This course introduces students to the basic concepts used in quantitative finance, which forms the basis for many applications such as derivatives pricing, financial engineering and asset pricing. Anyone interested in these areas will have to acquire a good grasp of the topics in this course. We will cover: the analysis of complete and incomplete markets in discrete and continuous time models; the discussion and extension of the assumptions of the Black-Scholes-Merton equation and the introduction of common numerical techniques that are widely applied in practice (along with practical lab sessions with real data); the introduction of structured finance products, their use in risk management and valuation techniques, most notably for mortgage-backed securities, credit default swaps and collateralized debt obligations.
Students require an adequate knowledge of mathematics, particularly in matrix algebra and analysis along with stochastic processes and stochastic calculus to follow this course. Appropriate readings to refresh your knowledge are given on request.
Outline:
Part I – Pricing Models
- Hedging of securities;
- No-arbitrage pricing;
- Pricing in multi-period models (Binomial Model);
- Pricing in continuous time (Black-Scholes-Merton Model)
Part II - Numerical techniques
- Beyond Black-Scholes-Merton Model;
- Binomial lattices;
- Monte-Carlo simulation;
- Finite differences
Part III – Structured Finance
- Mortgage-backed securities;
- Modeling and pricing corporate default;
- Credit Default Swaps;
- Designing CDOs and exotic CDOs
Prerequisites: Stochastic Processes and Stochastic Calculus