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Abstract:
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 intensityy-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 amplitude as well as jump timing.

Abstract:
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 hightlights 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.

Abstract:
This paper characterizes, interprets, and tests the over-identifying restrictions imposed in affine models of the term" structure. Letting r(t) = e Y(t), where Y is an unobserved vector affine process, our analysis proceeds in three steps. First, we show that affine models can be categorized according to the different over-identifying restrictions they impose on (i) e, and (ii) the parameters of the diffusion matrices. Second, this formulation is shown to be equivalent to a model in which there is a terraced drift structure with one of the state variables being the stochastic long-run mean of r. This equivalence allows direct comparisons of the substantive restrictions on the dynamics of interest rates imposed in CIR-style models and models in which the state variables are the stochastic long-run mean and volatility of r. Third, we compute simulated method of moments estimates of a three-factor affine term structure model, and test the over-identifying restrictions on the joint distribution of long- and short-term interest rates implied by extant affine models of r. We find allowing for correlated factors is key to simultaneously describing the short and long ends of the yield curve. This finding is interpreted in terms of the properties of the risk factors underlying term structure movements.

Abstract:
In this paper, we explore the features of affine term structure models that are empirically important for explaining the joint distribution of yields on short- and long-term interest rate swaps. We begin by showing that the family of N-factor affine models can be classified into N+1 non-nested sub-families of models. For each sub-family, we derive a maximal model with the property that every admissible member of this family is equivalent to or a nested special case of our maximal model. Second, using our classification scheme and maximal models, we show that many of the three-factor models in the literature impose potentially strong over-identifying restrictions on the joint distribution of short- and long-term rates. Third, we compute simulated-method-of-moments estimates for several members of one of the four branches of three-factor models, and test the over-identifying restrictions implied by these models. We conclude that many of the extant affine models in the literature fail to describe important features of the distribution of long- and short-term rates. The source of the model misspecification is shown to be overly strong restrictions on the correlations among the state variables. Relaxing these restrictions leads to a model that passes several goodness-of-fit tests over our sample period.

Abstract:
We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios.

Abstract:
We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios.

Abstract:
Though linear projections of returns on the slope of the yield curve have contradicted the implications of the traditional "expectations theory," we show that these findings are not puzzling relative to a large class of richer dynamic term structure models. Specifically, we are able to match all of the key empirical findings reported by Fama and Bliss and Campbell and Shiller, among others, within large subclasses of affine and quadratic-Gaussian term structure models. Key to this matching are parameterizations of the market prices of risk that let us separately "control" the shape of the mean yield curve and the correlation structure of excess returns with the slope of the yield curve. The risk premiums have a simple form consistent with Fama's findings on the predictability of forward rates, and are shown to also be consistent with interest rate, feedback rules used by a monetary authority in setting monetary policy.

Abstract:
We study the quantitative properties of a dynamic general equilibrium model in which agents face both idiosyncratic and aggregate income risk, state-dependent borrowing constraints that bind in some but not all periods and markets are incomplete. Optimal individual consumption-savings plans and equilibrium asset prices are computed under various assumptions about income uncertainty. Then we investigate whether our general equilibrium model with incomplete markets replicates two empirical observations: the high correlation between individual consumption and individual income, and the equity premium puzzle. We find that, when the driving processes are calibrated according to the data from wage income in different sectors of the U.S. economy, the results move in the direction of explaining these observations, but the model falls short of explaining the observed correlations quantitatively. If the incomes of agents are assumed independent of each other, the observations can be explained quantitatively.

Abstract:
This paper develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete-time counter-parts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Moreover, we allow the market price of risk, linking the risk-neutral and historical distributions of X, to depend generally on the state Xt. The conditional likelihood functions for coupon bond yields for the resulting nonlinear models under the historical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift significantly improves the models statistical fit as well as its out-of-sample forecasting performance.

Nonlinear, Discrete time, Dynamic Term Structure Models, Esscher Transform, Generalized Market Prices of Risks

Abstract:
This chapter surveys the literature on fixed-income pricing models, including dynamic term structure models (DTSMs) and interest rate sensitive, derivative pricing models. This literature is vast with both the academic and practitioner communities having proposed a wide variety of models and model-selection criteria. Central to all pricing models, implicitly or explicitly, are: (i) the identity of the state vector: whether it is latent or observable and, in the latter case, which observable series; (ii) the law of motion (conditional distribution) of the state vector under the pricing measure; and (iii) the functional dependence of the short-term interest rate on this state vector. A primary objective, then, of research on fixed-income pricing has been the selection of these ingredients to capture relevant features of history, given the objectives of the modeler, while maintaining tractability, given available data and computational algorithms. Accordingly, we overview alternative conceptual approaches to fixed-income pricing, highlighting some of the tradeoffs that have emerged in the literature between the complexity of the probability model for the state, data availability, the pricing objective, and the tractability of the resulting model.

