Numerical Methods in Financial Engineering


Objective

The course focuses on numerical methods for EDPs in finance: pricing methods (numerical calculation of prices and Greeks of derivatives) and model calibration methods

Planning

 

  1. Fourier Transform Pricing Methods.
  2. Tree Pricing Methods – Cox Ross Rubinstein Binomial Tree. Trinomial Tree by Kamrad Ritchken. Case Study: Barrier and Bermuda shorts options.
  3. Finite Difference Pricing Methods – Theta-Schemes in Dimension One Space. ADI method in upper dimension. Case Study: Asian Options, Clicks, Volatility and Variance Swaps.
  4. Calibration Methods – Calibration of non-linear least squares parametric models. Calibration of nonparametric nonlinear regularized least squares models. Case Study: Effective Volatility Extraction.

Références

AVELLANEDA M. and LAURENCE P. (2000) : Quantitative Modeling of Derivative Securities: From Theory to Practice, Chapman & Hall.
CONT R. and TANKOV P. (2003) : Modelling with Jump Processes, Chapman & Hall.
GATHERAL J. (2006) : Volatility Surface: A Practitioner's Guide. Wiley.
KWOK Y.W. (1998) : Mathematical models of financial derivatives, Springer (2nd edition à paraître).
LAMBERTON D. et LAPEYRE B. (1997) : Introduction au Calcul Stochastique Appliquée à la Finance. Editions Eyrolles.