*Spring 2023*

This course introduces futures, options and related financial contracts, which are widely used for risk management in the form of traded derivative securities, but also represent features that are found in common corporate securities, not typically thought of as derivatives. The course develops in depth a conceptual and analytical framework for understanding the pricing of these features, as well as strategies for managing risk. Covered topics include the following. Basic risk-management strategies using forward contracts, call and put options. Arbitrage relationship between spot prices and forward prices based on the role of dividends, cost of carry and convenience yields, with applications to securities lending, commodities and foreign exchange. An overview of futures markets: OTC markets versus exchanges, mark-to-market, margins, the role of clearinghouses. Statistical hedging with futures and the notion of basis risk. Introduction to swaps as a natural extension of forwards and futures. Fundamental option-pricing results such as put-call parity (including for hard-to-short stocks), general patterns in the optimal exercise of American options, and how risk and its pricing through options relate to the time horizon. Binomial pricing and hedging. The Black-Scholes model as a high-frequency limit of the binomial model, and associated hedging and market-making techniques. Overview of option pricing applications in corporate and other settings.

**Prerequisites:** Finance I or equivalent, and willingness to engage in analytically challenging reasoning. Students should take the class with a clear understanding that excess returns in liquid financial markets are compensation for risk taking. Strategies using options, futures and related contracts enrich the menu of available risk profiles, but do not bypass the fundamental risk-return trade-off. Since such contracts typically involve leverage, they can be outright dangerous if not thoroughly understood and regarded with maturity. This course is for those looking for a deeper understanding of financial markets, it is *not* suitable for anyone looking for a quick path to riches.

**Optional Recommended Text:** The course materials are self-contained. Those looking for additional explanations, as well as material beyond the scope of this course, should consider *Derivatives Markets,* by Robert L. McDonald, Prentice Hall.

**Grading:** homework (70%), final assignment (30%).

**Homework Groups:** Problem sets should be prepared in groups of up to four people. Only a single solution set per group should be turned in. You do not have to belong to the same group for every problem set. It is also okay to complete homework individually.