Abstract:
This chapter surveys the literature on fixed-income pricing models, including dynamic term structure models (DTSMs) and interest rate sensitive, derivative pricing models. This literature is vast with both the academic and practitioner communities having proposed a wide variety of models and model-selection criteria. Central to all pricing models, implicitly or explicitly, are: (i) the identity of the state vector: whether it is latent or observable and, in the latter case, which observable series; (ii) the law of motion (conditional distribution) of the state vector under the pricing measure; and (iii) the functional dependence of the short-term interest rate on this state vector. A primary objective, then, of research on fixed-income pricing has been the selection of these ingredients to capture relevant features of history, given the objectives of the modeler, while maintaining tractability, given available data and computational algorithms. Accordingly, we overview alternative conceptual approaches to fixed-income pricing, highlighting some of the tradeoffs that have emerged in the literature between the complexity of the probability model for the state, data availability, the pricing objective, and the tractability of the resulting model.

Abstract:
This chapter surveys the literature on fixed-income pricing models, includ- ing dynamic term structure models (DTSMs) and interest rate sensitive, derivative pricing models. This literature is vast with both the academic and practitioner communities having proposed a wide variety of models and model-selection criteria. Central to all pricing models, implicitly or explic- itly, are: (i) the identity of the state vector: whether it is latent or observable and, in the latter case, which observable series; (ii) the law of motion (con- ditional distribution) of the state vector under the pricing measure; and (iii) the functional dependence of the short-term interest rate on this state vector. A primary objective, then, of research on fixed-income pricing has been the selection of these ingredients to capture relevant features of history, given the objectives of the modeler, while maintaining tractability, given available data and computational algorithms. Accordingly, we overview alternative concep- tual approaches to fixed-income pricing, highlighting some of the tradeoffs that have emerged in the literature between the complexity of the proba- bility model for the state, data availability, the pricing objective, and the tractability of the resulting model.

Abstract:
We study the nature of sovereign credit risk using an extensive sample of CDS spreads for 26 developed and emerging-market countries. Sovereign credit spreads are surprisingly highly correlated, with just three principal components accounting for more than 50 percent of their variation. Sovereign credit spreads are generally more related to the U.S. stock and high-yield bond markets, global risk premia, and capital flows than they are to their own local economic measures. We find that the excess returns from investing in sovereign credit are largely compensation for bearing global risk, and that there is little or no country-specific credit risk premium. A significant amount of the variation in sovereign credit returns can be forecast using U.S. equity, volatility, and bond market risk premia.

Abstract:
Though linear projections of returns on the slope of the yield curve have contradicted the implications of the 'traditional expectations theory,' we show that these findings are not puzzling relative to a large class of richer dynamic term structure models. Specifically, we are able to match all of the key empirical findings reported by Fama and Bliss and Campbell and Shiller, among others, within large subclasses of affine and quadratic-Gaussian term structure models. Additionally, we show that certain 'risk-premium adjusted' projections of changes in yields on the slope of the yield curve recover the coefficients of unity predicted by the models. Key to this matching are parameterizations of the market prices of risk that let the risk factors affect the market prices of risk directly, and not only through the factor volatilities. The risk premiums have a simple form consistent with Fama's findings on the predictability of forward rates, and are shown to also be consistent with interest rate, feedback rules used by a monetary authority in setting monetary policy.

Abstract:
This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in which the risk factors follow diffusions, jump-diffusion, or have switching regimes." Then the goodness-of-fits of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixed-income derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads.

Abstract:
This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by over viewing the dynamic term structure models that have been fit to treasury or swap yield curves and in whichthe risk factors follow diffusions, jump-diffusion, or have \switching regimes." Then the goodness-of- ts of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixed-income derivatives. For thecase of defaultable securities we explore the relative ts to historical yield spreads.

Abstract:
This paper shows that, within any Gaussian dynamic term structure model (GDTSM), the historical distribution of the pricing factors P is invariant to the imposition of no-arbitrage restrictions, as well as to additional constraints that impinge only on the risk-neutral dynamics of P. It follows that, in these settings, GDTSM-implied forecasts of future values of P are identical to those from an unrestricted vector autoregressive model of P. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We also extend our analysis to GDTSMs with reduced-rank risk premiums and to those with macroeconomic variables as pricing factors. Empirical estimates and out-of-sample forecasting results are presented for several GDTSMs using data on U.S. Treasury bond yields.

