Welcome to the M.O.O.C on interest rate models. I'm Damir Filipovic, and I will be your professor for this course. A component that is common to various financial products and transactions, is the interest rate. Interest is the rent paid for a loan of money over a period of time. Interest exists because an amount of money has a different value at different times. Interest accounts for these value changes. Interest is the time value of money. Interest rates themselves change over time because the economy changes. Future interest rates are as uncertain as the future state of the economy is. Stochastic models for the evolution of interest rates are an important ingredient for financial risk management and the pricing of interest rate products. The volume of such products indeed is huge. The outstanding notional amount is in the order of hundreds of trillions of U.S dollars currently. This course gives you an introduction to stochastic interest rate models. It consists of the 4 parts as shown here. And I will now briefly comment on each part separately. In the first part, I introduce the notion of interest rates and some related basic contracts. A bond is the securitized, that is, tradable form of a loan. There exist coupon paying bonds and zero coupon bonds. The latter, are also called discount bonds. The price of a discount bond is simply the present value of a cash flow, of one unit of currency at some future maturity date. Interest rates and bond prices depend on their maturity. The term structure, is the function that maps the maturity to the corresponding interest rate, or bond price. An important reference rate for many interest rate contracts is The L.I.B.O.R. The London Inter-Bank Offered Rate. It is daily fixed for various currencies and maturities. Loans can also be borrowed over future time intervals at rates that are agreed upon today. These rates are called Forward or Futures rates depending on the type of the agreement. In an interest rate swap, counter parties exchange a stream of fixed rate payments for a stream of floating rate payments. Typically indexed to L.I.B.O.R of a particular maturity. When it comes to managing the interest rate risk of a bond portfolio, Duration and Convexity are the basic tools. We will also review some of the most common market conventions that come along with interest rate market data. In the second part, we will learn how to estimate the term structure for market data. There are 2 types of methods. Exact methods produce term structures that exactly match the market data. This comes at a cost of somewhat irregular shapes of the term structure. Smooth methods penalize irregualar shapes and trade off exactness of fit versus regularity of the term structure. We will also see what Principal Component Analysis tells us about the basic shapes of the term structure. Models for the evolution of the term structure of interest rates build on stochastic calculus. In the third part, I will give a crash course in stochastic calculus. I will introduce Brownian motion, stochastic integration and processes, but without going into mathematical details. The good news is that this will give you the necessary tools to engineer a large variety of stochastic interest rate models. We will then study some of the most prevalent so called, Short rate models, and Heath-Jarrow-Morton models. I will also review the arbitrage pricing theorem from finance. That provides the foundation for pricing financial derivatives. Eventually, we will see how we can use these models to price options on bonds. In the fourth part, we will then apply what we learned to price interest rate derivatives. Specifically, we will focus on the standard derivatives, interest rate futures, caps and floors, and swaptions. We will see and understand the industry standard Black and Bachelier formulas for cap, floor, and swaption prices. And eventually in a case study we will see how to calibrate a stochastic interest rate model to market data.
