Fixed Income Derivatives: Risk Management and Financial Institutions (F)

In the world of today, both public and private institutions rely heavily on bond issuance to raise capital, and fixed income markets have come to play a central role in the global economy. This development has led to a rapid increase in the use of ever more sophisticated derivatives playing a dual role on one hand as means to insure against losses and on the other as tools of risky speculation. Interest rate derivatives have often played a central role in times of financial distress highlighting the need for financial actors to have a solid framework for pricing, hedging and risk management of these instruments.

Throughout this course, students will develop a thorough understanding of how fixed income markets can be modeled and how pricing and hedging of the most commonly traded fixed income derivatives can be performed within these models. Much of the course will be set in continuous time, and we will begin by covering the basics of stochastic calculus including Brownian motion, stochastic differential equations, Ito's formula, etc. This portion of the course will be somewhat technical, however emphasis will be on application of the methods and results we introduce. Once we have laid the mathematical foundation for the course, we will proceed to study dynamic models for the short rate and how the term structure of interest rates evolves in these types of models. As part of our discussion, we will learn how to fit term structure models to market data and how forward rate agreements, interest rate swaps and exchange options can be priced in the context of these models. Next, we will study the pricing, and hedging of more complicated interest rate options such as caps, floors, digital options and swaptions as well as how the “greeks” can be used for hedging and risk management of such contracts. Finally, we will cover more exotic financial derivatives including currency contracts such as FX forwards, FX swaps and cross currency swaps and credit derivatives such as asset swaps and credit default swaps.

The course will be somewhat technical and quantitative in nature, but emphasis will be placed on developing results that have applications in practice. The many methods and tools, we will develop, will be implemented using Python and hence, experience with a scripting language such as Python, Matlab, Julia or R will be helpful. By the end of this course, we will have developed a substantial library in Python containing some of the methods and algorithms most commonly used by financial practitioners.