Introduction to derivative products - 4MMIPD4

Goal(s)

The goal of this course is to present the concepts of pricing and hedging products in continuous time. At the end of the lecture, students will know how to handle vanilla options in the one dimensional Black Scholes model.

Content(s)

• Stochastic processes and Brownian motion
  • Gaussian vectors
  • Continuous time stochastic processes
  • Brownian motion : definition and first properties

• Continuous time martingales
  • Filtrations and stopping times
  • Martingales : stopping time theorem, applications to Brownian motion, strong Markov property

• Stochastic integral and Itô formula
  • Wiener's integral
  • Itô's integral
  • Itô's formula
  • Applications of Itô's formula : representing the Brownian martingales and the Cameron Martin theorem
  • Stochastic differential equations
    

• The Black Scholes model
  • The underlying asset
  • Replicating strategies
  • Pricing and hedging options