# Module 6: Advanced Numerical Methods (2019-2020)

*Finite differences: HJB equations and multi-dimensional problems

*Calibration of derivative pricing models

*Monte Carlo for SDEs, Euler-Maruyama method, weak and strong convergence; exotic options: continuity corrections for discretely sampled paths for barriers and lookbacks; workshop %; correlation and basket options; variance reduction; workshop;

*Advanced Monte Carlo techniques: Longstaff-Schwartz regression for Bermudan/American options, randomised Quasi-Monte Carlo for more accurate estimation, computing Greeks by bumping, Likelihood Ratio method, and pathwise sensitivities;

*Advanced Financial Data Analysis: The objective of this course is to provide the statistical foundations required for time series analysis and probabilistic forecasting. Participants will receive an introduction to quantitative techniques for analysing, modelling and forecasting time series using real-life examples. The emphasis of this course would be on investigating the following key questions - given a time series, how do we: 1) Analyse the underlying structure (for example, trend, seasonality); 2) Select a suitable time series model/modelling strategy; 3) Estimate the model parameters; 4) Generate point, quantile and density forecasts; 5) Evaluate a time series model using different performance scores and perform error diagnostic checks. This course will have a strong focus on practical data analysis based on time series with different structural patterns.