This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric muitivariate Markov diffusion process with “stochastic volatility.” the yield of any zero-coupon bond is taken to be a maturity-dependent affine combination of the selected “basis” set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as well as numerical techniques for calculating the prices of term-structure derivative prices. the case of jump diffusions is also considered.

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A yield-factor model of interest rates

In the setting of ‘‘affine’’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

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Transform analysis and asset pricing for affine jump-diffusions

Recursive methods offer a powerful approach in dynamic macroeconomics. This book contains both an introduction to recursive tools, including standard applications such as asset pricing, and advanced material, including analyses of reputational mechanisms and contract design. The tools are presented with enough technical sophistication to get the reader started working on practical problems. When numerical simulations are called for, the book provides suggestions for how to proceed, as well as references for further reading. The applications cover many substantive issues in macroeconomics, such as equilibrium asset prices, market incompleteness, wealth distribution, fiscal-monetary theories of inflation, government debt, optimal labour and capital taxation, time consistency and credible government policies, optimal social insurance, economic growth and labour market dynamics.

Recursive Macroeconomic Theory

Among financial economists, the dominant approach to the study of executive compensation views managers' pay arrangements as a (partial) remedy to the agency problem. Under this approach, which we label the “optimal contracting approach,” boards are assumed to design compensation schemes to provide managers with efficient incentives to maximize shareholder value. Financial economists have done substantial work within this optimal contracting model in an effort to understand executive compensation practices; recent surveys of this work include Murphy (1999) and Core, Guay and Larcker (2001). To some researchers working within the optimal contracting model, the main flaw with existing practices seems to be that, due to political limitations on how generously executives can be treated, compensation schemes are not sufficiently high-powered (Jensen and Murphy, 1990). Another approach to studying executive compensation focuses on a different link between the agency problem and executive compensation. Under this approach, which we label the “managerial power approach,” executive compensation is viewed not only as a potential instrument for addressing the agency problem but also as part of the agency problem itself. As a number of researchers have recognized, some features of pay arrangements seem to reflect managerial rent-seeking rather than the provision of efficient incentives (for example, Blanchard, Lopez-de-Silanes and Shleifer, 1994; Yermack, 1997; and Bertrand and Mullainathan, 2001). We seek to develop a full account of how managerial influence shapes the executive compensation landscape in a forthcoming book (Bebchuk and Fried, 2004) that builds substantially on a long article written jointly with David Walker (Bebchuk, Fried and Walker, 2002).

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Executive Compensation as an Agency Problem

We re-examine the evidence on the relationship between credit spreads and economic activity, by constructing a credit spread index based on an extensive data set of prices of outstanding corporate bonds trading in the secondary market. Compared with the standard default-risk indicators, our credit spread index is a robust predictor of economic activity at both the short- and longer-term horizons. Using an empirical framework, we decompose the index into a predictable component that captures the available firm-specific information on expected defaults and a residual component—the excess bond premium—which we argue likely reflects variation in the price of default risk rather than variation in the risk of default. Our results indicate that the predictive content of credit spreads for economic activity is due primarily to movements in the excess bond premium. Innovations in the excess bond premium that are orthogonal to the current state of the economy are shown to lead to significant declines in economic activity and equity prices. We also show that a deterioration in the creditworthiness of broker-dealers—key financial intermediaries in the corporate cash market—causes an increase in the excess bond premium. These findings support the notion that a rise in the excess bond premium represents a reduction in the e!ective risk-bearing capacity of the financial sector and, as a result, a contraction in the supply of credit with significant adverse consequences for the macroeconomy.

