arXiv subjects

Guido Germano

Publications and source records attributed to Guido Germano.

At least 19 recordsLinked to original sources

arXiv2025

Large language models in finance : what is financial sentiment?

Financial sentiment has become a crucial yet complex concept in finance, increasingly used in market forecasting and investment strategies. Despite its growing importance, there remains a need to define and understand what financial sentiment truly represents and how it can be effectively measured. We explore the nature of financial sentiment and investigate how large language models (LLMs) contribute to its estimation. We trace the evolution of sentiment measurement in finance, from market-based and lexicon-based methods to advanced natural language processing techniques. The emergence of LLMs has significantly enhanced sentiment analysis, providing deeper contextual understanding and greater accuracy in extracting sentiment from financial text. We examine how BERT-based models, such as RoBERTa and FinBERT, are optimized for structured sentiment classification, while GPT-based models, including GPT-4, OPT, and LLaMA, excel in financial text generation and real-time sentiment interpretation. A comparative analysis of bidirectional and autoregressive transformer architectures highlights their respective roles in investor sentiment analysis, algorithmic trading, and financial decision-making. By exploring what financial sentiment is and how it is estimated within LLMs, we provide insights into the growing role of AI-driven sentiment analysis in finance.

q-fin.ST↗

arXiv2024

Sentiment trading with large language models

We investigate the efficacy of large language models (LLMs) in sentiment analysis of U.S. financial news and their potential in predicting stock market returns. We analyze a dataset comprising 965,375 news articles that span from January 1, 2010, to June 30, 2023; we focus on the performance of various LLMs, including BERT, OPT, FINBERT, and the traditional Loughran-McDonald dictionary model, which has been a dominant methodology in the finance literature. The study documents a significant association between LLM scores and subsequent daily stock returns. Specifically, OPT, which is a GPT-3 based LLM, shows the highest accuracy in sentiment prediction with an accuracy of 74.4%, slightly ahead of BERT (72.5%) and FINBERT (72.2%). In contrast, the Loughran-McDonald dictionary model demonstrates considerably lower effectiveness with only 50.1% accuracy. Regression analyses highlight a robust positive impact of OPT model scores on next-day stock returns, with coefficients of 0.274 and 0.254 in different model specifications. BERT and FINBERT also exhibit predictive relevance, though to a lesser extent. Notably, we do not observe a significant relationship between the Loughran-McDonald dictionary model scores and stock returns, challenging the efficacy of this traditional method in the current financial context. In portfolio performance, the long-short OPT strategy excels with a Sharpe ratio of 3.05, compared to 2.11 for BERT and 2.07 for FINBERT long-short strategies. Strategies based on the Loughran-McDonald dictionary yield the lowest Sharpe ratio of 1.23. Our findings emphasize the superior performance of advanced LLMs, especially OPT, in financial market prediction and portfolio management, marking a significant shift in the landscape of financial analysis tools with implications to financial regulation and policy analysis.

q-fin.CP↗

arXiv2021

Pricing methods for $α$-quantile and perpetual early exercise options based on Spitzer identities

We present new numerical schemes for pricing perpetual Bermudan and American options as well as $α$-quantile options. This includes a new direct calculation of the optimal exercise barrier for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener-Hopf method. Our direct calculation of the price of $α$-quantile options combines for the first time the Dassios-Port-Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of Lévy processes.

q-fin.CP↗

arXiv2021

Solution of Wiener-Hopf and Fredholm integral equations by fast Hilbert and Fourier transforms

We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based method for the Wiener-Hopf equation due to Henery, expressing it in terms of the Hilbert transform, and computing the latter in a more sophisticated way with sinc functions. We then generalise our method to the Fredholm equation reformulating it as two coupled Wiener-Hopf equations and solving them iteratively. We provide numerical tests and open-source code.

math.NA↗

arXiv2020

Hilbert transform, spectral filters and option pricing

We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (2008) and Fusai, Germano and Marazzina (2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Lévy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering.

q-fin.CP↗

arXiv2017

Fluctuation identities with continuous monitoring and their application to price barrier options

We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential Lévy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener-Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-$z$ domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme.

q-fin.CP↗

arXiv2016

Stability of calibration procedures: fractals in the Black-Scholes model

Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-call parity. Solving for the implied volatility that reproduces a given market price yields not only a real root, but also infinitely many complex roots in a neighbourhood of the origin. The Newton-Raphson calculation of the complex implied volatility has a chaotic nature described by fractals.

