Description

This course, Advanced Methods in Quantitative Finance, teaches modern methods for measuring market risk and extracting information from derivative prices. It begins with Value-at-Risk (VaR), including its historical, regulatory, and statistical foundations, then develops practical techniques such as delta-gamma approximations, Cornish-Fisher methods, Fourier inversion, and Monte Carlo variance reduction.

The course then moves into high-dimensional portfolio risk, focusing on multivariate volatility and correlation models such as MGARCH, CCC, and DCC. The later chapters study implied volatility, volatility smiles and surfaces, PCA-based volatility dynamics, and smoothing methods. Finally, the materials cover state-price density estimation, showing how option prices can reveal risk-neutral probability distributions and how these can be compared with historical densities for trading and risk-management applications.