Stochastic Modeling of Path-Dependence

Terças e Quintas de 11:10h às 12:50h (Zoom)
Syllabus

Introduction: Markov process, examples of path dependence: final functional, dynamics and noise (fractional Brownian motion), techniques to compute averages that are path-dependent: Monte Carl and PDE, functional derivatives: Frechét and Gateaux. Malliavin calculus: Malliavin derivative, integration by parts, adjoint operator, Brownian case, Greek computation using Malliavin calculus. Functional Itô Calculus: non-anticipative derivatives, functional Itô formula, applications, adjoint operator, weak path dependence, computation of Greeks using functional Itô calculus.

Bibliography
  • Nualart, David. The Malliavin calculus and related topics. Vol. 1995. Berlin: Springer, 2006. 

  • Dupire, Bruno. "Functional itô calculus." Quantitative Finance 19.5 (2019): 721-729. 

  • Fournié, Eric, et al. "Applications of Malliavin calculus to Monte Carlo methods in finance." Finance and Stochastics 3.4 (1999): 391-412.

  • Jazaerli, Samy, and Yuri F. Saporito. "Functional Itô calculus, path-dependence and the computation of Greeks." Stochastic Processes and their Applications 127.12 (2017): 3997-4028.

Provas e Avisos
  • Aulas começam dia 15/6 e o link do Zoom será enviado aos alunos inscritos.

  • Avaliação: uma prova ao final do curso

  • Data da prova: 2/9

  • A prova será liberadas pelo eclass e os alunos terão 24h até a entrega pelo sistema.