arXiv subjects

Matteo Gardini

Publications and source records attributed to Matteo Gardini.

8 recordsLinked to original sources

arXiv2023

A Heath-Jarrow-Morton framework for energy markets: a pragmatic approach

In this article we discuss the application of the Heath-Jarrow-Morton framework Heath et al. [26] to energy markets. The goal of the article is to give a detailed overview of the topic, focusing on practical aspects rather than on theory, which has been widely studied in literature. This work aims to be a guide for practitioners and for all those who deal with the practical issues of this approach to energy market. In particular, we focus on the markets' structure, model calibration by dimension reduction with Principal Component Analysis (PCA), Monte Carlo simulations and derivatives pricing. As application, we focus on European power and gas markets: we calibrate the model on historical futures quotations, we perform futures and spot simulations and we analyze the results.

q-fin.MF↗

arXiv2022

Exchange option pricing under variance gamma-like models

In this article we focus on the pricing of exchange options when the dynamic of logprices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al [19]. In particular, for the former model we can derive a Margrabe's type formula whereas, for the latter one we can write an "integral free" formula. Furthermore, we show how to construct a general multidimensional versions of the variance gamma++ processes preserving both the mathematical and numerical tractability. Finally we apply the derived models to German and French energy power markets: we calibrate their parameters using real market data and we accordingly evaluate exchange options with the derived closed formulas, Fourier based methods and Monte Carlo techniques.

q-fin.CP↗

arXiv2020

A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and L\'evy-driven Ornstein-Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang [23] because it does not rely on an acceptance-rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques

q-fin.CP↗

arXiv2020

Correlating L\'evy processes with Self-Decomposability: Applications to Energy Markets

Based on the concept of self-decomposability, we extend some recent multivariate L\'evy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related markets after a certain stochastic time delay. Consequently, we study the properties of such processes, derive closed form expressions for the characteristic function and detail how a Monte Carlo scheme can be easily implemented. We illustrate the applicability of our approach in the context of gas and power Energy markets focusing on the calibration and on the pricing of spread options written on different underlying assets using simulations techniques.

q-fin.PR↗

arXiv2019

On the structure of quantum vertex algebras

A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which satisfies associativity and braided locality axioms. We develop a structure theory of quantum vertex algebras, parallel to that of vertex algebras. In particular, we introduce braided n-products for a braided state-field correspondence and prove for quantum vertex algebras a version of the Borcherds identity.

math.QA↗

arXiv2017

FIEMS: Fast Italian Energy Market Simulator

The article describes the algorithm used to define the electricity price in day-ahead and itraday energy markets in Italy. Details of Matlab implementation of one of its simplified versions, capable of producing good results in a extremely short time, are then provided and numerical results are discussed.

q-fin.CP↗

arXiv2016

Hydropower optimization: an industrial approach

Nowadays hydroelectric energy is one of the best energy sources: it is cleaner, safer and more programmable than other sources. For this reason, its manage could not be done in an approssimative way, but advance mathematical models must be use. In this article we consider an overview of the problem: we introduce the problem, then we show its simplest but quite exaustive mathematical formulation and in the end we produce numerical results under the ipothesis that all input are deterministic.

cs.CE↗

arXiv2016

Viral Search algorithm

The article, after a brief introduction on genetic algorithms and their functioning, presents a kind of genetic algorithm called Viral Search. We present the key concepts, we formally derive the algorithm and we perform numerical tests designed to illustrate the potential and limits.

cs.NE↗