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Credit Spreads and Business Cycle Fluctuations

LOUIS SCOTT is associate professor of finance at the University of Georgia in Athens. model of the term structure of interest necessary for the valuation of bonds and interest rate options; and parameter valestimates, are necessary for the implementation of a specific model. This article presents a method for estimating the parameters of a particular class of continuous-time equilibrium models of the term structure. The theoretical framework for the analysis is the model of Cox, Ingersoll, and Ross [1985a, 1985b1, where a general equilibrium model of asset pricing is used to examine the behavior of the term structure and related issues such as the valuation of interest ratecontingent claims. The Cox, Ingersoll, Ross model, hereafter the CIR model, is a single-factor equilibrium model of the term structure that is consistent with an asset pricing equilibrium, free of arbitrage opportunities, and retains the feature that the interest rate must be non-negative. The one-factor model, however, has the undesirable property that all bond returns are perfectly correlated, and it may not be adequate to characterize the term structure of interest rates and its changing shape over time. The advantage of this one-factor model is the relatively simple closed-form solution for bond prices. As CIR show, the model can be extended to a multifactor setting, with closed-form solutions for bond prices. We follow suggestions in CIR and develop a multifactor equilibrium model of the term structure. The primary objective is to estimate the parameters of the processes that drive interest rate changes and determine the number of factors necessary to characterize the term structure adequately over time. This analysis

Maximum Likelihood Estimation for a Multifactor Equilibrium Model of the Term Structure of Interest Rates

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

With the recent significant growth in the single-name credit default swap (CDS) market has come the need for accurate and computationally efficient models to value these instruments. While the model developed by Duffie, Pan, and Singleton (2000) can be used, the solution is numerical (solving a series of ordinary differential equations) rather than explicit. In this paper, we provide an explicit solution to the valuation of a credit default swap when the interest rate and the hazard rate are correlated by using the “change of measure” approach and solving a bivariate Riccati equation. CDS transaction data for the period 2/15/2000 through 4/8/2003 for 60 firms are used to test both the goodness of fit of the model and provide estimates of the influence of economic variables in the market for credit-risky bonds.

An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors

In a credit default swap (CDS) trade, a credit protection buyer acquires credit protection from the counterparty by paying a premium. The CDS premium has been viewed as a clean representation of the price of credit risk. As a result, in the past few years, researchers have used data on CDS trades where the reference entity is a corporation to determine the liquidity component of corporate bond spreads. Using a transaction dataset, the authors discover very large bid–ask spreads in CDS quotes. With a two-factor model, they show that such large bid–ask spreads can profoundly affect the estimation of credit risk, which in turn has a significant effect on the estimation of the liquidity spread for corporate bonds. Contrary to the literature, the authors show that although the bond and CDS markets appear to have two different values for the credit spread, once liquidity is accounted for they no longer find such a difference.

Corporate Credit Default Swap Liquidity and Its Implicationsfor Corporate Bond Spreads

Using a large data set on credit default swaps, we study how default risk interacts with interest-rate risk and liquidity risk to jointly determine the term structure of credit spreads. We classify the reference companies into two broad industry sectors, two broad credit rating classes, and two liquidity groups. We develop a class of dynamic term structure models that include (i) two benchmark interest-rate factors to capture the libor and swap rates term structure, (ii) two credit-risk factors to capture the credit swap spreads of high-liquidity group of each industry and rating class, and (iii) both an additional credit-risk factor and a liquidity-risk factor to capture the difference between the high- and low-liquidity groups. Estimation shows that companies in different industry and credit rating classes have different credit-risk dynamics. Nevertheless, in all cases, credit risks exhibit intricate dynamic interactions with the interest-rate factors. Interest-rate factors both affect credit spreads simultaneously, and impact subsequent moves in the credit-risk factors. Within each industry and credit rating class, we also find that the average credit default swap spreads for the high-liquidity group are significantly higher than for the low-liquidity group. Estimation shows that the difference is driven by both credit risk and liquidity differences. The low-liquidity group has a lower default arrival rate and also a much heavier discounting induced by the liquidity risk.

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Ren-Raw Chen

Papers

Maximum Likelihood Estimation for a Multifactor Equilibrium Model of the Term Structure of Interest Rates

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors

Corporate Credit Default Swap Liquidity and Its Implicationsfor Corporate Bond Spreads

Dynamic Interactions Between Interest Rate, Credit, and Liquidity Risks: Theory and Evidence from the Term Structure of Credit Default Swap Spreads