Derivative pricing and numerical solving of PDE for finance

    En bref
  • Crédits ECTS : 3
  • Nombre d'heures : 10



  • Hypotheses, derivation and interpretation of Black and Scholes p.d.e. model for pricing European Vanilla options.
  • Extensions of Black and Scholes p.d.e. model to non-vanilla options (Barrier options, Asiatic options …)
  • Finite difference method applied to Black and Scholes p.d.e. model: usual schemes, consistency, stability, explicit versus implicit schemes
  • Stochastic interpretation of Black and Scholes equation, Feynmann-Kac formula.
  • Monte-Carlo method for solving parabolic p.d.e. Basic methods for variance reduction.
  • Labwork devoted to the numerical solution of Black-Scholes pde models by several methods.
  • Introduction to the hedging theory
  • Notions of hedging in continuous time