Dynamic term structure model, gaussian, estimation

Abstract:
This paper develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete-time counter parts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Moreover, we allow the market price of risk ¤t, linking the risk-neutral and historical distributions of X, to depend generally on the state Xt. The conditionallikelihood functions for coupon bond yields for the resulting nonlinear models under thehistorical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift significantly improves the models statistical fit as well as its out-of-sampleforecasting performance.

Abstract:
We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differentialacross different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios.

Abstract:
Though linear projections of returns on the slope of the yield curve have contradicted the implications of the traditional "expectations theory," we show that these findings are not puzzling relative to a large class of richer dynamic terms structure models. Specifically, we are able to match all of the key empirical findings reported by Fama and Bliss and Campbell and Shiller, among others, within large subclasses of affine and quadractic-Gaussian term structure models. Key to this matching are parameterizations of the market prices of risk that let us separately "control" the shape of the mean yield curve and the correlation structure of excess returns with the slope of the yield curve. The risk premiums have a simple form consistent with Fama's findings on the predictability of forward rates, and are shown to also be consistent with interest rate, feedback rules used by a monetary authority in setting monetary policy.

Abstract:
Though linear projections of returns on the slope of the yield curve have contradicted the implications of the traditional "expectations theory," we show that these findings are not puzzling relative to a large class of richer dynamic terms structure models. Specifically, we are able to match all of the key empirical findings reported by Fama and Bliss and Campbell and Shiller, among others, within large subclasses of affine and quadractic-Gaussian term structure models. Key to this matching are parameterizations of the market prices of risk that let us separately "control" the shape of the mean yield curve and the correlation structure of excess returns with the slope of the yield curve. The risk premiums have a simple form consistent with Fama's findings on the predictability of forward rates, and are shown to also be consistent with interest rate, feedback rules used by a monetary authority in setting monetary policy.

Abstract:
Though linear projections of returns on the slope of the yield curve have contradicted the implications of the traditional "expectations theory," we show that these findings are not puzzling relative to a large class of richer dynamic terms structure models. Specifically, we are able to match all of the key empirical findings reported by Fama and Bliss and Campbell and Shiller, among others, within large subclasses of affine and quadractic-Gaussian term structure models. Key to this matching are parameterizations of the market prices of risk that let us separately "control" the shape of the mean yield curve and the correlation structure of excess returns with the slope of the yield curve. The risk premiums have a simple form consistent with Fama's findings on the predictability of forward rates, and are shown to also be consistent with interest rate, feedback rules used by a monetary authority in setting monetary policy.

Abstract:
No abstract is available for this paper.

Abstract:
This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in whichthe risk factors follow diffusions, jump-diffusion, or have \switching regimes." Then the goodness-of- ts of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixed-income derivatives. For thecase of defaultable securities we explore the relative fits to historical yield spreads.

Abstract:
We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios.

Abstract:
We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios.

Abstract:
This paper investigates the term structure relations implied by a two-good model in which goods are durable and the preference function of consimters may be non separable both over time and the decision variables. The parameters characterizing preferences are estimated and the implied restrictions on the comovements of consumptions and the returns from following different investment strategies in bonds are examined. Both the durability of goods (modeled by a linear service technology) and the nonseparability of preferences over services from goods are important factors in explaining the time paths of individual returns. However, substantial evidence against our model is obtained when the restrictions associated with two different investment strategies are studied simultaneously. Specifically, the difference between the sample mean returns are too large relative to the difference between the sample covariances of the returns and the marginal utility from acquiring a unit of the numeraire good. Our findings suggest that these discrepancies are not a consequence of either the relatively small variability in aggregate acquisitions of goods, or our small estimates of relative risk aversion.

Abstract:
This paper provides a numerically accurate and computationally fast approximation to the prices of European options on coupon-bearing instruments that is applicable to the entire family of affine term structure models. Exploiting the typical shapes of the conditional distributions of the risk factors in affine diffusions, we show that one can reliably compute the relevant probabilities needed for pricing options on coupon-bearing instruments by the same Fourier inversion methods used in the pricing of options on zero-coupon bonds. We apply our theoretical results to the pricing of options on coupon bonds and swaptions, and the calculation of "expected exposures" on swap books. As an empirical illustration, we compute the expected exposures implied by several affine term structure models fit to historical swap yields.

Abstract:
In this paper, we explore the features of affine term structure models that are empirically important for explaining the joint distribution of yields on short and long-term interest rate swaps. We begin by showing that the family of N-factor affine models can be classified into N+1 non-nested sub-families of models. For each sub-family, we derive a maximal model with the property that every admissible member of this family is equivalent to or a nested special case of our maximal model. Second, using our classification scheme and maximal models, we show that many of the three-factor models in the literature impose potentially strong over-identifying restrictions on the joint distribution of short- and long-term rates. Third, we compute simulated method-of-moments estimates for several members of one of the four branches of three-factor models, and test the over-identifying restrictions implied by these models. We conclude that many of the extant affine models in the literature fail to describe important features of the distribution of long- and short- term rates. The source of the model misspecification is shown to be overly strong restrictions on the correlations among the state variables. Relaxing these restrictions leads to a model that passes several goodness-of-fit tests over our sample period.

