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.     

New bond pricing models with applications to Japanese data

In this paper, the cross-sectional bond pricing model for individual bonds Kariya (1993) proposed by formulating stochastic discount function (term structure) is first applied to Japanese Government bond (JG-bond) data. The model performs very well as it stands. Second, we generalize the cross-sectional model to two types of time-dependent Markov models (TDM's) with the term structure of discount rates of each bond att being dependent on the one att−1, and apply them to the same data to find significantly improved results over those of the cross-sectional model. In fact, almost all the differences between actual prices and model values are less than 0.5 yen in each month over 12 years, implying that the error rate is less than 0.5%. On the basis of our analysis, we propose a TDM as a model for JG-bond trading.     

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.     

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.     

Presentation of the English translation of Ettore Majorana's paper: The value of statistical laws in physics and social sciences

We consider a consistent pricing model of government bonds, interest-rate swaps and basis swaps in one currency within the no-arbitrage framework. To this end, we propose a three yield-curve model, one for discounting cash flows, one for calculating LIBOR deposit rates and one for calculating coupon rates of government bonds. The derivation of the yield curves from observed data is presented, and the option prices on a swap or a government bond are studied. A one-factor quadratic Gaussian model is proposed as a specific model, and is shown to provide a very good fit to the current Japanese low-interest-rate environment.     

Forward-neutral valuation relationships for options on zero coupon bonds

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds.     

Differential taxation and the equilibrium structure of interest rates

Equilibrium coupon bond pricing relationships given differential taxation are derived under uncertainty assuming that both corporate and municipal bonds were originally issued at par but are currently selling at a discount. The impact of differential taxation upon the term structure and coupon structure of interest rates is investigated, while the tax structure of interest rates is uniquely characterized. Differential taxation substantially alters the prevailing equilibrium structure of interest rates.     

Trading strategies based on term structure model residuals

The term structure of interest rates is an important input for basically every pricing model and is mostly calibrated on coupon bond prices. Therefore, the estimated interest rates should accurately explain the market prices of these bonds. However, nearly all empirical papers on interest rate estimation, e.g. Svensson, L.E.O. 1994. Estimating and interpreting forward interest rates: Sweden 1992–1994, IMF Working Paper, International Monetary Fund, report significant pricing errors in their sample. So an important question is what drives these pricing errors of the bonds. One simple explanation would be different tax treatment or different liquidity, but most papers on this research topic, e.g. Elton, E., and T.C. Green. 1998. Tax and liquidity effects in pricing government bonds. Journal of Finance 53: 1533–62, cannot fully explain the observed pricing errors. Therefore, these errors must be at least partially caused by either model misspecification or by the deviation of particular bond prices from general market conditions, i.e. mispricing revealing insufficient market efficiency. We provide empirical evidence for the German government bond market that risk-adjusted trading strategies based on bond pricing errors can yield about 15 basis points p.a. abnormal return compared to benchmark portfolios. Furthermore, the abnormal returns are continuously achieved over the whole time period and not randomly on a few days and show a relation to changes in the level and the curvature of the term structure of interest rates. Therefore, pricing errors contain economic information about deviations of bond prices from general market conditions and are not exclusively caused by model misspecification and/or differences in liquidity and tax treatment of individual bonds.     

OPTIONS ON U.S. TREASURY COUPON ISSUES

Pricing models for options on default-free coupon bonds are developed and tested under the assumption that the bond prices, rather than interest rates, are the underlying stochastic factors. Under the assumption that coupon bond prices, excluding accrued interest, follow a generalized Brownian bridge process, preference-free, continuous-time pricing models are developed for European put and call options, and a discrete-time model is developed for American puts and calls. The empirical validity of the models is assessed using a six-moth sample of daily closing prices.     

Stochastic durations,the convexity effect,and the impact of interest rate changes

This article shows that the equilibrium models of bond pricing do not preclude arbitrage opportunities caused by convexity. Consequently, stochastic durations derived from these models are limited in their ability to act as interest rate risk measures. The research of the present article makes use of an intertemporal utility maximization framework to determine the conditions under which duration is an adequate interest rate risk measure. Additionally, we show that zero coupon bonds satisfy those equilibrium conditions, whereas coupon bonds or bond portfolios do not as a result of the convexity effect. The results are supported by empirical evidence, which confirms the influence of convexity on the deviation of coupon bond returns from equilibrium.     

Option pricing for GARCH-type models with generalized hyperbolic innovations

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets being modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk-neutral distribution is unique and again implies a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options, respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach with natural competitors in order to test its efficiency. More generally, our empirical investigations analyse the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.     

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.     

