This class offers a broad investigation of derivatives and quantitative methods. It starts with reminders on stochastic processes and Brownian motion. It also covers stochastic integrals, martingales, Ito’s lemma and Girsanov’s theorem. Then, it constructs the Black Scholes framework and discusses arbitrage relationships.
This class relies a lot on numerical methods and explains the mechanics of trees, PDE schemes and Monte Carlo simulations. Other advanced concepts examined are stochastic volatility (with the Heston model derived from one end to the other) and the volatility smile.
Basic interest rate models, such as the Vasicek and CIR models are studied before looking at the Heath-Jarrow-Morton and Brace-Gatarek-Musiela frameworks. Credit intensity and structural models are also studied in this class.