The course provides a broad overview of the field of derivatives. First, 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 is likely to yield less accurate results (e.g., if there are short-sale constraint).
After that, 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. 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
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 is considered for risk management of an options portfolio.
Lars Lochstoer was a Columbia Business School faculty member from 2008 to 2016.