Diversification of volatility risk. Applications to hedging barrier options and other exotics. Lecture 4 Analyzing the Volatility Smile . The Breeden-Litzenberger and Dupire theorems. Parametric versus non-parametric fits of the volatility smile.
Volatility smiles arising from stochastic volatility models.
Hamilton-Jacobi Bellman equations for calculating the log of the partition function. Lecture 5 Monte Carlo Simulation in Quantitative Finance . Weighted Monte Carlo. Application to the calibration of stochastic volatility models and multi-smile models. Coding issues and demonstration.