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.     

Credit ratings and convertible bond prices: a simulation-based valuation

This study presents a simulation-based model of convertible bond prices under the assumption of stochastic interest rates. The model is developed such that the convertible bond price explicitly depends on the credit rating at the time of issuance. Key ideas explored in this study include terminating the simulated sample path immediately when the issuer defaults on the bond at time t, which is the same as the investor and the issuer optimally exercising their options and discounting the resulting cash flows at a risk-free rate. In turn, the defaulted group of sample paths belongs to the bottom xth percentile of the realized stock prices at each time, which is exogenously given by the cumulative or marginal default probability of a firm that has the same rating as the issuer. Upon calibrating the model, we can see that the moneyness of convertible bonds is strongly responsible for influencing the convertible bond price when the rating changes. Furthermore, the effects of stochastic interest rates are shown to be possibly significant when the interest rate risk’s market price is not zero.     

Quantifying time value errors

Time valuation of cash flows is an essential part of personal financial planning and management. Many financial arrangements are priced according to a cash-flow valuation model. Expected cash flows associated with a stock or bond are discounted at an appropriate risk-adjusted rate in order to determine the fair value of the financial asset. Home mortgage loans are priced according to the discounted value of the future principal and interest cash flows. Yet, despite the importance of the discounted cash flow methodology in pricing assets, computational errors are often made when discount factors are not calculated precisely. This article attempts to quantify the magnitude of the error when the mathematical function for present value is ignored and interpolation is used instead to determine the discount factor.     

Interest Rate Futures Options and Interest Rate Options

This paper derives pricing models of interest rate options and interest rate futures options. The models utilize the arbitrage-free interest rate movements model of Ho and Lee. In their model, they take the initial term structure as given, and for the subsequent periods, they only require that the bond prices move relative to each other in an arbitrage-free manner. Viewing the interest rate options as contingent claims to the underlying bonds, we derive the closed-form solutions to the options. Since these models are sufficiently simple, they can be used to investigate empirically the pricing of bond options. We also empirically examine the pricing of Eurodollar futures options. The results show that the model has significant explanatory power and, on average, has smaller estimation errors than Black's model. The results suggest that the model can be used to price options relative to each other, even though they may have different expiration dates and strike prices.     

THE IMPACT OF SPLIT BOND RATINGS ON RISK PREMIA

Interest rates for bonds are negatively correlated with credit ratings assigned by agencies such as Moody's Investor Service and Standard & Poor's. Still in dispute is whether or not the ratings themselves convey information that is reflected in prices, hence interest rates in the bond markets. Disagreement between these two agencies' ratings leads to “split” ratings, and in this paper, the authors use the phenomenon of split ratings to assess whether or not ratings have a separate impact on bond prices. The results indicate that a downside split appears to have greater bond yield impact than an upside split. The findings are inconsistent with bond market efficiency, at least in the strong form. The market considers the quality of a split-rated bond to reflect the lower of the two ratings. Finally, the symmetry of the results with respect to the ratings agencies indicates that neither agency has more influence than the other in determining bond yields.     

Stochastic Volatilities and Correlations of Bond Yields

I develop an interest rate model with separate factors driving innovations in bond yields and their covariances. It features a flexible and tractable affine structure for bond covariances. Maximum likelihood estimation of the model with panel data on swaptions and discount bonds implies pricing errors for swaptions that are almost always lower than half of the bid–ask spread. Furthermore, market prices of interest rate caps do not deviate significantly from their no‐arbitrage values implied by the swaptions under the model. These findings support the conjectures of Collin‐Dufresne and Goldstein (2003) , Dai and Singleton (2003) , and Jagnnathan, Kaplin, and Sun (2003) .     

Fundamental Properties of Bond Prices in Models of the Short-Term Rate

This article develops restrictions that arbitrage-constrainedbond prices impose on the short-term rate process in order tobe consistent with given dynamic properties of the term structureof interest rates. The central focus is the relationship betweenbond prices and the short-term rate volatility. In both scalarand multidimensional diffusion settings, typical relationshipsbetween bond prices and volatility are generated by joint restrictionson the risk-neutralized drift functions of the state variablesand convexity of bond prices with respect to the short-termrate. The theory is illustrated by several examples and is partiallyextended to accommodate the occurrence of jumps and default.     

Mutual Funds and Stock and Bond Market Stability

The unprecedented growth of mutual funds has raised questions about the impact of mutual fund flows on stock and bond prices. Many believe that the equity bull market of the 1990s is attributable to the huge flows of funds into equity mutual funds during this period and that a withdrawal of those funds could send stock prices plummeting. This article investigates the relationship between aggregate monthly mutual fund flows (sales, redemptions, and net sales) and stock and bond monthly returns during a 30-year period beginning January 1961 utilizing Granger causality and instrumental variables analysis. With one exception, flows into stock and bond funds have not affected either stock and bond returns. The exception is 1971–1981, when widespread redemptions from equity mutual funds significantly depressed stock returns. In contrast, the magnitude of flows into both stock and bond funds are affected significantly by stock and bond returns.     

Is the Real Interest Rate Stable?

Univariate time-series models for consumption, nominal interest rates, and prices each appear to have a single unit root before 1979. If nominal interest rates have a unit root but inflation and inflation forecast errors do not, then ex ante real interest rates have a unit root and are therefore nonstationary. This deduction does not depend on the properties of the unobservable ex post observed real return, which combines the ex ante real interest rate and inflation-forecasting errors. The unit-root characteristic of real interest rates is puzzling from at least two perspectives: many models imply that the growth rate of consumption and the real interest rate should have similar time-series characteristics; also, nominal returns for other assets (e.g., stocks and bonds) appear to have different times-series properties from those of treasury bills.     

