Prediction of Individual Bond Prices via a Dynamic Bond Pricing Model: Application to Japanese Government Bond Price Data

In this paper, we propose a dynamic bond pricing model and report the usefulness of our bond pricing model based on analysis of Japanese Government bond price data. We extend the concept of the time dependent Markov (TDM) model proposed by Kariya and Tsuda (Financial Engineering and the Japanese Markets, Kluwer Academic Publishers, Dordrecht, The Netherlands, Vol. 1, pp. 1–20) to a dynamic model, which can obtain information for future bond prices. A main feature of the extended model is that the whole stochastic process of the random cash-flow discount functions of each individual bond has a time series structure. We express the dynamic structure for the models by using a Bayesian state space representation. The state space approach integrates cross-sectional and time series aspects of individual bond prices. From the empirical results, we find useful evidence that our model performs well for the prediction of the patterns of the term structure of the individual bond returns.     

Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model

We develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. We derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed-form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model.     

Empirically Effective Bond Pricing Model and Analysis on Term Structures of Implied Interest Rates in Financial Crisis

In his book (1993) Kariya proposed a government bond (GB) pricing model that simultaneously values individual fixed-coupon (non-defaultable) bonds of different coupon rates and maturities via a discount function approach, and Kariya and Tsuda (Financ Eng Japanese Mark 1:1–20, 1994) verified its empirical effectiveness of the model as a pricing model for Japanese Government bonds (JGBs) though the empirical setting was limited to a simple case. In this paper we first clarify the theoretical relation between our stochastic discount function approach and the spot rate or forward rate approach in mathematical finance. Then we make a comprehensive empirical study on the capacity of the model in view of its pricing capability for individual GBs with different attributes and in view of its capacity of describing the movements of term structures of interest rates that JGBs imply as yield curves. Based on various tests of validity in a GLS (Generalized Least Squares) framework we propose a specific formulation with a polynomial of order 6 for the mean discount function that depends on maturity and coupon as attributes and a specific covariance structure. It is shown that even in the middle of the Financial Crisis, the cross-sectional model we propose is shown to be very effective for simultaneously pricing all the existing JGBs and deriving and describing zero yields.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.     

Consumption risk and the cross-section of government bond returns

In this paper we provide a consumption-based explanation of risk in nominal US Treasury bond portfolios. We use a consumption-CAPM with Epstein–Zin–Weil recursive preferences. Our model introduces two sources of risk: uncertainty about current consumption (reflected in contemporaneous consumption growth) and uncertainty about prospects of consumption in a long run (reflected in innovations to expectations about future consumption growth). We use a novel approach to estimate pricing factors in our model: we employ a factor-augmented VAR model with common factors, extracted from a large panel of macroeconomic and financial data, as state variables. We find that the important source of risk in US bonds is related to uncertainty in prospects in future consumption and it induces a positive and significant risk premium. We find as well that covariance risk related to innovations in expectations about future consumption growth is greater for long term bond portfolios than for short term bond portfolios, which is consistent with a duration measure of risk and justifies why long term bonds require greater premium than short term bonds. Our model explains well the cross-sectional variation in average excess returns of bonds with different maturities over the period 1975–2011 and compares favorably with competing models.     

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.     

How much of the corporate bond spread is due to personal taxes?

Existing term structure models of defaultable bonds have often underestimated corporate bond spreads. A potential problem is that investors’ taxes are ignored in these models. We propose a pricing model that accounts for stochastic default probability and differential tax treatments for discount and premium bonds. By estimating parameters directly from bond data, we obtain significantly positive estimates for the income tax rate of a marginal corporate bond investor after 1986. This contrasts sharply with the previous finding that the implied tax rates for Treasury bonds are close to zero. Results show that taxes explain a substantial portion of corporate bond spreads.     

Mean-variance cointegration and the expectations hypothesis

The present paper sheds further light on a well-known (alleged) violation of the expectations hypothesis of the term structure (EHT): the frequent finding of unit roots in interest rate spreads. We show that the EHT implies (i) that the nonstationarity stems from the holding premium, which is hence (ii) cointegrated with the spread. In a stochastic discount factor framework, we model the premium as being driven by the integrated variance of excess returns. Introducing the concept of mean-variance cointegration, we actually find cointegration relations between the conditional first and second moment of US bond data.     

The Jarrow/Turnbull default risk model—Evidence from the German market

Abstract

This article estimates default intensities within the continuous-time Jarrow and Turnbull model for German bank and corporate bond prices. It is shown that a joint implicit estimation of the default intensity and the recovery rate is numerically unstable. In addition to cross-sectional estimations, separate estimations (for each bond individually) are performed. Results strongly support separate estimation over the building of any cross-sections. In contrast to preceeding literature, the optimum volume of data required to provide reasonable estimates of the default intensity is also investigated. It is shown that calibration based on daily data as a rule does not minimize the ex ante mean squared pricing errors. Finally, it is shown that the constant default intensity assumption is not sound with the underlying data and the determinants of the default intensity are investigated. Regressions show that the lagged default intensity estimate, the level of the default-free term structure and liquidity proxies affect the estimated default intensity via joint parameters.     

AN EMPIRICAL STUDY OF A NEW CLASS OF NO-ARBITRAGE-BASED DISCRETE MODELS OF THE TERM STRUCTURE

We present empirical tests of the new no-arbitrage-based term structure paradigm in discrete time. We derive and test empirical specifications for deterministic one-factor forward rate volatility models and examine the compatibility of these forward rate volatility functions using term structure dynamics. Our estimation technique uses the generalized method of moments and is based on forward bond price deviations. We do not impose restrictions on the market price of risk, and we incorporate all available term structure information. Our data consist of four sets of pure discount bonds derived from the CRSP bond files and U.S. Treasury bill quotes.     

A Model of Intertemporal Discount Rates in the Presence of Real and Inflationary Autocorrelations

This paper discusses the pricing of assets in an intertemporal rational-expectations model when real production and inflation evolve according to first-order autocorrelated processes. The focus is on the structure of the various intertemporal discount rates (yields) exhibited by this economy. Yield curves are identified for consumption claims, indexed bonds, and nominally riskless bonds and can be extended to any claim that can be approximated by a (finite) linear combination of such securities. The model demonstrates that, if the average term structure for nominally riskless securities is upward sloping, then the yield curve for consumption (market) claims is downward sloping, suggesting that conventional methods for computing long-term discount rates err by not accounting for maturity factors. The paper also explores the relationship between the intertemporal equilibrium and its embedded single-period equilibria. The single-period risk measures in this economy are derived and shown to be (generally) functions of maturity. A model of nominal bond betas is constructed along these lines. It is shown that bond betas that are increasing functions of maturity do not necessarily imply an upward-sloping term structure.     

Pricing of discount bonds with a Markov switching regime

We consider a Markov switching regime and price a discount bond using a CIR-type short rate model. An explicit formula is obtained for the bond price which includes the solution of a matrix ODE. Our model is easy to calculate and captures the effect of regime uncertainty in the price and term structure.     

Evaluating asset pricing models in the Korean stock market

This paper evaluates and compares asset pricing models in the Korean stock market. The asset pricing models considered are the CAPM, APT-motivated models, the Consumption-based CAPM, Intertemporal CAPM-motivated models, and the Jagannathan and Wang conditional CAPM model. By using various test portfolios as well as individual stocks, we conduct time-series tests and cross-sectional regression tests based on individual t-tests, the joint F-tests, the Hansen and Jagannathan (1997) distance, and R-squares. Overall, the Fama and French (1993) five-factor model performs most satisfactorily among the asset pricing models considered in explaining the intertemporal and cross-sectional behavior of stock returns in Korea. The Fama and French (1993) three-factor model, the Chen et al. (2010) three-factor model, and the Campbell (1996) model are the next. The results indicate that the two bond portfolios, term spread and default spread, play an important role in explaining stock returns in Korea.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models

To value mortgage-backed securities and options on fixed-income securities, it is necessary to make assumptions regarding the term structure of interest rates. We assume that the multi-factor fixed parameter term structure model accurately represents the actual term structure of interest rates, and that the values of mortgage-backed securities and discount bond options derived from such a term structure model are correct. Differences in the prices of interest rate derivative securities based on single-factor term structure models are therefore due to pricing bias resulting from the term structure model. The price biases that result from the use of single-factor models are compared and attributed to differences in the underlying models and implications for the selection of alternative term structure models are considered.     

Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves

This paper analyses the UK interest rate term structure over the period since October 1992, when the United Kingdom adopted an explicit inflation target, using an affine term structure model estimated using both government bond yields and survey data. The model imposes no-arbitrage restrictions across nominal and real yields, which enables interest rates to be decomposed into expected real policy rates, expected inflation, real term premia and inflation risk premia. The model is used to shed light on major developments over the period, including the impact of Bank of England independence and the low real bond yield ‘conundrum’.     

Measuring Credit Risk of Individual Corporate Bonds in US Energy Sector

In this paper, using the measures of the credit risk price spread (CRiPS) and the standardized credit risk price spread (S-CRiPS) proposed in Kariya’s (A CB (corporate bond) pricing model for deriving default probabilities and recovery rates. Eaton, IMS Collection Series: Festschrift for Professor Morris L., 2013) corporate bond model, we make a comprehensive empirical credit risk analysis on individual corporate bonds (CBs) in the US energy sector, where cross-sectional CB and government bond price data is used with bond attributes. Applying the principal component analysis method to the S-CRiPSs, we also categorize individual CBs into three different groups and study on their characteristics of S-CRiPS fluctuations of each group in association with bond attributes. Secondly, using the market credit rating scheme proposed by Kariya et al. (2014), we make credit-homogeneous groups of CBs and show that our rating scheme is empirically very timely and useful. Thirdly, we derive term structures of default probabilities for each homogeneous group, which reflect the investors’ views and perspectives on the future default probabilities or likelihoods implicitly implied by the CB prices for each credit-homogeneous group. Throughout this paper it is observed that our credit risk models and the associated measures for individual CBs work effectively and can timely provide the market credit information evaluated by investors.     

Determinants of the Dollar Value of Default Risk: A Put Option Perspective

This study uses the option valuation framework to identify andinvestigate the factors affecting the cross-sectional difference inindividual corporate bonds' default risk. The dollar value of defaultrisk (DVDR) is measured by subtracting the observed trading price of arisky corporate bond from a Cox-Ingersoll-Ross model value of acorresponding pseudo-default-free bond. From an option pricingperspective, DVDR can be modeled as the value of a put option on thefirm's risky assets. The DVDR of an individual investment-grade corporatebond is hypothesized to be related to the bond rating, time to maturity ofthe bond, size of the issuing firm, volatility of firm value, and dividendyield of the issuing firm. In the case of the first four factors, theempirical results are consistent with the predictions from a put optionperspective. There is a mixed relationship between DVDR and dividendyield, however, which provides a weaker support for the prediction of theoption valuation model. Such a mixed relationship documents the importantrole that dividend payments play in signaling a firm's future earnings andreducing overall agency costs. ["In particular, the formula can be usedto derive the discount that should be applied to a corporate bond becauseof the possibility of default." (Black and Scholes (1973), Journal of Political Economy, Abstract, p. 637.)]     

Pricing of credit default index swap tranches with one-factor heavy-tailed copula models

In this paper, we provide two one-factor heavy-tailed copula models for pricing a collateralized debt obligation and credit default index swap tranches: (1) a one-factor double t distribution with fractional degrees of freedom copula model and (2) a one-factor double mixture distribution of t and Gaussian distribution copula model. A time-varying tail-fatness parameter is introduced in each model, allowing one to change the tail-fatness of the copula function continuously. Fitting our model to comprehensive market data, we find that a model with fixed tail-fatness cannot fit market data well over time. The two models that we propose are capable of fitting market data well over time when using a proper time-varying tail-fatness parameter. Moreover, we find that the time-varying tail-fatness parameters change dramatically over a one-year period.