B8309 Derivatives Course Description
The course provides a broad overview of the field of derivatives. The course focus is on developing a keen understanding of the basic principles and modelling techniques of applied derivative pricing, as well as the practical use of derivatives for hedging and speculative purposes.
In the first part of the course we consider the valuation of forwards, futures, and swaps (equity, foreign exchange, commodity, and fixed income). Here we introduce the notion of no-arbitrage pricing, but also pay attention to cases where, for one reason or another, no-arbitrage pricing may yield less accurate results (e.g., if there are short-sale constraint). Some students seem to have the impression that equilibrium pricing (as in, e.g., the Capital Asset Pricing Model) and no-arbitrage pricing are two separate concepts. They are not, and we will discuss their relation and how prices might be determined within no-arbitrage bounds.
We will devote quite some time throughout the course discussing the role leverage and margins (performance bonds) may have played in many of the historical derivatives 'mishaps', such as the LTCM debacle and other hedge fund collapses, as well as in the recent financial crisis. These historical episodes are great case studies for understanding the importance of appropriate risk and liquidity management.
The second part of the course is concerned with 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, which we use to value plain vanilla European and American options, as well as exotic optios. This part of the course is fundamental in everything that follows. It contains the two main concepts of 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 on an important empirical flaw ofthe 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 and Jump models.
We will also cover 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. Finally, the use of Value-at-Risk, its potential and pitfalls, is considered for risk management of an options portfolio.
Formerly called Options Markets
Fall 2012 Sections:
