The counter parties of the swap regularly exchange fixed interest rate payments (coupons) C for periods T 0 < T 1 < ⋯ < T m versus payments linked to floating interest rates, such as Libor or Euribor, for example. A coupon bond is nothing but a linear combination of zero bonds, and its price B( t) at time t is given by B ( t ) = ∑ i = 1, t < T i m C i B ( t, T i ).Īn interest rate swap is another type of highly liquid instrument. Section snippets Primary interest rate related instrumentsĪ coupon bond promises a stream of cash flows (coupons) C 1, … , C m to occur at times T 1, … , T m. Nowadays, a variety of excellent books on the topic are available for further reading we recommend Brigo and Mercurio, 2006, Hunt and Kennedy, 2004, Cairns, 2004, James and Webber, 2000, Rebonato, 1996 and the upcoming comprehensive reference book by Andersen and Piterbarg (2010). Proofs are given only when they are short and support the understanding of the main ideas. Some results are formulated by skipping technical conditions. We tried to make the exposition as compact as possible, keeping all facts that are necessary to follow the central ideas. We conclude with an outlook on further developments. We then concentrate on the mainstream approaches to term structure modelling: Markovian factor and short rate models, the Heath–Jarrow–Morton framework, and, market models. Therefore a primer on arbitrage pricing including the technique of change of numeraire is indispensable. In practice, based on the principles of arbitrage pricing theory, such models are used for pricing and hedging interest rate products. Section 4 focusses on modelling the random evolution of the term structure of interest rates over time. To understand the objectives of term structure modelling, some knowledge of primary interest rate related instruments, such as bonds and swaps, is necessary and is provided together with a discussion of modelling objectives in Section 3. In Section 2 we start by defining what is meant by the term structure of interest rates and discuss some stylized facts. The goal is to provide an entry point into the fascinating and mathematically challenging world of interest rate modelling. No special pre-knowledge of interest rates and interest rate products is required. This survey article targets readers with prerequisites in probability theory and Brownian motion calculus.
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