Numerical Methods (2019-2020)

2019-2020
Lecturer(s): 
Prof. Christoph Reisinger
Course Term: 
Michaelmas
Course Overview: 

This course gives a comprehensive introduction to Monte Carlo and finite difference methods for pricing financial options, and evaluating their sensitivities to various input parameters. At the end of the course, the student should have a thorough understanding of the basic theory behind Monte Carlo and finite difference methods, and be able to implement them for standard applications.

Course Syllabus: 

Lectures 1-8:
Monte Carlo estimation, Central Limit Theorem, confidence intervals; generation of random numbers; variance reduction and the estimation of Greeks; Euler-Maruyama approximation of SDEs.

Lectures 9-16:
Finite differences for the heat equation, explicit Euler time stepping; implementation and numerical experiments; consistency and stability; implicit and Crank-Nicolson schemes; sensitivities; boundary conditions.

Reading List: 

P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer-Verlag, 2004.
K. in 't Hout, Numerical Partial Differential Equations in Finance Explained, Palgrave, 2017.

Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO.