Browsing by Author "López-Salas, José Germán"
Now showing items 1-19 of 19
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AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models
López-Salas, José Germán; Pérez-Rodríguez, Soledad; Vázquez, Carlos (Society for Industrial and Applied Mathematics (SIAM), 2021-01)[Abstract]: In this work, we mainly develop a new numerical methodology to solve a PDE model recently proposed in the literature for pricing interest rate derivatives. More precisely, we use high-order-in-time AMFR-W-methods, ... -
An efficient implementation of parallel simulated annealing algorithm in GPUs
Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio; López-Salas, José Germán; Vázquez, Carlos (Springer, 2012-09-26)[Abstract]: In this work we propose a highly optimized version of a simulated annealing (SA) algorithm adapted to the more recently developed graphic processor units (GPUs). The programming has been carried out with compute ... -
Analysis and numerical methods for stochastic volatility models in valuation of financial derivatives
López-Salas, José Germán (2016)[Abstract] The main objective of this thesis concerns to the study of the SABR stochastic volatility model for the underlyings (equity or interest rates) in order to price several market derivatives. When dealing with ... -
Boundary Treatment for High-Order IMEX Runge–Kutta Local Discontinuous Galerkin Schemes for Multidimensional Nonlinear Parabolic PDEs
González Taberner, Víctor; López-Salas, José Germán; Castro, M.J.; García Rodríguez, José Antonio (Society for Industrial and Applied Mathematics, 2024)[Abstract]: In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge–Kutta time discretization is used for solving convection-diffusion-reaction problems with ... -
Efficient Calibration and Pricing in LIBOR Market Models with SABR Stochastic Volatility Using GPUs
Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio; López-Salas, José Germán; Vázquez, Carlos (Springer, 2016)[Abstract]: In order to overcome the drawbacks of assuming deterministic volatility coefficients in the standard LIBOR market models, several extensions of LIBOR models to incorporate stochastic volatilities have been ... -
Global optimization for data assimilation in landslide tsunami models
Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio; López-Salas, José Germán; Escalante Sánchez, Cipriano; Castro Díaz, Manuel Jesús (Elsevier, 2020-02-15)[Abstract]: The goal of this article is to make automatic data assimilation for a landslide tsunami model, given by the coupling between a non-hydrostatic multi-layer shallow-water and a Savage-Hutter granular landslide ... -
IMEX-RK Finite Volume Methods for Nonlinear 1d Parabolic PDEs. Application to Option Pricing
López-Salas, José Germán; Suárez Taboada, María; Castro Díaz, Manuel Jesús; Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio (Springer Nature, 2024-06-06)[Abstract]: The goal of this paper is to develop 2nd order Implicit-Explicit Runge-Kutta (IMEX-RK) finite volume (FV) schemes for solving 1d parabolic PDEs for option pricing, with possible nonlinearities in the source and ... -
Mathematical models and numerical methods for a capital valuation adjustment (KVA) problem
Trevisani, Davide; López-Salas, José Germán; Vázquez, Carlos; García Rodríguez, José Antonio (Elsevier B.V., 2025-03)[Abstract]: In this work we rigorously establish mathematical models to obtain the capital valuation adjustment (KVA) as part of the total valuation adjustments (XVAs). For this purpose, we use a semi-replication strategy ... -
Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements
Agarwal, A.; De Marco, S.; Gobet, Emmanuel; López-Salas, José Germán; Noubiagain, F.; Zhou, A. (EDP Science, 2019-04-02)[Abstract]: We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results ... -
PDE formulation of some SABR/LIBOR market models and its numerical solution with a sparse grid combination technique
López-Salas, José Germán; Vázquez, Carlos (Elsevier, 2018-03-01)[Abstract]: SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, ... -
PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)
López-Salas, José Germán; Pérez-Rodríguez, Soledad; Vázquez, Carlos (Elsevier, 2024-09-01)[Abstract]: In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in [1] ... -
Quasi-Regression Monte-Carlo Method for Semi-Linear PDEs and BSDEs
Gobet, Emmanuel; López-Salas, José Germán; Vázquez, Carlos (MDPI AG, 2019-08-06)[Abstract] In this work we design a novel and efficient quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the ... -
Quasi-Regression Monte-Carlo Scheme for Semi-Linear PDEs and BSDEs with Large Scale Parallelization on GPUs
Gobet, Emmanuel; López-Salas, José Germán; Vázquez, Carlos (Springer, 2019-04-04)[Abstract]: In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations, and we analyze the convergence of the ... -
SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives
Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio; López-Salas, José Germán; Vázquez, Carlos (Elsevier, 2014-09-01)[Abstract]: In order to overcome the drawbacks of assuming deterministic volatility coefficients in the standard LIBOR market models to capture volatility smiles and skews in real markets, several extensions of LIBOR models ... -
Second Order Finite Volume IMEX Runge-Kutta Schemes for Two Dimensional Parabolic PDEs in Finance
López-Salas, José Germán; Suárez Taboada, María; Castro Díaz, Manuel Jesús; Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio (Springer Nature, 2024-06-06)[Abstract]: We present a novel and general methodology for building second order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two dimensional financial parabolic PDEs with mixed derivatives. ... -
Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model
López-Salas, José Germán; Vázquez, Carlos (Springer, 2017-09-20)[Abstract]: SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, ... -
Speedup of Calibration and Pricing with SABR Models: From Equities to Interest Rates Derivatives
Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio; López-Salas, José Germán; Vázquez, Carlos (Springer, 2015)[Abstract]: In the more classical models for equities and interest rates evolution, constant volatility is usually assumed. However, in practice the volatilities are not constant in financial markets and different models ... -
Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs
Fernández, J. L.; Ferreiro Ferreiro, Ana María; García Rodríguez, José Antonio; Leitao, Álvaro; López-Salas, José Germán; Vázquez, Carlos (Elsevier, 2013-08)[Abstract]: For the calibration of the parameters in static and dynamic SABR stochastic volatility models, we propose the application of the GPU technology to the Simulated Annealing global optimization algorithm and to ... -
Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs
Gobet, Emmanuel; López-Salas, José Germán; Turkedjiev, Plamen; Vázquez, Carlos (Society for Industrial and Applied Mathematics (SIAM), 2016-06)[Abstract]: In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows ...