General equilibrium pricing with multiple dividend streams and regime switching

In this paper, we investigate a regime switching Lucas economy in continuous time, with multiple dividend streams and labour income. We determine the asset prices in equilibrium in the economy with regime switching, and derive a system of partial differential equations for the asset prices and the short interest rate. The solutions for the endogenous short interest rate, the bond price and the yield of the bond are obtained. We also consider applications of the equilibrium model and show that the model implies a rich framework for the term structure of interest rates. We demonstrate how the regime switching economy helps to improve the model-implied annual excess rate of return. This assists in explaining the famous equity premium puzzle.     

Stock market bubbles, inflation and investment risk

This paper proposes an autoregressive regime-switching model of stock price dynamics in which the process creates pricing bubbles in one regime while error-correction prevails in the other. In the bubble regime the stock price depends negatively on inflation. In the error-correction regime it depends on the price-dividend ratio. We find that the probability of regime-switch depends on exogenous inflation and lagged price. The model is consistent with Shleifer and Vishny's theoretical noise trader and arbitrageur model and Modigliani's inflation illusion phenomenon. The results emphasize the importance of inflation and the price-dividend ratio when assessing investment risk.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Are regime-shift sources of risk priced in the market?

In this paper we develop a discrete-time pricing model for European options where the log-return of the underlying asset is subject to discontinuous regime shifts in its mean and/or volatility which follow a Markov chain. The model allows for multiple regime shifts whose risk cannot be hedge out and thus must be priced in option market. The paper provides estimates of the price of regime-shift risk coefficients based on a joint estimation procedure of the Markov regime-switching process of the underlying stock and the suggested option pricing model. The results of the paper indicate that bull-to-bear and bear-to-crash regime shifts carry substantial prices of risk. Risk averse investors in the markets price these regime shifts by assigning higher transition (switching) probabilities to them under the risk neutral probability measure than under the physical. Ignoring these sources of risk will lead to substantial option pricing errors. In addition, the paper shows that investors also price reverse regime shifts, like the crash-to-bear and bear-to-bull ones, by assigning smaller transition probabilities under the risk neutral measure than the physical. Finally, the paper evaluates the pricing performance of the model and indicates that it can be successfully employed, in practice, to price European options.     

Higher order asymptotic bond price valuation for interest rates with non-Gaussian dependent innovations

This paper considers the effect on zero-coupon bond price valuation when short rate model has non-Gaussian dependent innovations. Higher order asymptotic theory enables us to obtain the approximate bond price formula. Some numerical examples are presented, where the process of innovations follows particular model. These examples indicate non-Gaussianity and dependency of innovations have a great influence on zero-coupon bond price.     

Price discovery in Taiwan's foreign exchange market

This paper investigates the dynamics of price adjustments and the price discovery roles of two markets on Taiwan's foreign exchange, TFI and CFE. Results from the multivariate threshold model indicate prices are integrated nonlinearly. The roles of price discovery are asymmetric, depending on the size and sign of the price discrepancies between the two markets. In the lower regime of discrepancies, each market employs information from its counterpart and reacts to each other with different adjustment speeds. When the discrepancy is in the upper regime, CFE's role of price discovery is characterized by its exogenous behavior within the error-correction process.     

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.     

Can credit spreads help predict a yield curve?

In this paper we investigate whether information in credit spreads helps improve the forecasts of government bond yields. To do this, we propose and estimate a joint dynamic Nelson–Siegel (DNS) model of the U.S. Treasury yield curve and the credit spread curve. The model accounts for the possibility of regime changes in yield curve dynamics and incorporates a zero lower bound constraint on yields. We show that our joint model produces more accurate out-of-sample density forecasts of bond yields than does the yield-only DNS model. In addition, we demonstrate that incorporating regime changes and a zero lower bound constraint is essential for forecast improvements.     

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.     

Bubbles in the dividend–price ratio? Evidence from an asymmetric exponential smooth-transition model

Recent stock price movements have led to a re-examination of the present value model. An increasing belief is that although dividends and prices are indeed cointegrated, they may exhibit non-linear dynamics in the process of reversion. This paper implements an empirical model designed to capture two possible explanations for such non-linearity, namely transaction costs and noise traders. Utilising data from a number of countries we show that the dynamics of the log dividend yield are, first, characterised by an inner random walk regime, where the benefits of engaging in trade do not outweigh the costs and so the process moves randomly. Second, a reverting outer regime where the dynamics of reversion differ between positive and negative deviations, such that price rises greater than the level supported by dividends exhibit a greater degree of persistence than price falls relative to dividends.     

An interest rate model with a Markovian mean reverting level

Abstract

A two‐factor Vasicek model, where the mean reversion level changes according to a continuous time finite state Markov chain, is considered. This model could capture the behaviour of monetary authorities who normally set a reference rate which changes from time to time. We derive the term structure via the analytic expression of the bond price that involves a fundamental matrix. The validity of the bond price closed form solution is verified via the forward rate dynamics.     

