The course provides a broad overview of the fields of derivatives and financial market. It is
divided in three parts. Part I is devoted to the basic knowledge of bonds and stocks and valuation
of forwards and futures.
After that, in Part II, we turn to the problem of option valuation. We first deal with simple
no arbitrage restrictions that can be imposed on the price of European and American call and
put options. These are the slope and convexity restrictions, useful bounds that are model-free.
We then cover in detail the Binomial Option pricing Model. This part of the course is
fundamental in everything that follows. It contains the two main concepts in what concerns
derivatives valuation: the concept of dynamic replication and the principle of risk neutral
valuation. Once the Binomial Option Pricing Model is well understood the transition to the
Black-Scholes Model is rather straightforward. Finally, we dwell in an important empirical flaw
of the Black-Scholes Model, the volatility smile. We study the consequences of this important
empirical regularity for option valuation. We then cover one important applications of option
valuation: the valuation of corporate securities.
Part III, the last part of the course, is devoted to fixed income derivatives valuation. We
study the valuation of swap contracts, the futures on interest rate and then options on interest
rate.