Numerical Methods in Financial Engineering


Objective

This course covers numerical methods for PDEs in finance: pricing methods (numerical calculation of derivative prices and Greeks) and model calibration.

Planning

  1. Pricing methods using Fourier transforms.
  2. Tree-based pricing methods –The Cox-Ross-Rubinstein binomial tree. The Kamrad-Ritchken trinomial tree. Case study: barrier and Bermuda options.
  3. Finite difference methods forpricing –Theta-schemes in dimension one of space. ADI methods in higher dimensions. Case study: Asian options, cliquet options, volatility and variance swaps.
  4. Calibration methods –Calibration of parametric models by non-linear least squares. Calibration of non-parametric models by regularised non-linear least squares. Case study: Extraction of effective volatility.

Références

S. CREPEY, Financial Modeling (Springer, 2013), chapters 5 à 9.
+ Articles de recherché qui seront fournis lors des TDs