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Derivative pricing and numerical solving of PDE for finance

Presentation

Program:

  • 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.

Objectives

At the end of this module, the student should know the main p.d.e.-based models for derivative pricing and as well the numerical methods (finite difference, Monte-Carlo) that are used to solve these models.

 

The student will be able to:

  • derive a p.d.e model for pricing a derivative,
  • solve this p.d.e. model by using either a finite difference method or a Monte-Carlo method,
  • program each of this method in MATLAB or VBA. 

Needed prerequisite

Basis of stochastic calculus (Brownian motion, Ito integral, Ito formula)

Basis of Financial mathematics

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...