NSCPHD1059 Numerical solution of stochastic differential equations with jumps

Volume 2013/2014
Content

The aim of this lecture series is to present various modern numerical methods for stochastic differential equations, including jump diffusions. It develops further mathematical concepts, techniques and intuition necessary for modern modelling of dynamical phenomena such as derivative pricing and risk management in finance. This lecture series provides the foundations for a sufficiently rigorous understanding of advanced numerical methods. Emphasis will be laid on developing skills that allow students to deal with numerical questions related to models involving the simulation of solutions for stochastic differential equations. Questions of numerical stability and convergence will be discussed in detail.

Learning Outcome
  • Knowledge: The student should be familiar with modern numerical methods for stochastic differential equations (including jump diffusions) and with tools necessary for the modelling of dynamical phenomena.
  • Skills: The student should be able to simulate solutions to stochastic differential equations (also with jumps), apply the mathematical theory of the numerical methods for sde's to practical modelling situations and rate concrete numerical methods based on their stability and convergence.
  • Competences: The student should be able to use the mathematical concepts, techniques and intuition developed at the lectures to tailor the numerical methods to other modelling scenarios than those encountered during the course. 
Literature

The course will be based on the 2010 Springer book “Numerical Solution of Stochastic Differential Equations with Jumps in Finance” by Platen and Bruti-Liberati. The chapters covered and a brief description of their content are listed below:

Ch 4: Stochastic Expansions

Presents stochastic Taylor expansions and their application.

Ch 5-8: Scenario Simulation

Introduces strong discrete time approximations for stochastic differential equations for the application in scenario simulation. Jump diffusions are covered.

Ch 11-14: Monte Carlo Simulation


Presents modern techniques for Monte Carlo simulation of stochastic differential equations.

Ch 14: Numerical Stability

The propagation of errors is analysed and stability regions are discussed.

Ch 16: Variance Reduction Techniques

Describes a range of powerful methods that permit significant variance reductions in Monte Carlo simulation.

PhD student in statistics, actuarial science, finance or similar
Lectures & self-study
  • Category
  • Hours
  • Lectures
  • 16
  • Preparation
  • 28
  • Total
  • 44
Credit
1,5 ECTS
Type of assessment
Course participation
Marking scale
passed/not passed
Censorship form
No external censorship