arXiv subjects

Josep Vives

Publications and source records attributed to Josep Vives.

15 recordsLinked to original sources

arXiv2026

Topological analysis of hemodynamic response to cardiac resynchronization therapy

Objective: The Mapper algorithm is a qualitative method in topological data analysis that constructs graphs from point clouds by combining dimensionality reduction and clustering techniques. The aim of this study is to apply Mapper, together with novel quantitative indices, to compare the effects of biventricular pacing from the left ventricular epicardium versus the endocardium in a swine model of pacing-induced non-ischemic cardiomyopathy. Methods: The distributions of four hemodynamic variables from a previous study on endocardial and epicardial cardiac resynchronization in an experimental swine model of nonischemic cardiomyopathy were analyzed using the Mapper algorithm, enhanced with numerical indices quantifying self-connectivity, scattering, and homogeneity of the resulting colored graphs. Results: Statistically significant differences were observed between pacing from basal regions versus mid or apical regions, with the following self-connectivity index values: basal $0.57$; mid $0.14$ ($p < 0.01$); apical $0.24$ ($p < 0.01$). Endocardial stimulation at lateral sites increased the contrast between the distributions of basal versus mid or apical data, when compared with epicardial stimulation. Conclusions: Topological analysis using the Mapper algorithm, enhanced with quantitative statistical measures, revealed new and biologically plausible significant differences in pacing effects across heart regions.

q-bio.QM↗

arXiv2025

Volatility Modeling with Rough Paths: A Signature-Based Alternative to Classical Expansions

We study two complementary methodologies for calibrating implied volatility surfaces: analytical approximations and data-driven models based on rough path theory. On the analytical side, we revisit a second-order asymptotic expansion for the Heston model, and we propose a new, VIX-based calibration scheme for the rough Bergomi model. Both methods yield highly accurate and computationally efficient calibration formulas when the underlying dynamics are well specified. In parallel, we develop a signature-based approach in which volatility is represented as a linear functional of the truncated signature of a primary stochastic process, providing a flexible and model-agnostic alternative. Our numerical experiments compare the two approaches across both Markovian and non-Markovian settings. In the Heston case, signature-based models achieve a level of accuracy comparable to analytical expansions. In the rough Bergomi setting, using a fractional Brownian motion as the primary process, the signature approach continues to perform strongly and in some cases improves upon the Markovian specification, reflecting its ability to capture more complex temporal dependencies. Overall, the results illustrate that analytical methods are highly effective when the model is correctly specified, while signature-based methods offer a robust and flexible framework for calibration across a wider range of volatility dynamics.

q-fin.MF↗

arXiv2025

Short-time behavior of the At-The-Money implied volatility for the jump-diffusion stochastic volatility Bachelier model

In this paper we use Malliavin Calculus techniques in order to obtain expressions for the short-time behavior of the at-the-money implied volatility (ATM-IV) level and skew for a jump-diffusion stock price. The diffusion part is assumed to be the stochastic volatility Bachelier model and the jumps are modeled by a pure-jump L\'evy process with drift so that the stock price is a martingale. Regarding the level, we show that the short-time behavior of the ATM-IV level is the same for all pure-jump L\'evy processes and, regarding the skew, we give conditions on the law of the jumps for the skew to exist. We also give several numerical examples of stochastic volatilities and L\'evy processes that confirm the theoretical results found in the paper.

q-fin.MF↗

arXiv2023

Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach

Using Malliavin calculus techniques, we obtain formulas for computing Greeks under different rough Volterra stochastic volatility models. Due to the fact that underlying prices are not always square integrable, we extend the classical integration by parts formula to integrable but not necessarily square integrable functionals. First of all, we obtain formulas for general stochastic volatility (SV) models, concretely the Greeks Delta, Gamma, Rho, Vega and we introduce the Greek with respect to the roughness parameter. Then, the particular case of rough Volterra SV models is analyzed. Finally, three examples are treated in detail: the family of alpha-RFSV models, that includes rough versions of SABR and Bergomi models, a mixed alpha-RFSV model with two different Hurst parameters representing short (roughness) and long memory, and the rough Stein-Stein model. For different models and Greeks we show a numerical convergence of our formulas in Monte Carlo simulations and depict for example a dependence of the Greeks on the roughness parameter.

q-fin.MF↗

arXiv2023

Neural SDEs for Conditional Time Series Generation and the Signature-Wasserstein-1 metric

(Conditional) Generative Adversarial Networks (GANs) have found great success in recent years, due to their ability to approximate (conditional) distributions over extremely high dimensional spaces. However, they are highly unstable and computationally expensive to train, especially in the time series setting. Recently, it has been proposed the use of a key object in rough path theory, called the signature of a path, which is able to convert the min-max formulation given by the (conditional) GAN framework into a classical minimization problem. However, this method is extremely expensive in terms of memory cost, sometimes even becoming prohibitive. To overcome this, we propose the use of \textit{Conditional Neural Stochastic Differential Equations}, which have a constant memory cost as a function of depth, being more memory efficient than traditional deep learning architectures. We empirically test that this proposed model is more efficient than other classical approaches, both in terms of memory cost and computational time, and that it usually outperforms them in terms of performance.

