Probabilistic numerical methods

Additional Info

  • ECTS credits: 6
  • Semester: 3
  • University: University of Nice - Sophia Antipolis
  • Objectives:

     

    Probabilistic numerical methods are widely used in mathematical finance for pricing financial derivatives and computing strategies. The course will present the basic methods used for simulating random variables and implementing the Monte-Carlo method. Simulation of stochastic processes used in mathematical finance, such as Brownian motion and solutions to stochastic differential equations, will be addressed. Several examples of applications to pricing of financial derivatives will be also proposed.

  • Topics:

     

    Sampling methods in finite dimension. Discretization of diffusion processes; strong and weak errors. Monte-Carlo methods for option pricing, variance reduction, control variates method, importance sampling. Monte-Carlo methods in risk management.

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