrate both models using derivatives of the S\&P GSCI Crude Oil excess-return index and compare their pricing and sensitivities on path-dependent options, such as autocallable contracts. This research provides insights into the suitability of macroscopic models for pricing and hedging purposes in real scenarios.

q-fin.CP↗

arXiv2024

Deep Joint Learning valuation of Bermudan Swaptions

This paper addresses the problem of pricing involved financial derivatives by means of advanced of deep learning techniques. More precisely, we smartly combine several sophisticated neural network-based concepts like differential machine learning, Monte Carlo simulation-like training samples and joint learning to come up with an efficient numerical solution. The application of the latter development represents a novelty in the context of computational finance. We also propose a novel design of interdependent neural networks to price early-exercise products, in this case, Bermudan swaptions. The improvements in efficiency and accuracy provided by the here proposed approach is widely illustrated throughout a range of numerical experiments. Moreover, this novel methodology can be extended to the pricing of other financial derivatives.

q-fin.CP↗

arXiv2022

Pricing commodity index options

We present a stochastic local volatility model for derivative contracts on commodity futures. The aim of the model is to be able to recover the prices of derivative claims both on futures contracts and on indices on futures strategies. Numerical examples for calibration and pricing are provided for the S&P GSCI Crude Oil excess-return index.

q-fin.PR↗

arXiv2021

Quantum Arithmetic for Directly Embedded Arrays

We describe a general-purpose framework to design quantum algorithms relying upon an efficient handling of arrays. The corner-stone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding the need to deal with square roots or encode the information in registers. We discuss the entire pipeline, from data loading to information extraction. Particular attention is devoted to the definition of an efficient tool-kit of quantum arithmetic operations on arrays. We comment on strong and weak points of the proposed manipulations, especially in relation to an effective exploitation of quantum parallelism. Eventually, we give explicit examples regarding the manipulation of generic oracles.

quant-ph↗

arXiv2020

A stochastic $θ$-SEIHRD model: adding randomness to the COVID-19 spread

In this article we mainly extend the deterministic model developed in [10] to a stochastic setting. More precisely, we incorporated randomness in some coefficients by assuming that they follow a prescribed stochastic dynamics. In this way, the model variables are now represented by stochastic process, that can be simulated by appropriately solve the system of stochastic differential equations. Thus, the model becomes more complete and flexible than the deterministic analogous, as it incorporates additional uncertainties which are present in more realistic situations. In particular, confidence intervals for the main variables and worst case scenarios can be computed.

math.NA↗

arXiv2020

Asymptotic Stability of Empirical Processes and Related Functionals

Let $E$ be a space of observables in a sequence of trials $ξ_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $ψ$-weak topology of measures, when the sequence $ξ_n$ is assumed to be stationary. In this respect, the limit variable is naturally described as a certain canonical conditional distribution. Then, given some functional $τ$ defined on a space of laws, the consistency of the estimators $τ(m_n)$ is investigated. Hence, a criterion for a refined notion of robustness, that applies when considering random measures, is provided in terms of the modulus of continuity of $τ$.

math.PR↗

arXiv2019

Transient hysteresis and inherent stochasticity in gene regulatory networks

Cell fate determination, the process through which cells commit to differentiated states is commonly mediated by gene regulatory motifs with mutually exclusive expression states. The classical deterministic picture for cell fate determination includes bistability and hysteresis, which enables the persistence of the acquired cellular state after withdrawal of the stimulus, ensuring a robust cellular response. However, the stochasticity inherent to gene expression dynamics is not compatible with hysteresis, since the stationary solution of the governing Chemical Master Equation does not depend on the initial conditions. In this work, we provide a quantitative description of a transient hysteresis phenomenon that reconciles experimental evidence of hysteretic behaviour in gene regulatory networks with their inherent stochasticity. Under sufficiently slow dynamics, the dependency of the non-stationary solutions on the initial state of the cells can lead to what we denote here as transient hysteresis. To quantify this phenomenon, we provide an estimate of the convergence rate to the equilibrium. We also introduce the equation of a natural landscape capturing the evolution of the system that, unlike traditional cell fate potential landscapes, is compatible with the notion of coexistence at the microscopic level.

q-bio.MN↗

arXiv2015

A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees

FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language") is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic Programming, a fuzzy logic language with explicitly annotated rules) and Bousi~Prolog (which uses a weak unification algorithm and is well suited for flexible query answering). Hence, it properly manages similarity and truth degrees in a single framework combining the expressive benefits of both languages. This paper presents the main features and implementations details of FASILL. Along the paper we describe its syntax and operational semantics and we give clues of the implementation of the lattice module and the similarity module, two of the main building blocks of the new programming environment which enriches the FLOPER system developed in our research group.

cs.PL↗