Practical analysis for investment professionals
19 July 2019

Book Review: Bond Pricing and Yield Curve Modeling

Bond Pricing and Yield Curve Modeling: A Structural Approach. 2018. Riccardo Rebonato. Cambridge University Press.

In Bond Pricing and Yield Curve Modeling: A Structural Approach, Riccardo Rebonato, professor of finance at the EDHEC Business School and the EDHEC-Risk Institute, combines theory with current empirical evidence to build a robust understanding of what drives the government bond market. The book provides the theoretical foundations (no-arbitrage, convexity, expectations, and affine modeling) for a treatment of government bond markets, presents and discusses the vast amount of empirical findings that have appeared in the finance literature in the past 10 years, and introduces the “structural” models used by central banks, institutional investors, academics, and practitioners to, among other things, model the yield curve, answer policy questions, gauge market expectations, and assess investment opportunities.

The book is organized into seven parts. Part I presents the foundations of the book, including a reasonable taxonomy that describes four different types of models. Two are statistical and structural no-arbitrage models that Rebonato explores extensively. Statistical models aim to describe how the yield curve moves. They fit observed market yield curves well and have good predictive power but lack a strong theoretical foundation, because they cannot guarantee the absence of arbitrage among the predicted yields. Structural no-arbitrage models make assumptions about how a handful of important driving factors behave, ensure that the no-arbitrage condition is satisfied, and derive how the three components that drive the yield curve (expectations, risk premiums, and convexity) should affect the yield curve shape. The no-arbitrage conditions ensure that the derived price of bonds does not translate into a free lunch. One of the underlying themes the author develops is the attempt to combine the predictive and fitting virtues of statistical models with the theoretical solidity of the no-arbitrage models.

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Part II is devoted to presenting two of the three building blocks of term-structure building: expectations and convexity. Part III introduces the glue that holds the three building blocks together — namely, the conditions of no-arbitrage. With the three building blocks and the conditions of arbitrage fully explained, the author focuses on the Vasicek model in Part IV, providing a simple derivation of its salient results, along with a deeper discussion of its strengths and weaknesses. The Vasicek model explains the evolution of interest rates. A one-factor, short-rate model, it describes interest rate movements as driven by only one source of market risk. Part V returns to the topic of convexity, and Part VI deals with excess returns by presenting the bridge between the real world and the risk-neutral description. Finally, in Part VII, the author discusses a number of models that attempt to overcome the limitations of the simple Vasicek-like models discussed in Parts I–VI.

The author analyzes affine yield curve modeling from a structural perspective and starts by using a simple Vasicek model to build his intuition about the workings of more-complex affine models. Despite the elegance and beauty of the Vasicek model, Rebonato includes a substantial extension of it based on recent empirical data about excess returns and term premiums. He argues that for a model to have predictive ability, it must have a nonconstant market price of risk that is state dependent and must capture the dependence of the expected excess returns on the slope of the yield curve. The author analyzes new models he has built that incorporate this key insight and compares their predictions about term premiums and rate expectations with what has been found empirically in the past decade.

Rebonato finds that after a considerable investment of time and energy, the more-complex structural models predict risk premiums and expectations that are very similar to those produced by purely statistical models. Despite these comparable results, the author explores five reasons structural models can be useful and why relying only on statistical information is unsatisfactory. One reason is that models are enforcers of parsimony: They are useful because they tell us not only what the phenomenon at hand depends on but also which variables it does not depend on. Absent a model, the econometrician is faced with a very large number of state variables, as well as their lags, as potentially “significant regressors.” A model, with its simplified depiction of the workings of the economy, can reinforce some drastic and principled pruning. One of the virtues of a structural model is the ability it affords to reduce the number of parameters that require estimation and to constrain the signs and relative magnitudes of the parameters that remain.

Structural models are also enforcers of cross-sectional restrictions, revealers of forward-looking information, and integrators. The models-as-statistical-regularizers view can be seen as a special case of statistical shrinkage in a direction reflecting prior views. Models that are fitted to today’s yield curve and today’s covariance matrix account for the forward-looking information embedded in the prices of the relevant instruments. Models provide relevant integrated information because prices are expectations of exponential functions of the path of the state variables, while yields are immediately obtainable from prices.

The author makes the strongest argument for why structural models are necessary, however, when explaining that they are “enhancers of understanding.” Structural models afford an understanding of what drives the yield curve that is difficult for a purely statistical analysis to provide. Because statistical information is associative, it does not lend itself to a causal interpretation. The human mind works in a causal mode but often fails when presented with association-based information. The main virtue of models is the power they confer on their users to engage in a critical analysis of what the model may be lacking and how it should be improved.

In Bond Pricing and Yield Curve Modeling: A Structural Approach, Rebonato takes readers on a thought-provoking journey that will elevate their thinking about term-structure modeling. In this journey, they will likely become increasingly familiar and comfortable with some simple mathematical techniques that are new to them.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

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About the Author(s)
Mark K. Bhasin, CFA

Mark K. Bhasin, CFA, is senior vice president of Basis Investment Group, LLC, New York City.

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