Monetary policy regimes: Implications for the yield curve and bond pricing

We develop a multivariate dynamic term structure model, which takes into account the nonlinear (time-varying) relation between interest rates and the state of the economy. In contrast to the classical term structure literature, in which nonlinearities are captured by increasing the number of latent state variables or by latent regime shifts, in our no-arbitrage framework the regimes are governed by thresholds and are directly linked to economic fundamentals. Specifically, starting from a simple monetary policy model for the short rate, we introduce a parsimonious and tractable model for the yield curve, which takes into account the possibility of regime shifts in the behavior of the Federal Reserve. In our empirical analysis, we show the merit of our approach three dimensions: interpretable bond dynamics, accurate short end yield curve pricing, and yield curve implications.     

Functional gradient descent for financial time series with an application to the measurement of market risk

The estimation and forecast of the volatility matrix are two of the main tasks of financial econometrics since they are essential ingredients in many practical applications. Unfortunately the use of classical multivariate methods in large dimensions is difficult because of the curse of dimensionality. We present a general semiparametric technique, based on functional gradient descent (FGD) and able to overcome most problems associated with a multivariate GARCH-type estimation. By testing the accuracy of the volatility estimates for the measurement of market risk on real data we provide empirical evidence of the strong predictive potential of the FGD approach, also in comparison to other standard methods.     

Binary interest rate sensitivities of emerging market corporate bonds

We develop a framework to assess interest rate sensitivities of emerging market corporate debt. Our analysis, based on yield indexes, is applied to investment grade and high yield portfolios. We reach beyond correlation-based analyses of interest rate sensitivity and keep our scope centered at capital gains of emerging market corporates and U.S. government bonds portfolios. Our empirical analysis spans over the period 2002–2015. We address interest rate sensitivity of assets during the ignition, apogee, and the aftermath of the global financial crisis. Based on historical data series, we evidence that the emerging market corporate bonds exhibit two different regimes of sensitivity to interest rate changes. We observe switching from a positive sensitivity under the normal market conditions to a negative one during distressed phases of business cycles and provide economical explanations of such phenomena. We show that emerging market corporate bonds, which on average could appear rather insensitive to the interest rate risk, in fact, present binary interest rate sensitivities. This research sheds light on how financial institutions may approach interest rate risk management including the downside risk hedge. Our findings allow banks and financial institutions to optimize economic capital under Basel III regulatory capital rules.     

Stressing correlations and volatilities — A consistent modeling approach

We propose a new approach to the definition of stress scenarios for volatilities and correlations. Correlations and volatilities depend on a common market factor, which is the key to stressing them in a consistent and intuitive way. Our approach is based on a new asset price model where correlations and volatilities depend on the current state of the market, which captures market-wide movements in equity-prices. For sample portfolios we compare correlations and volatilities in a normal market and under stress and explore consequences for value-at-risk.We compare our modeling approach with multivariate GARCH models. For all data analyzed our model performs well in capturing the dynamics of volatilities and correlations under stress.     

The value of convexity: a theoretical and empirical investigation

We explore from a theoretical and an empirical perspective the value of convexity in the US Treasury market. We present a quasi-model-agnostic approach that is rooted in the existence of some affine model capable of recovering with good accuracy the market yield curve and covariance matrix. As we show, at least one such model exists, and this is all we require for our results to hold. We show that, as a consequence, the theoretical ‘value of convexity’ purely depends on observable features of the yield curve, and on statistically determinable yield volatilities. We then address the question of whether the theoretical convexity is indeed correctly reflected in the shape of the yield curve. We present empirical results about the predictive power of a strategy based on the discrepancies between the theoretical and the predicted value of convexity. By looking at 30 years of data, we find that neither the strategy of being systematically long or short convexity (and immunized against ‘level’ and ‘slope’ risk) would have been profitable. However, a conditional strategy that looks at the difference between the ‘implied’ and the statistically estimated value of convexity would have identified extended periods during which the proposed approach would have delivered attractive Sharpe Ratios.     

