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Empirical modeling of the yield curve is often inconsistent with absence of arbitrage. In fact, many parsimonious models, like the popular Nelson-Siegel model, are inconsistent with absence of arbitrage. In other cases, arbitrage-free models are often used in inconsistent ways by recalibrating parameters that are assumed constant. For these cases, this paper introduces an arbitrage smoothing device to control arbitrage errors that arise in fitting a sequence of yield curves. The device is applied to the US term structure for the family of Nelson-Siegel curves. It is shown that the arbitrage smoothing device contributes to parameter stability and smoothness.

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

In this paper, we show how to construct dynamic forward rate models in terms of exogenously specified eigenfunctions (or factor loadings). We also show how to link forward rate models with different number of driving Brownian motions to each other in a way consistent with the implied eigenfunctions. Finally, we discuss how to best parameterize the models in the sense of maximizing the number of free parameters for a given set of eigenfunctions.

We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates. In particular, we show that the shapes normal, inverse, humped, dipped and hump-dip are always attainable. In certain parameter regimes, up to four additional shapes can be produced. Our results apply to both forward and yield curves and show that the correlation and the difference in mean-reversion speeds of the two factor processes play a key role in determining the scope of attainable shapes. The key mathematical tool is the theory of total positivity, pioneered by Samuel Karlin and others in the 1950s.

In this paper, we analyze the shapes of forward curves and yield curves that can be attained in the two-factor Vasicek model. We show how to partition the state space of the model, such that each partition is associated to a particular shape (normal, inverse, humped, etc.). The partitions and the corresponding shapes are determined by the winding number of a single curve with possible singularities and self-intersections, which can be constructed as the envelope of a family of lines. Building on these results, we classify possible transitions between term structure shapes, give results on attainability of shapes conditional on the level of the short rate, and propose a simple method to determine the relative frequency of different shapes of the forward curve and the yield curve.

Estimation of benchmark yield curve in developing markets is often influenced by liquidity concentration. Based on an affine term structure model, we develop a long run liquidity weighted fitting method to address the trading concentration phenomenon arising from horizon-induced clientele equilibrium as well as information discovery. Specifically, we employ arguments from models of liquidity concentration and benchmark security information. After examining time series behavior of price errors against our fitted model, we find results consistent with both the horizon and information hypotheses. Our evidence indicates that trading liquidity carries information effect in the long run, which cannot be fully captured in the short run. Trading liquidity plays a key role in long run term structure fitting. Markets for liquid benchmark government bond issues collectively form a long term equilibrium. Compared with previous studies, our results provide a robust and realistic characterization of the spot rate term structure and related price forecasting over time, which in turn help portfolio investment of fixed income and long run pricing of financial instruments.

This paper proposes a novel state-space approach to explain stock market dynamics driven by different types of trading, which leads to a new promising scheme for proactive risk management in financial investment. Particularly, it is assumed that the current price changes are formulated through daily trading by multiple types of traders, each of whom follows a specific investment strategy based on technical indicators and a fuzzy logic using past data of stock prices, volumes and yield curves. Moreover, the current price changes are represented by a linear combination of those multiple trading types, where the coefficients corresponding with the size of impact on the price changes are regarded as time-varying state variables to be sequentially estimated under a state-space framework. Thereby, this work develops a new factor decomposition method on price changes from a perspective of different traders’ demand and supply to analyze the current situations and potential risks in financial markets. In empirical experiments, it is shown that the implementation of particle filtering algorithm makes it possible to replicate market price changes. Further, new signals based on the estimated states are developed, which are applied to proactive risk management in financial investment. Especially, it has been found that the demands of yield curve-based traders subtracting those of trend-followers could be a promising signal of stock market crashes, which has successfully enhanced simple buy-and-hold strategy of SP, as well as constant proportion strategies.

Examining monthly data from May of 1985 to May of 2008, we find that increases in Chinese purchases of U.S government debt lead to decreases in Treasury yields. The effect is stronger as the maturity increases: a one percent increase in purchases of U.S. Treasuries by Chinese investors lowers the two-year (ten-year) Treasury yield by 10 to 38 basis points (39 to 55 basis points) on average, ceteris paribus . Overall, the demand-side variable capturing Chinese purchases of U.S. Treasuries improves the cointegrating properties of U.S. interest rates. In-sample and out-of-sample forecasts reinforce that the model with Chinese purchases greatly outperforms basic models of the yield curve. This study has implications for the business world since we document that Chinese investors contribute to lower U.S. Treasury yields and thus to lower U.S. interest rates in general.

This study has two main purposes. The paper first derives the shift function and bond price formulas for the Hull-White extended Vasicek model, which simultaneously fits current yield curve and volatility curve. The result of Kijima and Nagayama (1994) is extended by allowing the instantaneous standard deviation of the short rate to be time-dependent, which permits the closed-form formulas for the shift function and bond price to be derived. By applying these formulas, the shift function and the bond price at each node can be obtained without calculation on a tree. Some numerical examples are given to demonstrate the effectiveness of these formulas. The second purpose of this study is to discuss how to estimate the “unobservable” time-dependent standard deviation of the short rate from the “observable” spot rate volatility curve. The theoretical relation between the time-dependent standard deviation of the short rate and the volatility curve of the spot rate is derived. This paper demonstrates this relation for two different functional forms of the time-dependent standard deviation of the short rate, and also shows how to estimate the time-dependent standard deviation via this relation.

Models of forward interest rates often use high-dimensional Brownian motions to capture imperfect correlations between near term and long term rates. Several statistical analyses suggest the practicality of using a simpler model. Principal component analyses reveal a pattern of correlations which can be essentially explained with a properly chosen three-dimensional Brownian motion.

We describe the well known mathematical difficulties in implementing this approach, and we provide a substantial resolution of these obstacles. By focusing on no-arbitrage models using a long bond as a numeraire, we avoid problems with infinities which appeared in conventional risk-neutral models.