stat.ML↗

arXiv2019

Decomposition formula for rough Volterra stochastic volatility models

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple non-linear financial derivatives as vanilla European options are typically priced by means of Monte-Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility -- a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models with rough fractional volatility and we derive an explicit semi-closed approximation formula. Numerical properties of the approximation for a popular model -- the rBergomi model -- are studied and we propose a hybrid calibration scheme which combines the approximation formula alongside MC simulations. This scheme can significantly speed up the calibration to financial markets as illustrated on a set of AAPL options.

q-fin.PR↗

arXiv2019

Decomposition formula for jump diffusion models

In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston (1993) SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models - models utilizing a variance process postulated by Heston (1993). In particular, we inspect in detail the approximation formula for the Bates (1996) model with log-normal jump sizes and we provide a numerical comparison with the industry standard - Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behaviour under a specific SVJ model.

q-fin.PR↗

arXiv2019

Higher order approximation of call option prices under stochastic volatility models

In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Alòs, Gatheral and Radoičić. We use the new decomposition to obtain various approximations to the call price in the Heston model with sharper estimates of the error term than in the previously known approximations. One of the formulas obtained in the present paper has five significant terms and an error estimate of the form $O(ν^{3}(\left|ρ\right|+ν))$, where $ν$ is the vol-vol parameter, and $ρ$ is the correlation coefficient between the price and the volatility in the Heston model. Another approximation formula contains seven more terms and the error estimate is of the form $O(ν^4(1+|ρ|)$. For the uncorrelated Hestom model ($ρ=0$), we obtain a formula with four significant terms and an error estimate $O(ν^6)$. Numerical experiments show that the new approximations to the call price perform especially well in the high volatility mode.

q-fin.CP↗

arXiv2016

A Malliavin-Skorohod calculus in $L^0$ and $L^1$ for additive and Volterra-type processes

In this paper we develop a Malliavin-Skorohod type calculus for additive processes in the $L^0$ and $L^1$ settings, extending the probabilistic interpretation of the Malliavin-Skorohod operators to this context. We prove calculus rules and obtain a generalization of the Clark-Hausmann-Ocone formula for random variables in $L^1$. Our theory is then applied to extend the stochastic integration with respect to volatility modulated Lévy-driven Volterra processes recently introduced in the literature. Our work yields to substantially weaker conditions that permit to cover integration with respect, e.g. to Volterra processes driven by $α$-stable processes with $α< 2$. The presentation focuses on jump type processes.

math.PR↗

arXiv2015

About the decomposition of pricing formulas under stochastic volatility models

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Alòs in [2] for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used are non anticipative. In particular, we see also that equivalent results can be obtained using Functional Itô Calculus. Using the same generalizing ideas we also extend to non exponential models the alternative call option price decompostion formula obtained in [1] and [3] written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both, the anticipative and the non anticipative case.

q-fin.MF↗

arXiv2014

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-diffusion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

q-fin.PR↗

arXiv2012

Local Malliavin Calculus for Lévy Processes and Applications

In this paper a Malliavin calculus for Lévy processes based on a family of true derivative operators is developed. The starting point is an extension to Lévy processes of the pioneering paper by Carlen and Pardoux [8] for the Poisson process, and our approach includes also the classical Malliavin derivative for Gaussian processes. We obtain a sufficient condition for the absolute continuity of functionals of the Lévy process. As an application, we analyze the absolute continuity of the law of the solution of some stochastic differential equations.

math.PR↗

arXiv2012

Anticipating Linear Stochastic Differential Equations Driven by a Lévy Process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformation on Wiener space and developped by Buckdahn to the canonical Lévy space.

math.PR↗

arXiv2010

Two-sided estimates for stock price distribution densities in jump-diffusion models

We consider uncorrelated Stein-Stein, Heston, and Hull-White models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Similar perturbations of the Black-Scholes model were studied by S. Kou. For perturbed stochastic volatility models, we obtain two-sided estimates for the stock price distribution density and compare the tail behavior of this density before and after perturbation. It is shown that if the value of the parameter, characterizing the right tail of the double exponential law, is small, then the stock price density in the perturbed model decays slower than the density in the original model. On the other hand, if the value of this parameter is large, then there are no significant changes in the behavior of the stock price distribution density.

q-fin.GN↗

arXiv2008

An anticipating Itô formula for Lévy processes

In this paper, we use the Malliavin calculus techniques to obtain an anticipative version of the change of variable formula for Lévy processes. Here the coefficients are in the domain of the anihilation (gradient) operator in the "future sense", which includes the family of all adapted and square-integrable processes. This domain was introduced on the Wiener space by Alòs and Nualart.

math.PR↗