In Hwan (David) Chung
PhD Student
Ph: +61 2 9514 7756
Fax: +61 2 9514 7711
E-mail: InHwan.Chung@uts.edu.au 

Thesis title: "Speeding up Monte Carlo Simulation in Lognormal LIBOR Market Models"
Supervisors: Dr Erik Schlögl (principal), TBA (co-supervisor)

Summary:

Alternatives to the standard Monte Carlo method are sought to speed up the BGM simulation. Firstly, BGM model is implemented to price a cap under two measures, terminal measure and rolling spot measure, using the standard Monte Carlo simulation. The results are compared to Black’s market formula. To speed up the simulation, next, Quasi Monte Carlo using Sobol’s sequence is introduced. Issues in the construction of Sobol’s sequence are discussed. Several issues on the use of Quasi Monte Carlo are studied. such issues include dimensionality, confidence interval, and cumulative inverse normal function problems. Possible solutions are sought and tested. Solutions comprise the Brownian Bridge construction, random shift method, and Moro approximation. The concept of constructive dimensionality and a naïve approach without this concept are explained and tested. An alternative approach (‘Predictor-Corrector ‘) to discretisation is introduced and tested. Finally, the concept of Impor tance sampling is explained and the results using this approach are exhibited.