Course Detail

The course provides a broad overview of the field of derivatives. It is divided in three parts. Part I is devoted to the valuation of forwards and futures. After that, in Part II, we turn to the problem of option valuation, which is the heart of the course. 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. We sketch three different ways of deriving the Black-Scholes formula, each providing a different insight into the mechanics of derivative pricing. 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 and address it in the context of Stochastic Volatility models and the implied
binomial tree of Derman and Kani.
We then turn to two important applications of option valuation: Risk management and the valuation of corporate securities. We introduce the concept of the Greeks and apply it to the hedging of option-like payoffs. We discuss here some of the recent developments in markets
for hedging volatility risk. The valuation of corporate securities such as warrants, defaultable debt, convertible securities, and callable convertible bonds is also covered.

Part III, the last part of the course, is devoted to fixed income derivatives valuation. We start with some very important instruments like Treasury Notes futures, eurodollar futures, and fed funds futures. Next we study the valuation of swap contracts: plain vanilla interest rate swaps, foreign currency swaps, and, finally, commodity and equity swaps. We then introduce
the concept of swaption, or the option on the swap.
In order to value options on interest rates, like caps and
oors we need models that are slightly different than the ones covered in Part II. We first cover Black's Model, which is the market standard for the valuation of interest rate caps, oors, collars, and swaptions. If
time permits, we then study the Black-Derman-Toy Model. Black-Derman-Toy belongs to a class of models called no arbitrage models, which are those that are designed to be perfectly consistent with the current term structure of interest rates. We cover the uses of this model for option valuation through an example of the pricing of a swaption. Finally the last lecture is devoted to a fascinating new field, credit derivatives. Here we introduce the basic instruments, such as Credit Default Swaps, TRORS, and Collateralized
Debt Obligations and discuss some of the issues related to their hedging and valuation.