This version: March 15, 2004

The outline of this book is as follows. The first two chapters deal with the most common fixedincome securities, fix much of the notation and terminology, and discuss basic relations between key concepts. The main part of the book discusses models of the evolution of the term structure of interest rates over time. Chapter 3 introduces much of the mathematics needed for developing and analyzing modern dynamic models of interest rates. Chapter 4 reviews some of the important general results on asset pricing. In particular, we define and relate the key concepts of arbitrage, state-price deflators, and risk-neutral probability measures. The connection to market completeness and individual investors’ behavior is also addressed, just as the implications of the general asset pricing theory for the modeling of the term structure are discussed. Chapter 5 applies the general asset pricing tools to explore the economics of the term structure of interest rates. For example we discuss the relation between the term structure of interest rates and macro-economic variables such as aggregate consumption, production, and inflation. We will also review some of the traditional hypotheses on the shape of the yield curve, e.g. the expectation hypotheses. Chapter 6 further develops the consequences of the general asset pricing theory for the modeling of the term structure of interest rates and the pricing of derivatives. Chapters 7 to 12 develop models for the pricing of fixed income securities and the management of interest rate risk. Chapter 7 goes through so-called one-factor models. This type of models was the first to be applied in the literature and dates back at least to 1970. The one-factor models of Vasicek and Cox, Ingersoll, and Ross are still frequently applied both in practice and in academic research. Chapter 8 explores multi-factor models which have several advantages over one-factor models, but are also more complicated to analyze and apply. In Chapter 9 we discuss how one and multi-factor models can be extended to be consistent with current market information, such as bond prices and volatilities. Chapter 10 introduces and analyzes so-called Heath-Jarrow-Morton models, which are characterized by taking the current market term structure of interest rates as given and then modeling the evolution of the entire term structure in an arbitrage-free way. We will explore the relation between these models and the factor models studied in earlier chapters. Yet another class of models is the subject of Chapter 11. These “market models” are designed for the pricing and hedging of specific products that are traded on a large scale in the international markets, namely caps, floors, and swaptions. Chapter 12 discusses how the different interest rate models can be applied for interest rate risk management. The subject of Chapter 13 is how to construct models for the pricing and risk management of mortgage-backed securities. The main concern is how to adjust the models studied in earlier chapters to take the prepayment options involved in mortgages into account. In Chapter 14 (only some references are listed in the current version) we discuss the pricing of corporate bonds and other fixed-income securities where the default risk of the issuer cannot be ignored. Chapter 15 focuses on the consequences that stochastic variations in interest rates have for the valuation of securities with payments that are not directly related to interest rates, such as stock options and currency options. Finally, Chapter 16 (only some references are listed in the current version) describes several numerical techniques that can be applied in cases where explicit pricing and hedging formulas are not available.

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