I survey and assess the development of continuous‐time methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. During the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance. This latter subperiod has seen significant progress in econometric theory, computational and estimation methods to test and implement continuous‐time models. Capital market frictions and bargaining issues are being increasingly incorporated in continuous‐time theory.

Interest rate swap pricing theory traditionally views swaps as a portfolio of forward contracts with net swap payments discounted at LIBOR rates. In practice, the use of marking‐to‐market and collateralization questions this view as they introduce intermediate cash flows and alter credit characteristics. We provide a swap valuation theory under marking‐to‐market and costly collateral and examine the theory's empirical implications. We find evidence consistent with costly collateral using two different approaches; the first uses single‐factor models and Eurodollar futures prices, and the second uses a formal term structure model and Treasury/swap data.

The 3e of this well-respected textbook continues the tradition of providing clear and concise explanations for fixed income securities, pricing, and markets. The book matches well with fixed income securities courses. The book's organization emphasizes institutions in the first part, analytics in the second, selected segments of fixed income markets in the third, and fixed income derivatives in the fourth. This enables instructors to customize the material to suit their course structure and the mathematical ability of their students. In this title, new material on Credit Default Swaps, Collateralized Debt Obligations, and an integrated discussion of the Credit Crisis have been added. Online Resources for instructors on password protected website provides worked out examples for each chapter. A detailed description of all key financial terms is provided in a glossary at the back of the book.

The 30‐year U.S. swap spreads have been negative since September 2008. We offer a novel explanation for this persistent anomaly. Through an illustrative model, we show that underfunded pension plans optimally use swaps for duration hedging. Combined with dealer banks' balance sheet constraints, this demand can drive swap spreads to become negative. Empirically, we construct a measure of the aggregate funding status of defined benefit pension plans and show that this measure helps explain 30‐year swap spreads. We find a similar link between pension funds' underfunding and swap spreads for two other regions.

Contingent capital (CC), which aims to internalize the costs of too‐big‐to‐fail in the capital structure of large banks, has been under intense debate by policy makers and academics. We show that CC with a market trigger, in which direct stakeholders are unable to choose optimal conversion policies, does not lead to a unique competitive equilibrium unless value transfer at conversion is not expected ex ante. The “no value transfer” restriction precludes penalizing bank managers for taking excessive risk. Multiplicity or absence of equilibrium introduces the potential for price uncertainty, market manipulation, inefficient capital allocation, and frequent conversion errors.

Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates. It is shown that the pricing errors caused by ignoring the location of the interest rate (relative to its long-run mean) range from −5% to 7%, when the current rate is ±200 basis points from its long-run value. The role of interest rate expectations is, therefore, crucial to the valuation. Optimal exercise policies are found from numerical methods for both models.

Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates. It is shown that the pricing errors caused by ignoring the location of the interest rate (relative to its long‐run mean) range from −5% to 7%, when the current rate is ±200 basis points from its long‐run value. The role of interest rate expectations is, therefore, crucial to the valuation. Optimal exercise policies are found from numerical methods for both models.

Explicit presence of reorganization in addition to liquidation leads to conflicts of interest between borrowers and lenders. In the first–best outcome, reorganization adds value to both parties via higher debt capacity, lower credit spreads, and improved overall firm value. If control of the ex ante reorganization timing and the ex post decision to liquidate is given to borrowers, most of the benefits are appropriated by borrowers ex post. Lenders can restore the first–best outcome by seizing this control or by the ex post transfer of control rights. Reorganization is more likely and liquidation is less likely relative to the benchmark case with liquidation only.