q-fin.MF↗

arXiv2016

Full and fast calibration of the Heston stochastic volatility model

This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston characteristic function and modify it to avoid discontinuities caused by branch switchings of complex functions. Using this representation, we obtain the analytical gradient of the price of a vanilla option with respect to the model parameters, which is the key element of all variants of the objective function. The interdependency between the components of the gradient enables an efficient implementation which is around ten times faster than a numerical gradient. We choose the Levenberg-Marquardt method to calibrate the model and do not observe multiple local minima reported in previous research. Two-dimensional sections show that the objective function is shaped as a narrow valley with a flat bottom. Our method is the fastest calibration of the Heston model developed so far and meets the speed requirement of practical trading.

q-fin.CP↗

arXiv2015

Velocity and energy distributions in microcanonical ensembles of hard spheres

In a microcanonical ensemble (constant $NVE$, hard reflecting walls) and in a molecular dynamics ensemble (constant $NVE\mathbf{PG}$, periodic boundary conditions) with a number $N$ of smooth elastic hard spheres in a $d$-dimensional volume $V$ having a total energy $E$, a total momentum $\mathbf{P}$, and an overall center of mass position $\mathbf{G}$, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on $d$, $N$, $E$, the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in $d$ dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of $N$.

cond-mat.stat-mech↗

arXiv2010

First-passage and first-exit times of a Bessel-like stochastic process

We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt + \sqrt{2D} dW_t$, where $W_t$ is the Wiener process. Due to the singularity of the drift term for $X_t = 0$, different natures of boundary at the origin arise depending on the real parameter $n$: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behaviour is observed in the case of a regular boundary.

cond-mat.stat-mech↗

arXiv2010

Efficiency of linked cell algorithms

The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its efficiency, because a large part of CPU time is spent to identify the interacting particles. Several recent publications proposed improvements to the algorithm and investigated their efficiency by applying them to particular setups. In this publication we develop a general method to evaluate the efficiency of these algorithms, which is mostly independent of the parameters of the simulation, and test it for a number of linked cell list algorithms. We also propose a combination of linked cell reordering and interaction sorting that shows a good efficiency for a broad range of simulation setups.

physics.comp-ph↗

arXiv2009

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.

cond-mat.stat-mech↗

arXiv2009

Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Levy stable random variables and validate it by Monte Carlo simulation.

cond-mat.stat-mech↗

arXiv2009

Automatic generation of non-uniform random variates for arbitrary pointwise computable probability densities by tiling

We present a rejection method based on recursive covering of the probability density function with equal tiles. The concept works for any probability density function that is pointwise computable or representable by tabular data. By the implicit construction of piecewise constant majorizing and minorizing functions that are arbitrarily close to the density function the production of random variates is arbitrarily independent of the computation of the density function and extremely fast. The method works unattended for probability densities with discontinuities (jumps and poles). The setup time is short, marginally independent of the shape of the probability density and linear in table size. Recently formulated requirements to a general and automatic non-uniform random number generator are topped. We give benchmarks together with a similar rejection method and with a transformation method.

cs.MS↗

arXiv2009

Random numbers from the tails of probability distributions using the transformation method

The speed of many one-line transformation methods for the production of, for example, Levy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, is very high and satisfactory for most purposes. However, for the class of decreasing probability densities fast rejection implementations like the Ziggurat by Marsaglia and Tsang promise a significant speed-up if it is possible to complement them with a method that samples the tails of the infinite support. This requires the fast generation of random numbers greater or smaller than a certain value. We present a method to achieve this, and also to generate random numbers within any arbitrary interval. We demonstrate the method showing the properties of the transform maps of the above mentioned distributions as examples of stable and geometric stable random numbers used for the stochastic solution of the space-time fractional diffusion equation.

cs.MS↗

arXiv2009

Stochastic calculus for uncoupled continuous-time random walks

The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Ito integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral and its Ito integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Levy alpha-stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, that generalize the standard diffusion equation solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE, and check it by Monte Carlo.

cond-mat.stat-mech↗

arXiv2008

Fluctuating Interfaces in Liquid Crystals

We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.

cond-mat.soft↗

arXiv2008

Relaxation in statistical many-agent economy models

We review some statistical many-agent models of economic and social systems inspired by microscopic molecular models and discuss their stochastic interpretation. We apply these models to wealth exchange in economics and study how the relaxation process depends on the parameters of the system, in particular on the saving propensities that define and diversify the agent profiles.

physics.soc-ph↗