Advanced Monte Carlo Methods (2019-2020)

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

This course covers some advanced Monte Carlo methods, such as quasi Monte Carlo, regression-based methods for early exercise options, and multi-level Monte Carlo simulation. At the end of the course, the student should have a thorough understanding of the theory behind more advanced Monte Carlo methods, be able to implement them for a range of applications, and have an appreciation of some of the current research areas.

Course Syllabus: 

Milstein approximation of SDEs; weak and strong convergence and numerical analysis; low-discrepancy sequences, quasi-Monte Carlo with Brownian Bridge and PCA constructions; multi-level approach; Longstaff-Schwarz method for Bermudan and American options.

Reading List: 

P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer-Verlag, 2004.
P.E Kloeden, E Platen Numerical Solutions of Stochastic Differential Equations, Springer Verlag, 1992.
S. Asmussen, P. Glynn, Stochastic Simulation: Algorithms and Analysis, Springer, 2007 (or 2010).

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