Yield curve modeling and forecasting using semiparametric factor dynamics

Using a dynamic semiparametric factor model (DSFM) we investigate the term structure of interest rates. The proposed methodology is applied to monthly interest rates for four southern European countries: Greece, Italy, Portugal and Spain from the introduction of the Euro to the recent European sovereign-debt crisis. Analyzing this extraordinary period, we compare our approach with the standard market method – dynamic Nelson–Siegel model. Our findings show that two nonparametric factors capture the spatial structure of the yield curve for each of the bond markets separately. We attributed both factors to the slope of the yield curve. For panel term structure data, three nonparametric factors are necessary to explain 95% variation. The estimated factor loadings are unit root processes and reveal high persistency. In comparison with the benchmark model, the DSFM technique shows superior short-term forecasting in times of financial distress.     

人口学特征与利率期限结构:老年社会平缓的收益率曲线

本文将刻画人口结构的生命周期模型引入消费-资本资产定价模型,考察人口结构对利率期限结构的影响。模型表明,人口结构及其家庭生命周期特征不仅决定利率水平,而且将通过人对债券期限的不同偏好,影响利率期限结构。少年人口占比对利率期限结构的影响为正,中年和老年人口占比的影响为负。相比少年人口,中老年人口更偏好长期债券,使长期收益率下降,期限结构的斜率更为平缓。基于全球数据的经验研究验证了这一结论。少年人口占比增加期限利差,中老年人口占比则起反向作用。因此,在年长的经济体中,期限利差更小,呈现更平缓的收益率曲线特征。在更换人口结构变量、期限利差变量、估计方法、赋权样本和处理遗漏变量后,结果表现稳健。本文从人口学视角拓宽了利率期限结构的决定因素,揭示了老年经济体可能面临一个平缓的收益率曲线,而这说明老龄化还可能通过抑制短期投机和促进长期投资来提高长期经济发展质量。     

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.     

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.     

On the Effect of Bank of Japan’s Outright Purchase on the JGB Yield Curve

This paper examines an impact of Bank of Japan (BOJ)’s outright purchase on the Japanese government bond (JGB) yield curve. Particularly, we develop a simple state space model, which incorporates new factors regarding the BOJ’s announcement for its outright purchase and the current market outstanding with standard level and spread factors. Based on the model with a filtering method, we also implement an empirical analysis with time series of the BOJ’s announcement records during 2014/10/22–2017/8/3 in the quantitative–qualitative easing period to estimate the sensitivities of interest rates against the changes in the market expectation for the net supply with each sector of JGB. We expect the current work provides a basis for considering quantitative effects on the term structure by BOJ’s policy changes such as termination or significant reduction of the BOJ’s outright purchase. For instance, our scenario analysis shows substantial increase in the 30 year yield with widening of 20–30 year spread.     

Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models

A widespread approach in the implementation of asset pricing models is based on the periodic recalibration of its parameters and initial conditions to eliminate any conflict between model-implied and market prices. Modern no-arbitrage market models facilitate this procedure since their solution can usually be written in terms of the entire initial yield curve. As a result, the model fits (by construction) the interest rate term structure. This procedure is, however, generally time inconsistent since the model at time t = 0 completely specifies the set of possible term structures for any t > 0. In this paper, we analyze the pros and cons of this widespread approach in pricing and hedging, both theoretically and empirically. The theoretical section of the paper shows (a) under which conditions recalibration improves the hedging errors by limiting the propagation of an initial error, (b) that recalibration introduces time-inconsistent errors that violate the self-financing argument of the standard replication strategy. The empirical section of the paper quantifies the trade-off between (a) and (b) under several scenarios. First, we compare this trade-off for two economies with and without model specification error. Then, we discuss the trade-off when the underlying economy is not Markovian.     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

