Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics

Given that infrastructure public REITs in China are still in the early stage of development, this paper firstly reviews their current status from relevant sources and briefly describes their definitions, development status and main characteristics. The option-adjusted spread method based on Monte Carlo simulation is chosen as the pricing model. The term adjusted spread method needs to consider the interest rate term structure, so the CIR model is used as the interest rate term structure model for interest rate forecasting, and the three CIR parameter values obtained by fitting are brought into the CIR model using Monte Carlo method simulation to obtain 1000 forward interest rate paths, and the spot interest rate is obtained according to the forward interest rate curve path, and the spot interest rate is used to combine with the option adjusted spread OAS to discount the 1000 present values. The average value of the 1000 present values is the pricing result. Comparing the pricing result with the market value, it is found that the two are basically equal. This shows that the option-adjusted spread method based on Monte Carlo simulation can evaluate the value of public REITs more scientifically and reasonably.

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

Risk Premiums of Excess Bond Returns Have a Unit Root

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi (2002). The result echoes the policy rule used by (1994) to rationalize the empirical failure of the `expectations hypothesis' applied to the term- structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. yield-curve smoothing), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss (1987). also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor (1993) rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term structure models studied in Duffie and Kan (1996): a stochastic volatility model and a stochastic price-of- risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by (i.e., the McCallum Rule). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzesi (2003)). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.

Recombining Trees for One-Dimensional Forward Rate Models

Modeling the Term Structure of Interest Rates: Where Do We Stand?

No-arbitrage models of term structure have the feature that the return on zero-coupon bonds is the sum of the short rate and the product of volatility and market price of risk.Well known models restrict the behavior of the market price of risk so that it is not dependent on the type of asset being modeled.We show that the models recently proposed by Goldstein and Santa-Clara and Sornette, among others, allow the market price of risk to depend on characteristics of each asset, and we quantify this dependence.A key tool in our analysis is a very general space-time change of measure theorem, proved by the first author in earlier work, and covers continuous orthogonal local martingale measures including space-time white noise.

This paper demonstrates that the term structure model of Heath, Jarrow and Morton (HJM, 1992) can be decomposed into two component functions, such that if one can represent the observed initial forward rate curve, then the other is the dynamic evolution of the forward rates. This decomposition simplifies the practical implementation of the HJM model for allowing the parameters of the model to be estimated from the initial forward rate function, since the evolution of the forward function has the same parameters. Because the estimation is essentially a cross-sectional curvefitting to which the treasury securities are sufficient, interest rate contingent claims are not required for the calibration of the HJM model; thus, the costly path-dependent computation can be completely avoided. Utilizing the functionality of the HJM model, this paper derives a simple and accurate estimation procedure. The empirical results show that a three-factor HJM specification is a consistent representation of the term structure...

The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks

Sheehan’s syndrome (SS) is ischaemic necrosis of the pituitary gland due to massive postpartum haemorrhage. The clinical manifestations may vary from subtle to life-threatening and may present immediately after delivery or many years later. We present a case history of a 58-year-old non-diabetic woman who had undetected SS and presented with two unusual manifestations, including recurrent hypoglycaemia and dilated cardiomyopathy 34 years after delivery. The dilated cardiomyopathy reversed partially after treatment.

Multi-Lag Term Structure Models with Stochastic Risk Premia

This paper presents a unifying theory for valuing contingent claims under a stochastic term of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processeE for its subsequent movements. A no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk. Examples are provided to illustrate the key results. IN RELATION TO the term of interest rates, arbitrage pricing theory has two purposes. The first, is to price all zero coupon (default free) bonds of varying maturities from a finite number of economic fundamentals, called state variables. The second, is to price all interest rate sensitive contingent claims, taking as given the prices of the zero coupon bonds. This paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context, of which all existing arbitrage pricing models are special cases (in particular, Vasicek (1977), Brennan and Schwartz (1979), Langetieg (1980), Ball and Torous (1983), Ho and Lee (1986), Schaefer and Schwartz (1987), and Artzner and Delbaen (1988)). The primary contribution of this paper, however, is a new methodology for solving the second problem, i.e., the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds. The methodology is new because (i) it imposes its stochastic directly on the evolution of the forward rate curve, (ii) it does not require an inversion of the term structure to eliminate the market prices of risk from contingent claim values, and (iii) it has a stochastic spot rate process with multiple stochastic factors influencing the term structure. The model can be used to consistently price (and hedge) all contingent claims (American or European) on the term structure, and it is derived from necessary and (more importantly) sufficient conditions for the absence of arbitrage. The arbitrage pricing models of Vasicek (1977), Brennan and Schwartz (1979), Langetieg (1980), and Artzner and Delbaen (1988) all require an IFormerly titled Bond Pricing and the Term Structure of Interest Rates: A New Methodology.

Dai and Singleton (2002) and Duffee (2002) show that there is a tension in affine term structure models between matching the mean and the volatility of interest rates. This article examines whether this tension can be solved by an alternative parametrization of the price of risk. The empirical evidence suggests that, first, the examined parametrization is not sufficient to solve the mean-volatility tension. Second, the usual result in the estimation of affine models, indicating that some of the state variables are extremely persistent, may have been caused by the lack of flexibility in the parametrization of the price of risk. Term structure models have several uses, including pricing fixed-income derivatives, managing the risk of fixed-income portfolios, and detecting relationships between the term structure of interest rates and macrovariables such as inflation and consumption. To perform well in these tasks, term structure models must be numerically and econometrically tractable while matching the empirical properties of the term structure movements. At least two empirical properties of the term structure of interest rates have been well established by financial economists over the years [see Dai and Singleton (2003) for a survey]. First, the term premium, or the expected excess return of Treasury bonds, has a high time variability. Second, the volatility of interest rates is time varying. These two properties are so prominent in the data that they will be referred to as stylized facts. While these two stylized facts are very well established in the empirical literature, affine term structure models are thoroughly discussed in the theoretical literature. Affine models are those in which the yield of zero coupon bonds are affine functions of the model state variables. Classic

Forward and futures rates are frequently used as measures of market expectations. In this paper we apply standard forecast efficiency tests, and some newer exact sign and rank tests, to a wide range of forward and futures rates, and in this way test whether these are in fact rational expectations of future actual prices. The forward and futures rates that we study under a common methodology include foreign exchange forward rates, U.S. and foreign interest rate futures and forward rates, oil futures and natural gas futures. For most, but not all, of these instruments, we find that we can reject the hypothesis that the forward or futures rates are rational expectations of actual future prices. It is well known that foreign exchange forward rates give less accurate forecasts than a random walk, but we show that this is also true for some interest rate futures and forward rates. We conclude that forward and futures prices are not generally pure measures of market expectations: they are also heavily affected by the market price of risk.

The Information Content of Forward and Futures Prices: Market Expectations and the Price of Risk