YIELD VOLATILITY OF DISCOUNT COUPON BONDS

In this research, the yield volatility of coupon-taxable discount bonds is analyzed. The relationship of before-tax yield changes on discounts as compared with changes in new, par issue (market) yields is developed in the form of a net yield factor (NYF). Also, the behavior of the NYF as dependent upon parameters such as maturity, coupon, market yield, and tax rates is examined. Then, the incorporation and impact of the NYF on price volatility are shown. Finally, results of empirical tests are reported, which validate the usefulness of NYFs in the measurement of yield volatility for discount bonds.     

Simulation-based pricing of convertible bonds

We propose and empirically investigate a pricing model for convertible bonds based on Monte Carlo simulation. The method uses parametric representations of the early exercise decisions and consists of two stages. Pricing convertible bonds with the proposed Monte Carlo approach allows us to better capture both the dynamics of the underlying state variables and the rich set of real-world convertible bond specifications. Furthermore, using the simulation model proposed, we present an empirical pricing study of the US market, using 32 convertible bonds and 69 months of daily market prices. Our results do not confirm the evidence of previous studies that market prices of convertible bonds are on average lower than prices generated by a theoretical model. Similarly, our study is not supportive of a strong positive relationship between moneyness and mean pricing error, as argued in the literature.     

Death and Taxes: The Market for Flower Bonds

Certain U.S. Government securities, known as flower bonds, can be redeemed at par plus accrued interest for the purpose of paying estate taxes, if held at the time of death. Thus, a flower bond, selling at a discount, is like a straight bond plus a life insurance policy. An equilibrium derived from a rational flower bond pricing model implies the existence of clienteles: individuals with the highest death probabilities hold the deepest discount flower bonds. The empirical implication, that bonds with the deepest discount should be redeemed at the fastest rate, is tested and the results support the proposition.     

The valuation of nonsystematic risks and the pricing of Swedish lottery bonds

Swedish government lottery bonds have coupon payments determinedby lottery. They offer a unique opportunity to study a securitywith uncertain payoffs having a known, observable distribution.The risk associated with the lotteries is idiosyncratic by constructionand should not command a risk premium in equilibrium. The bondsare traded in two forms, allowing us to evaluate the rewardsto bearing extra lottery risk. Despite its idiosyncratic nature,we find prices appear to reflect aversion to this risk. We evaluatethe empirical determinants of this differential pricing andpossible explanations for it.     

Actuarial pricing of deposit insurance

Using a pricing formula for options on coupon bonds (Jamshidian [1989], El Karoui and Rochet [1990]) we are able to compute the actuarial pricing of deposit insurance for a commercial bank. Our formula takes into account the maturity structure of the bank's balance sheet, as well as market parameters such as the term structure of interest rates and the volatilities of zero coupon bonds. The relation with asset liability management methods is explored.     

Asset Pricing Specification Errors and Performance Evaluation

Many evaluation techniques typically measure performance asdeviations of average returns on actively managed funds fromthose predicted by some asset pricing model. Empirical evidence,however, has so far suggested that all asset pricing modelslack empirical support, implying that the models contain mis-specificationerrors to various degrees. Evaluating mutual fund performancerelative to any of these models thus becomes problematic. Inthis paper, we propose an approach to performance measurementthat emphasizes minimizing explicitly the pricing error associatedwith an asset pricing function which is employed to computeperformance measures. This approach is henceforth called theminimum specification-error (MSE) method. We also discuss thestatistical properties for implementing MSE performance measure.To demonstrate the significance of the pricing error confoundedin evaluation measurement, we contrast our methodology withthe Grinblatt and Titman (1989) period weighting approach andwith the empirical implementation of Chen and Knez (1996). Wefind that the greater the pricing error of passive assets, thelarger the performance measures. Given the average pricing errorgenerated from a collection of 163 diverse passive portfoliosused in this analysis the performance values assigned to a largenumber of the funds become statistically and economically insignificant.     

A contingent claims analysis of the interest rate risk characteristics of corporate liabilities

This paper provides a contingent claims analysis of the interest rate risk characteristics of corporate liabilities by identifying Merton's (1973) option pricing model with Vasicek's (1977) mean reverting term structure model. Only a non-zero positive range of duration values for the firms' assets is shown to be consistent with the previous empirical evidence on the interest rate sensitivity of corporate stocks and bonds. Chance's (1990) duration measure is shown to be biased downward under empirically realistic conditions. Theoretical conditions are derived under which the duration of a default-prone zero coupon bond can be either higher or lower than the duration of the corresponding default-free bond. The duration of the default-prone bond of a firm with high (low) interest rate sensitive assets is shown to be an increasing (decreasing) function of the bond's default-risk.