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Term-Structure Models: A Graduate Course

Damir Filipović
Publication Date: 
Number of Pages: 
Springer Finance
[Reviewed by
Ita Cirovic Donev
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Term structure models play a significant role in applied financial mathematics. The structure and dynamics of the maturity of a financial asset is a vital variable in basic asset trading and later in risk measurement. The definition of term-structure that the author provides — “a term-structure is a function that relates a certain financial variable or parameter to its maturity” — is quite clear in the sense of general understanding. Observing the function, however, is another matter.

The book is the result of a series of graduate lectures, which can be clearly seen from the text. The table of contents is rather friendly and very inviting. Chapter 1 provides the reader, in just a few pages, the necessary motivation, literature and book overview. I was expecting a bit more, especially as the author does not mention any prerequisite knowledge in finance or economics. Chapter 2 goes directly into the general description of interest rates and related financial contracts, such as swaps, caps, floors, etc. This is also presented very fast; the main points and certain details are discussed, however, which should be enough for the reader to get a general grasp. For readers familiar with these financial contracts, this chapter will provide a very clean mathematical presentation of finance theory.

Next comes a discussion of estimation techniques. Bootstrapping, nonparametric, parametric and PCA methods are presented. Many useful examples are presented with illustrations, which complete the chapter perfectly. A theoretical account of arbitrage theory is given in chapter 4, in which the author also presents diffusion short-rate models and the Heath-Jarrow-Morton (HJM) framework. Very briefly, forwards and futures are presented. Extending the discussion of estimation from chapter three, the author presents an analysis of whether parameterized curve families used for estimating the forward curve are appropriate for arbitrage-free interest rate models. Given the importance of affine processes in term structure modeling as well as in credit risk modeling, a detailed account of the definitions and structure is presented in chapter 10. The book ends with a chapter on credit risk modeling, providing just a general theoretical glimpse of credit risk models.

Term-Structure Models is a theoretical text suitable for a graduate students and practitioners with some background knowledge of financial instruments. Of course graduate level mathematics is a must. Theoretical exercises are provided at the end of each chapter. The book is written in a theorem-proof style; it is structured very well. The writing is clear and to the point.

I would recommend this book as a graduate level text on term-structure models, as well as a reference for anyone dealing with or interested in term-structure models. However, I also do have to point out that the book lacks much of an applied side. It would be much more useful if the author provided more examples, or other means to illustrate the concepts and to connect the students, especially those who lack the real world experience, to the concepts.

Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.

1 Introduction.- 2 Interest Rates and Related Contracts.- 2.1 Zero-Coupon Bonds.- 2.2 Interest Rates.- 2.2.1 Market Example: LIBOR.- 2.2.2 Simple vs. Continuous Compounding.- 2.2.3 Forward vs. Future Rates.- 2.3 Bank Account and Short Rates.- 2.4 Coupon Bonds, Swaps and Yields.- 2.4.1 Fixed Coupon Bonds.- 2.4.2 Floating Rate Notes.- 2.4.3 Interest Rate Swaps.- 2.4.4 Yield and Duration.- 2.5 Market Conventions.- 2.5.1 Day-count Conventions.- 2.5.2 Coupon Bonds.- 2.5.3 Accrued Interest, Clean Price and Dirty Price.- 2.5.4 Yield-to-Maturity.- 2.6 Caps and Floors.- 2.7 Swaptions.- 3 Statistics of the Yield Curve.- 3.1 Principal Component Analysis (PCA).- 3.2 PCA of the Yield Curve.- 3.3 Correlation.- 4 Estimating the Yield Curve.- 4.1 A Bootstrapping Example.- 4.2 General Case.- 4.2.1 Bond Markets.- 4.2.2 Money Markets.- 4.2.3 Problems.- 4.2.4 Parameterized Curve Families.- 5 Arbitrage Theory.- 5.1 Self-Financing Portfolios.- 5.1.1 Financial Market.- 5.1.2 Self-financing Portfolios.- 5.1.3 Numeraires.- 5.2 Arbitrage and Martingale Measures.- 5.2.1 Contingent Claims.- 5.2.2 Arbitrage.- 5.2.3 Martingale Measures.- 5.2.4 Market Price of Risk.- 5.2.5 Admissible Strategies.- 5.2.6 The Fundamental Theorem of Asset Pricing.- 5.3 Hedging and Pricing.- 5.3.1 Attainable Claims.- 5.3.2 Complete Markets.- 5.3.3 Pricing.- 5.3.4 State-price Density.- 6 Short Rate Models.- Generalities.- 6.2 Diffusion Short Rate Models.- 6.2.1 Examples.- 6.3 Inverting the Yield Curve.- 6.4 Affine Term Structures.- 6.5 Some Standard Models.- 6.5.1 Vasicek Model.- 6.5.2 Cox-Ingersoll-Ross Model.- 6.5.3 Dothan Model.- 6.5.4 Ho-Lee Model.- 6.5.5 Hull-White Model.- 7 HJM Methodology.- Forward Curve Movements.- 7.2 Absence of Arbitrage .- 7.3 Short Rate Dynamics.- 7.4 Fubini's Theorem.- 7.5 Explosion of Lognormal Forward Rates.- 8 Forward Measures.- 8.1 T-Bond as Numeraire.- 8.2 An Expectation Hypothesis.- 8.3 Option Pricing in Gaussian HJM Models.- 8.4 Black-Scholes Model with Stochastic Short Rates.- 9 Forwards and Futures.- 9.1 Forward Contracts.- 9.2 Futures Contracts.- 9.3 Interest Rate Futures.- 9.4 Forward vs. Futures in a Gaussian Setup.- 10 Consistent Term Structure Parameterizations.- 10.1 No-Arbitrage Condition.- 10.2 Affine Term Structures.- 10.3 Polynomial Term Structures.- 10.4 Exponential-Polynomial Families.- 10.4.1 Nelson{Siegel Family.- 10.2 Svensson Family.- 11 Affine Processes.- 11.1 Option Pricing in Affine Models.- 11.1.1 Vasicek Model.- 11.1.2 Cox-Ingersoll-Ross Model.- 12 Market Models.- 12.1 Models of Forward LIBOR Rates.- 12.1.1 Discrete-tenor Case.- 12.1.2 Continuous-tenor Case.- 13 Default Risk.- 13.1 Transition and Default Probabilities.- 13.1.1 Historical Method.- 13.1.2 Structural Approach.- 13.2 Intensity Based Method.- 13.2.1 Construction of Intensity Based Models.- 13.2.2 Computation of Default Probabilities.- 13.2.3 Pricing Default Risk.- 13.2.4 Measure Change