Convergence rate of Markov chains and hybrid numerical schemes to jump-diffusions with application to the Bates model

Autor: Maya Briani, Lucia Caramellino, Giulia Terenzi

Publikováno v: SIAM journal on numerical analysis
(2021).
info:cnr-pdr/source/autori:M. Briani, L. Caramellino, G. Terenzi/titolo:Convergence rate of Markov chains and hybrid numerical schemes to jump-diffusions with application to the Bates model/doi:/rivista:SIAM journal on numerical analysis (Print)/anno:2021/pagina_da:/pagina_a:/intervallo_pagine:/volume

We study the rate of weak convergence of Markov chains to diffusion processes under quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree approximation of the CIR process.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49f284e3e96b5066a72be444f386702a
http://www.cnr.it/prodotto/i/413555

Large deviations of conditioned diffusions and applications

Autor: Paolo Baldi, Maurizia Rossi, Lucia Caramellino

We provide Large Deviation estimates for the bridge of a d -dimensional general diffusion process as the conditioning time tends to 0 and show that these results can be applied to the evaluation of the asymptotics of its exit time probabilities.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b3269c5c6f2afd09835385ab74a70dd
https://hdl.handle.net/2108/214919

Stochastic Integration by Parts and Functional Itô Calculus

Autor: Vlad Bally, Lucia Caramellino, Rama Cont, Frederic Utzet, Josep Vives

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012).The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by

Numerical stability of a hybrid method for pricing options

Autor: Lucia Caramellino, Antonino Zanette, Maya Briani, Giulia Terenzi

Publikováno v: International Journal of Theoretical and Applied Finance
International Journal of Theoretical and Applied Finance, World Scientific Publishing, 2019, pp.1950036. ⟨10.1142/S0219024919500365⟩
International journal of theoretical and applied finance (2019). doi:10.1142/S0219024919500365
info:cnr-pdr/source/autori:Briani M.; Caramellino L.; Terenzi G.; Zanette A./titolo:NUMERICAL STABILITY of A HYBRID METHOD for PRICING OPTIONS/doi:10.1142%2FS0219024919500365/rivista:International journal of theoretical and applied finance/anno:2019/pagina_da:/pagina_a:/intervallo_pagine:/volume
International Journal of Theoretical and Applied Finance, 2019, pp.1950036. ⟨10.1142/S0219024919500365⟩

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::634458c0a35cfaf70f892d04ec0394a2
https://hal.archives-ouvertes.fr/hal-02380723/file/Bates-Hybrid-revised-1.pdf

Total variation distance between stochastic polynomials and invariance principles

Autor: Vlad Bally, Lucia Caramellino

Publikováno v: Annals of Probability
Annals of Probability, Institute of Mathematical Statistics, 2019, 47, pp.3762-3811. ⟨10.1214/19-AOP1346⟩
Ann. Probab. 47, no. 6 (2019), 3762-3811
Annals of Probability, 2019, 47, pp.3762-3811. ⟨10.1214/19-AOP1346⟩

International audience; The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence, one obtains an in-variance principle for such polynomials. This generalizes known results concern

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a987a9f5a257e95e0014b74dd21eed0
https://hal-upec-upem.archives-ouvertes.fr/hal-02429560