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Preface
This book provides an introduction to the markets for fixed-income securities and the models
and methods that are used to analyze such securities.The class of fixed-income securities covers
securities where the issuer promises one or several fixed, predetermined payments at given points
in time. This is the case for standard deposit arrangements and bonds. However, several related
securities with payments that are tied to the development in some particular index, interest rate,
or asset price are typically also termed fixed-income securities. In the broadest sense of the term,
the many di erent interest rate and bond derivatives are also considered xed-income products.
Maybe a more descriptive term for this broad class of securities is \interest rate securities", since
the values of these nancial contracts are derived from current interest rates and expectations and
uncertainty about future interest rates. The key concept in the analysis of xed-income securities
is the term structure of interest rates, which is loosely de ned as the dependence between interest
rates and maturities.
The outline of this book is as follows. The rst two chapters deal with the most common xedincome
securities, x 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. In Chapters 4 and 5 we review some of the
important general results on asset pricing. In particular, we de ne and relate the key concepts of
arbitrage, state-price de
ators, 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 6 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 in
ation. We will also review some of the traditional hypotheses on the shape of the yield curve, e.g. the expectation hypotheses.
Chapters 7 to 12 develops models for the pricing of xed income securities and the management
of interest rate risk. Chapter 7 goes through so-called one-factor models. This type of models was
the rst 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 oneand
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. Chapter 12 discusses how the different interest rate models can be applied for interest rate risk management.
The subject of Chapter 13 (only some references are listed in the current version) 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 which
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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