Abstract:
This paper presents and interprets some rw evidence on the validity of the Real Business Cycle approach to business cycle analysis. The analysis is conducted in the context of a nnetary business cycle model which makes explicit one potential link between monetary policy and real allocations. This model is used to interpret Granger causal relations between nominal and real aggregates. Perhaps the nost striking empirical finding is that money growth does not Granger cause output growth in the context of several multivariate VARs and for various sample periods during the post war period in the U.S. Several possible reconciliations of this finding with both real and monetary business cycles models are discussed. We find that it is difficult to reconcile our npirical results with the view that exogenous monetary shocks were an important independent source of variation in output growth.

Abstract:
No abstract is available for this paper.

Abstract:
This paper explores in depth the nature of the conditional moment restrictions implied by log-linear intertemporal capital asset pricing models (ICAPMs) and shows that the generalized instrumental variables (GMM) estimators of these models (as typically implemented in practice) are inefficient. The moment conditions in the presence of temporally aggregated consumption are derived for two log-linear ICAPMs. The first is a continuous time model in which agents maximize expected utility. In the context of this model, we show that there are important asymmetries between the implied moment conditions for infinitely and finitely-lived securities. The second model assumes that agents maximize non-expected utility, and leads to a very similar econometric relation for the return on the wealth portfolio. Then we describe the efficiency bound (greatest lower bound for the asymptotic variances) of the CNN estimators of the preference parameters in these models. In addition, we calculate the efficient CNN estimators that attain this bound. Finally, we assess the gains in precision from using this optimal CNN estimator relative to the commonly used inefficient CMN estimators.

Abstract:
This article develops and empirically implements an arbitrage-free, dynamic term structure model with priced factor and regime-shift risks. The risk factors are assumed to follow a discrete-time Gaussian process, and regime shifts are governed by a discrete-time Markov process with state-dependent transition probabilities. This model gives closed-form solutions for zero-coupon bond prices, an analytic representation of the likelihood function for bond yields, and a natural decomposition of expected excess returns to components corresponding to regime-shift and factor risks. Using monthly data on U.S. Treasury zero-coupon bond yields, we show a critical role of priced, state-dependent regime-shift risks in capturing the time variations in expected excess returns, and document notable differences in the behaviors of the factor risk component of the expected returns across high and low volatility regimes. Additionally, the state dependence of the regime-switching probabilities is shown to capture an interesting asymmetry in the cyclical behavior of interest rates. The shapes of the term structure of volatility of bond yield changes are also very different across regimes, with the well-known hump being largely a low-volatility regime phenomenon.

G12

Abstract:
This paper characterizes the nature of yield curve risk in the Japanese government bond (JGB) market, and explores the effectiveness of risk management based on a linear factor representation of yield curve risk. The implied optimal hedges against factor risk are related to duration-based hedging strategies, which are shown in many cases to be substantially suboptimal. In addition, the drift over time in optimal hedge ratios due to the local nature of optimal hedging is investigated. The results show substantial drift especially for the weights on the factor representing the risk of a changing slope of the JGB yield curve. Though our focus is on government bond markets, the findings have implications for risk management for most interest-sensitive instruments, especially those that are priced relative to government bonds (e.g., corporate bonds).

Abstract:
This paper presents convenient reduced-form models of the valuation of contingent claims subject to default. A distinguishing feature of our approach is that losses at default are parameterized in terms of the fractional loss in market value. Under this assumption, and the assumption that default is an unpredictable event governed by a hazard-rate process, we show that many defaultable claims can be priced as if they are default-free by replacing the usual riskless discount rate by a default-adjusted short-rate process. This pricing framework is applied to callable and non-callable corporate bonds and a credit spread option. Additionally, we compare the pricing implications of models with fractional recovery of market value and fractional recovery of par upon default.

Abstract:
This paper develops a multi-factor econometric model of the term structure of interest-rate swap yields. The model accommodates the possibility of counterparty default and any differences in the liquidities of the Treasury and Swap markets. By parameterizing a model of swap rates directly, we are able to compute model-based estimates of the defaultable zero coupon bond rates implicit in the swap market without having to specify a priori the dependence of these rates on default hazard or recovery rates. The time series analysis of spreads between zero-coupon swap and treasury yields reveals that both credit and liquidity factors were important sources of variation in swap spreads over the past decade.