8348 - ADVANCED DERIVATIVES

The course is aimed at gaining a more advanced knowledge of financial derivatives with respect to a basic course of derivatives.
The course content is organized as follows.

• The first part focuses on the most popular models for the pricing of equity derivatives, beyond the basic Black-Scholes model. In particular, we focus the attention on stochastic volatility models for the modelling of the volatility surface.
• The second part of the course deals with the analysis, from both a theoretical and an empirical perspective, of the main credit derivatives, including the most recent structured derivatives such as synthetic CDOs and Index Tranches.

In both parts, the theoretical discussion of the most common pricing models are integrated with practical implementation of the models based on empirical data. A brief introduction to hybrid structured products are presented in the last part of the course.

• The limits of the Black-Scholes model for the pricing of equity derivatives. Implied volatility and its empirical features.
• Extensions to the Black and Scholes formulation: stochastic volatility models. A comparison of various volatility models and their impact on the modelling of the volatility surface.
• A brief introduction to volatility / variance derivatives and their pricing techniques.
• Credit derivatives. Single name Credit Default Swaps and their pricing. Structured credit derivatives (synthetic CDOs and index tranches).
• The gaussian copula model and its extensions. Compound and base correlation. Implied default distribution and alternative pricing techniques.
• Introduction to hybrid equity / credit and equity / interest rate derivatives.

Written exam at the end of the course and group assignments.

The course material includes academic papers, slides and other notes that will be made available by the course teachers on the learning space.

For additional reference, we suggest:

• J. Gatheral, The Volatility Surface: A Practitioners Guide, Wiley, 2006;
• P. Schönbucher, Credit Derivatives Pricing Models, Wiley, 2005