The intraday multivariate structure of the Eurofutures markets

We investigate the multivariate intraday structure in interest rates, focusing on implied forward rates from Eurofutures contracts. Since futures markets are the most liquid for interest rate instruments and they yield high-quality intraday data, it is somehow surprising that their intraday behavior has not been thoroughly studied in the literature.We find interesting similarities with the foreign exchange market: scaling law, intraday patterns, all of which point to the heterogeneity of market participants. Other properties like asymmetric causal information flow between fine and coarse volatilities for the same time series are present in our data. There are also lead–lag correlations across the term structure of implied forward rates, but they tend to disappear as markets mature.A principal component analysis of the short end of the yield curve allows us to determine the most important components and to reduce the number of time series needed to describe the term structure. We find the decomposition rather stable over time. The first component, which describes the curve level, shows an asymmetry in the information flow between volatilities of different time resolution, i.e., the coarse-grained volatility predicts the fine-grained volatility better than the other way around, as observed in the foreign exchange market. The remaining components do not show such an effect, having instead significant negative autocorrelations for the time series themselves. A heterogeneous autoregressive conditional heteroskedasticity (HARCH) model is estimated for the first component and the impact of different market agents is discussed.     

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

This paper specifies a multivariate stochasticvolatility (SV) model for the S & P500 index and spot interest rateprocesses. We first estimate the multivariate SV model via theefficient method of moments (EMM) technique based on observations ofunderlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S & P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premiumof stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficientin modeling short-term kurtosis of asset returns, an SV model withfatter-tailed noise or jump component may have better explanatory power.     

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.     

Representative Interest Rate Scenarios

Abstract

This paper suggests a possible flexible solution to the time and resource problems of running a large number of stochastic interest rate scenarios, that is, selecting a representative subset. Each interest rate scenario consists of 30 future spot yield curves, in which 12 points are specified on each curve. The distribution of the scenarios is approximated by the subset, and each scenario in the subset has equal weight. The method is independent of the interest rate generator used. Modeling research may be more similar to experimental or laboratory science than to a mathematical science. This paper presents a new tool to evaluate.     

Computation of Multivariate Barrier Crossing Probability and its Applications in Credit Risk Models

Abstract

In this paper we consider computational methods of finding exit probabilities for a class of multivariate diffusion processes. Although there is an abundance of results for one-dimensional diffusion processes, for multivariate processes one has to rely on approximations or simulation methods. We adopt a Large Deviations approach to approximate barrier crossing probabilities of a multivariate Brownian Bridge. We use this approach in conjunction with simulation methods to develop an efficient method of obtaining barrier crossing probabilities of a multivariate Brownian motion. Using numerical examples, we demonstrate that our method works better than other existing methods. We mainly focus on a three-dimensional process, but our framework can be extended to higher dimensions. We present two applications of the proposed method in credit risk modeling. First, we show that we can efficiently estimate the default probabilities of several correlated credit risky entities. Second, we use this method to efficiently price a credit default swap (CDS) with several correlated reference entities. In a conventional approach one normally adopts an arbitrary copula to capture dependency among counterparties. The method we propose allows us to incorporate the instantaneous variance-covariance structure of the underlying process into the CDS prices.     

The effect of interest rate volatility and equity volatility on corporate bond yield spreads: A comparison of noncallables and callables

This research investigates the impact of interest rate volatility upon corporate bond yield spreads. We first consider the impact of interest rate volatility upon noncallable bond spreads. Because greater interest rate volatility likely increases the volatility of the firm's debt, we hypothesize that the relation will be positive. Given that we do find a positive relation, we thus investigate whether the positive effect of interest rate volatility on yield spreads is stronger or weaker for callable bonds. We find that the effect is weaker for callable bonds. This result indicates that there is a negative relation between default spreads and call spreads, which is consistent with the theory of Acharya and Carpenter (2002), but in contrast to the theory of King (2002). Furthermore, our results for the relationship between equity volatility and yield spread tend to support Acharya and Carpenter (2002) more than King (2002).     

Bayesian approach to yield curve modelling with application to the simulation of EMU environments: generating scenarios by modelling yield curve movements

A Bayesian approach to yield curve modelling is developed where information on the current and recent yield curves is used to generate yield curve scenarios, and a model is proposed that generates return distribution for bonds. The predictive power of the model is developed by comparing out-of-sample lagged realized yields with forecast yields, and it is demonstrated that the returns generated by this scenario approach and those generated using the standard time series approach are consistent. The model is applied to pre-EMU and post-EMU environments. This paper assesses the implications of different assumptions on the early post-EMU environment for international bond portfolio selection, as well as the immediate short-term effect of EMU on risk and return.