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74
Term Structure of Interest Rates with Regime Shifts
 Journal of Finance
, 2002
"... We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifi ..."
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Cited by 78 (1 self)
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We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the welldocumented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles. MANY PAPERS DOCUMENT THAT THE UNIVARIATE short interest rate process can be reasonably well modeled in the time series as a regime switching process ~see Hamilton ~1988!, Garcia and Perron ~1996!!. In addition to this statistical evidence, there are economic reasons as well to believe that regime shifts are important to understanding the behavior of the entire yield curve. For example, business cycle expansion and contraction “regimes ” potentially
A ConsumptionBased Model of the Term Structure of Interest Rates
, 2004
"... This paper proposes a consumptionbased model that can account for many features of the nominal term structure of interest rates. The driving force behind the model is a timevarying price of risk generated by external habit. Nominal bonds depend on past consumption growth through habit and on expec ..."
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Cited by 72 (4 self)
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This paper proposes a consumptionbased model that can account for many features of the nominal term structure of interest rates. The driving force behind the model is a timevarying price of risk generated by external habit. Nominal bonds depend on past consumption growth through habit and on expected inflation. When calibrated to data on consumption, inflation, and the average level of bond yields, the model produces realistic volatility of bond yields and can explain key aspects of the expectations puzzle documented by Campbell and Shiller (1991) and Fama and Bliss (1987). When actual consumption and inflation data are fed into the model, the model is shown to account for many of the short and longrun fluctuations in the shortterm interest rate and the yield spread. At the same time, the model captures the high equity premium and
Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk
, 2004
"... It is now an accepted fact that stochastic mortality – the risk that actual future trends in mortality might differ from those anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated. This pape ..."
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Cited by 55 (24 self)
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It is now an accepted fact that stochastic mortality – the risk that actual future trends in mortality might differ from those anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated. This paper makes use of the similarities between the force of mortality and interest rates to show how we can model mortality risks and price mortalityrelated instruments using adaptations of the arbitragefree pricing frameworks that have been developed for interestrate derivatives. In so doing, it develops a range of arbitragefree (or riskneutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – shortrate models, forwardmortality models, positivemortality models and mortality market models – are all based on positiveinterestrate modelling frameworks since the force of mortality can be treated in a similar way to the shortterm riskfree rate of interest. These frameworks can be applied to a great variety of mortalityrelated instruments, from vanilla survivor bonds to exotic mortality derivatives.
Term structure dynamics in theory and reality
 Review of Financial Studies
, 2003
"... 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 ..."
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Cited by 47 (8 self)
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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, jumpdiffusion, or have “switching regimes. ” Then the goodnessoffits 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 fixedincome derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads. 1
The Affine Arbitragefree Class of NelsonSiegel Term Structure Models
 Journal of Econometrics
, 2011
"... We derive the class of arbitragefree affine dynamic term structure models that approximate the widelyused NelsonSiegel yieldcurve specification. Our theoretical analysis relates this new class of models to the canonical representation of the threefactor arbitragefree affine model. Our empirica ..."
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Cited by 39 (12 self)
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We derive the class of arbitragefree affine dynamic term structure models that approximate the widelyused NelsonSiegel yieldcurve specification. Our theoretical analysis relates this new class of models to the canonical representation of the threefactor arbitragefree affine model. Our empirical analysis shows that imposing the NelsonSiegel structure on the canonical representation of affine models greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage. † For helpful comments we thank seminar/conference participants at the University of Chicago, Copenhagen
Do Bonds Span the Fixed Income Markets? Theory and Evidence for ‘Unspanned’ Stochastic Volatility
 Journal of Finance
, 2002
"... Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on atthemoney straddles – portfolios mainly exposed to vola ..."
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Cited by 39 (0 self)
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Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on atthemoney straddles – portfolios mainly exposed to volatility risk. We term this empirical feature “unspanned stochastic volatility ” (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USVmodels, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.
Asset Pricing Under The Quadratic Class
 Journal of Financial and Quantitative Analysis
, 2002
"... We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative ..."
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Cited by 36 (6 self)
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We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative pricing in particular under the quadratic class. We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semiclosed form. We further illustrate how the quadratic model and the transform methods can be applied to more general settings. # Swiss Banking Institute, University of Zurich, Plattenstr. 14, 8032 Zurich, Switzerland and Graduate School of Business, Fordham University, 113 West 60th Street, New York, NY 10023, USA, respectively. We thank Marco Avellaneda, David Backus, Peter Carr, Pierre Collin, Silverio Foresi, Michael Gallmeyer, Richard Green, Massoud Heidari, Burton Hollifield, Regis Van Steenkiste, Chris Telmer, Stanley Zin, and, in particular, Jonathan M. Karpo# (the editor) as well as two anonymous referees for helpful comments. I.
The Statistical and Economic Role of Jumps in ContinuousTime Interest Rate Models
 Journal of Finance
, 2004
"... This paper provides an empirical analysis of the role of jumps in continuoustime models of the short rate. Statistically, if jumps are present di¤usion models are misspeci…ed and I develop a test to detect jumpinduced misspeci…cation. After …nding evidence for jumps, I introduce a nonparametric ju ..."
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Cited by 29 (0 self)
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This paper provides an empirical analysis of the role of jumps in continuoustime models of the short rate. Statistically, if jumps are present di¤usion models are misspeci…ed and I develop a test to detect jumpinduced misspeci…cation. After …nding evidence for jumps, I introduce a nonparametric jumpdi¤usion model and develop an estimation methodology. The results point toward a dominant statistical role for jumps in determining the dynamics of the short rate relative to di¤usive components. Estimates of jump times and sizes indicate that jumps serve an interesting economic purpose: they provide a main conduit for information about the macroeconomy to enter the term structure. Finally, I investigate the pricing implications of jumps. While jumps do not appear to have a large impact on the crosssection of bond prices, they do have important implications for interest rate derivatives.
How to Discount Cashflows with TimeVarying Expected Returns
 THE JOURNAL OF FINANCE • VOL. LIX, NO. 6 • DECEMBER 2004
, 2004
"... While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores timevarying risk premiums and betas. We develop a model to consistently value cashflows with changing riskfree rates, predictable risk premiums, and conditio ..."
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Cited by 19 (2 self)
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While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores timevarying risk premiums and betas. We develop a model to consistently value cashflows with changing riskfree rates, predictable risk premiums, and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large misvaluations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time variation in riskfree rates and factor loadings.
Guaranteed Annuity Options
 ASTIN Bulletin
, 2003
"... Under a guaranteed annuity option, an insurer guarantees to convert a policyholder’s accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insu ..."
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Cited by 18 (0 self)
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Under a guaranteed annuity option, an insurer guarantees to convert a policyholder’s accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970’s and 1980’s when longterm interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990’s, as longterm interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred. The emerging liabilities under these guarantees threatened the solvency of some companies 1