Modeling International Long-Term Interest Rates

This study investigates the relationship among interest rates on the long-term government bonds of five industrialized countries. Both standard and new unit root tests are applied, all of which confirm the presence of exactly one unit root. New cointegration tests are also applied to these data. In contrast to previous research on short-term bonds, stock prices, and exchange rates, these results find little evidence of cointegration among the five long-term interest rate series. Thus, when modeling or forecasting these central government long-term bond yields, one may assume separate sets of fundamentals and difference the data to achieve stationarity. An error correction model may not be appropriate.     

An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions

We propose a new method to calibrate the Vasicek and Cox--Ingersoll--Ross interest rate models from bond prices. We define an appropriate generating function and derive recursive relations between the derivatives of the generating function and the bond prices. The parameters of the Vasicek and CIR models are then obtained by solving a system of linearly independent equations arising from the recursive relations. We include numerical results that show the method’s accuracy when bond prices generated from the exact formulas are used.     

Implied volatilities,stochastic interest rates,and currency futures options valuation: an empirical investigation

Different models of pricing currency call and put options on futures are empirically tested. Option prices are determined using different models and compared to actual market prices. Option prices are determined using historical as well as implied volatility. The different models tested include both constant and stochastic interest rate models. To determine if the model prices are different from the market prices, regression analysis and paired t-tests are performed. To see which model misprices the least, root mean square errors are determined. It is found that better results are obtained when implied volatility is used. Stochastic interest rate models perform better than constant interest rate models.     

美联储货币政策对我国资产价格的影响

本文利用事件研究法考察了美联储货币政策对我国资产价格的影响。研究发现美联储货币政策会显著影响我国资产价格,美联储加息会降低我国债券和股票回报,降息则会提高债券和股票回报。将美联储货币政策进行细分后发现,预期到的货币政策调整对债券市场和股票市场的回报都有显著影响,而未预期到的货币政策调整和前瞻性指引只影响债券市场。进一步的研究表明,未预期到的美联储货币政策调整和前瞻性指引还会加剧我国金融市场的波动率。本文的研究结论为美联储货币政策对我国经济金融的影响提供了新的证据,对于投资者提高投资收益、降低投资风险以及货币当局完善我国货币政策调控和维护我国金融市场稳定具有重要意义。     

Structural models of credit risk are useful: Evidence from hedge ratios on corporate bonds

Structural models of credit risk provide poor predictions of bond prices. We show that, despite this, they provide quite accurate predictions of the sensitivity of corporate bond returns to changes in the value of equity (hedge ratios). This is important since it suggests that the poor performance of structural models may have more to do with the influence of non-credit factors rather than their failure to capture the credit exposure of corporate debt. The main result of this paper is that even the simplest of the structural models [Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29, 449–470] produces hedge ratios that are not rejected in time-series tests. However, we find that the Merton model (with or without stochastic interest rates) does not capture the interest rate sensitivity of corporate debt, which is substantially lower than would be expected from conventional duration measures. The paper also shows that corporate bond prices are related to a number of market-wide factors such as the Fama-French SMB (small minus big) factor in a way that is not predicted by structural models.     

Price behavior of deep discount bonds

With rising interest rate trends, deep discount bonds are more commonly observed. The traditional view has been that, for a given yield change, the changes in bond prices are larger, the longer the maturity. This note shows that, for a deep discount bond, there is a switchover point beyond which the traditional view no longer holds. This is true for percentage as well as for dollar price changes. The traditional view should be corrected to avoid misleading effects on the management of bond portfolios.     

THE DISPERSION OF BIDS ON INDIVIDUAL NEW MUNICIPAL ISSUES

This paper examines the determinants of the dispersion of interest rates bid on competitively sold, new municipal issues. Theory suggests that the dispersion of prices (interest rates) on a new municipal issue depends on the expected costs and benefits of underwriter search on that issue. The greater the expected costs and the lower the expected benefits, the smaller will be underwriter search and the greater will be municipal interest rate dispersion. For empirical testing, the expected costs and benefits of underwriter search are measured by characteristics of the bond issue, the bond issuer, and the market conditions. The empirical tests suggest that the theory holds.     

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.     

Term structure modelling of defaultable bonds

In this paper we present a model of the development of the term structure of defaultable interest rates that is based on a multiple-defaults model. Instead of modelling a cash payoff in default we assume that defaulted debt is restructured and continues to be traded.The term structure of defaultable bond prices is represented in terms of defaultable forward rates similar to the Heath-Jarrow-Morton (HJM) (Heath et al., 1992) approach, and conditions are given under which the dynamics of these rates are arbitrage-free. These conditions are a drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default.Financial Assistance by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303, at the University of Bonn and the DAAD is gratefully acknowledged.I thank Pierre Mella-Barral, David Lando and David Webb for helpful conversations, and the participants of the FMG Conference on Defaultable Bonds (March 1997) in London and the QMF 97 conference in Cairns for helpful comments. All errors are of course my own.     

THE DIFFERENTIAL EFFECTS OF SINKING FUNDS ON BOND RISK PREMIA

This study analyzes the effect that two options created by the inclusion of a sinking fund clause in a bond indenture have on the bond issue's secondary market risk premium. The impact of market prices that exceed current sinking fund redemption prices, and of par versus premium redemption, is clearly apparent when a set of issue-specific and macroeconomic control variables are incorporated into a model of bond risk premia. Thus, secondary market prices for the large-volume utility bond transactions in the sample reflect knowledge of individual-issue, time-varying indenture characteristics.     

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.