Regime Shifts in Price‐Dividend Ratios and Expected Stock Returns: A Present‐Value Approach

We incorporate regime shifts in the mean of price‐dividend ratios into the present value model of van Binsbergen and Koijen (2010) who propose a latent variable approach to modeling expected returns and dividend growth rates. We find that accounting for regime shifts results in much lower persistence of expected returns and higher volatility of expected returns, and thus higher in‐sample predictability, when compared to the results from the van Binsbergen and Koijen (2010) model. We also show that the main source of the increase in the mean of price‐dividend ratios in the mid‐1990s is a decrease in the mean of expected returns.     

最优多因子仿射利率期限结构模型选择

在利用NS模型估计出市场即期利率的基础上,采用卡尔曼滤波方法对多因子Vasieck和CIR模型进行参数估计,最后运用蒙特卡罗模拟方法对交易所国债价格进行模拟,并与实际价格进行比较,进而确定了符合我们国债市场的最优多因子仿射利率期限结构模型。研究结果表明：多因子CIR模型对数据的拟合效果及对国债价格模拟效果要明显优于多因子Vasicek模型;对于多因子CIR模型而言,因子个数增加并没有提高模型的价格模拟效果;两因子CIR模型具有最优的国债价格模拟效果。     

Exchange rate regimes and asset prices

We study the implications of alternative exchange rate regimes for asset prices in a portfolio balance model motivated by the recent US-China experience. We establish that asset price responses to various shocks differ across a flexible regime and a -unilateral- peg but the differences for most shocks tend to be rather small. Moreover, while both monetary and public debt expansions have inflationary effects on equity prices, the latter's impact is stronger under a flexible exchange rate regime. These two findings suggest that a flexible USD/rimni rate would not have limited the recent asset price inflation in the US.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

Do green bonds and economic policy uncertainty matter for carbon price? New insights from a TVP-VAR framework

Green bond shocks and economic policy uncertainty are essential factors affecting macroeconomic development and green finance. In this paper, the time-varying parameter vector autoregressive (TVP-VAR) framework is used to analyze the monthly data of China from April 2014 to March 2022 and to investigate the dynamic impact of green bond shock and economic policy uncertainty on carbon prices. The results show that economic policy uncertainty and the impact of the green bond have significant time-varying and short-term effects on carbon price. In the short term, economic policy uncertainty has a significant positive impact on carbon price most of the time, while green bond has a significant negative impact on carbon price most of the time. Meanwhile, economic policy uncertainty and the impact of green bond on carbon price in Hubei and Guangdong are heterogeneous. In addition, we also use Bayesian VAR (BVAR) model to test the robustness of the results. Based on the research results, some policy suggestions are put forward, including improving the stability of economic policies, implementing green bond support policies, and speeding up the improvement of the national unified carbon emission trading market.     

Convexity theory for the term structure equation

We study the convexity and model parameter monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide sharp conditions on the model parameters under which the convexity of the price in the short rate is guaranteed. Under these conditions, the price is decreasing in the drift and increasing in the volatility of the short rate. We also study the convexity properties of the logarithm of the price and find simple conditions on the coefficients that guarantee that the price is log-convex or log-concave.      

The analysis and valuation of interest rate options

This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the Black-Scholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general, and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps.     

Analytical bounds for Treasury bond futures prices

The pricing of delivery options, particularly timing options, in Treasury bond futures is prohibitively expensive. Recursive use of the lattice model is unavoidable for valuing such options, as Boyle in J Finance 14(1):101?C113, (1989) demonstrates. As a result, the main purpose of this study is to derive upper bounds and lower bounds for Treasury bond futures prices. This study first shows that the popular preference-free, closed form cost of carry model is an upper bound for the Treasury bond futures price. Then, the next step is to derive analytical lower bounds for the futures price under one and two-factor Cox-Ingersoll-Ross models of the term structure. The bound under the two-factor Cox-Ingersoll-Ross model is then tested empirically using weekly futures prices from January 1987 to December 2000.     

Relative asset price bubbles

In models of financial bubbles, the price of a stock is typically unbounded, and this plays a fundamental role in the analysis of finite horizon local martingale bubbles. It would seem that price bubbles do not apply to a priori bounded risky asset prices, such as bond prices. To avoid this limitation, to characterize, and to identify bond price mispricings consistent with an absence of arbitrage, we develop the concept of a relative asset price bubble. This notion uses a risky asset’s price as the numéraire instead of the money market account’s value. This change of numéraire generates some interesting mathematical complexities because many important numéraires, including risky bonds, can vanish with positive probability over the model’s horizon.