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We consider a convergence model of interest rates, in which the behaviour of the domestic instantaneous interest rate (so called short rate) depends on the short rate in a monetary union that the country is going to join. The short rate in the monetary union is modelled by a two-factor model, which leads to a three-factor model for the domestic rate. In this setting, term structures of interest rates are computed from bond prices, which are obtained as solutions to a parabolic partial differential equation. A closed-form solution is known only in special cases. An analytical approximation formula for the domestic bond prices has been proposed, with the error estimate only for certain parameter values, when the solution has a separable form. In this paper, we derive the order of accuracy in the general case. We also study a special case, which makes it possible to model the phenomenon of negative interest rates that were observed in the previous years. It turns out that it leads to a higher accuracy than the one achieved in the general case without restriction on parameters.

It is common for a corporate bond to include a call provision that gives the issuing company an option to call, or redeem, the bond at some prespecified set of call prices before the stated maturity date. Since the option is embedded in the bond, it is not traded publicly and thus its value is unknown to bondholders. This study is aimed to price these embedded options and their related bonds, both callable and noncallable, using the binomial method such that the method is set up to approximate the evolution of the short rate. Using reasonable values for the relevant factors and parameters, our results show that the prices of the options and the two types of bonds are noticeably affected by such factors and parameters as the maturity of the bonds, the coupon, the call price, the volatility of the short rate, and the initial short rate.

In this paper, a time-consistent and arbitrage-free state space for the one-, two-, and three-factor Vasicek models for long-term bonds is constructed. To account for the uncertainty in long-term bond yields, we propose a stochastic time-dependent mean-reversion model. The state-space model allows for the computation of measurement errors from observed yields. Appropriate state and measurement linear equations are derived to allow the use of the Kalman filter for model implementation. Based on weekly South African Government Bonds from February 2010 to February 2021, we give parameter estimates for the one-factor, two-factor, and three-factor models. The results from the study show that the developed model can fit the term structure of very long-term bonds. [ABSTRACT FROM AUTHOR]

This paper aims to simulate portfolio decisions under uncertainty when the diffusion parameters of the risky asset and short rate paid for a bond are both modulated by a time-inhomogeneous Markov chain, with transition probabilities dependent on states, time, and asset prices. To do this, we first found closed-form solutions of the corresponding utility-maximization problem, which solves a rational consumer that makes portfolio and consumption decisions by using the corresponding infinitesimal generator associated with the Markov chain. Subsequently, as an illustration of the theoretical results obtained, several scenarios were simulated for the Mexican case. The expected economic policy was inferred from announced monetary policy decisions regarding the reference rate and possible changes in trend due to the lack of fiscal stimuli. Under this framework, states were defined from the current and expected economic policies, and transition probabilities were expressed in terms of the ratio between the prices of the risky asset and the bond. It should be noted, as far as the authors know, that no analytical solutions are known in the literature for the case of Markov-modulated time-inhomogeneous chains with transition probabilities that, themselves, are stochastic processes. [ABSTRACT FROM AUTHOR]

We study an information asymmetry problem in a bond market. Especially we derive bond price dynamics of traders with different levels of information. We allow all information processes as well as the short rate to have jumps in their sample paths, thus representing more dramatic movements. In addition we allow the short rate to have instantaneous feedbacks from the current levels of itself and these information processes. A fully informed trader observes all information which affects the bond price while a partially informed trader observes only a part of it. We first obtain the bond price dynamic under the full information, and also derive the bond price of the partially informed trader using Bayesian filtering method. The key step is to perform a change of measure so that the dynamic under the new measure becomes computationally efficient. [ABSTRACT FROM AUTHOR]

A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein–Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula. With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model.

This study takes a comprehensive and unified approach to investigating the yield curve. Specifically, we begin from scratch with the derivation of a formula for the yield curve within the state-preference framework assuming that the short rate is subject to multiple sources of disturbance, then we explore in detail whether the formula can generate yield curves with different shapes similar to those observed in practice, and finally, by Monte Carlo simulation, we examine the performance (in terms of annualized returns) of four popular fixed-income strategies. Our study shows that the formula can generate yield curves with a wide variety of shapes, including the three typical shapes, fairly representative of those observed in actual financial market. In particular, our simulation results provide strong evidence that returns from a strategy are highly positively related to the degree to which the strategy takes advantage of the characteristics of the yield curve. [ABSTRACT FROM AUTHOR]

A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula.With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model. [ABSTRACT FROM AUTHOR]

Short rate models are formulated in terms of a stochastic differential equation for the instantaneous interest rate, so called short rate. The interest rates with other maturities, forming the term structure of interest rates, are then deter- mined by bond prices which are solutions to the partial differential equation. We study the Chan-Karolyi-Longstaff-Sanders model and estimate the dependence of volatility on the short rate using the observed term structures together with esti- mating the unobservable short rate process. Starting with minimizing the sum of squares of erros, we make two approximations of this original optimization problem: Firstly, we relax the constraints regarding zero short rates and allow only positive vales. Secondly, the partial differential equation for the bond prices has a closed form solution only in special cases, so we use an analytical approximation formula in a convenient form. Finally, we apply the proposed algorithm to real data. [ABSTRACT FROM AUTHOR]

We consider an individual or household endowed with an initial capital and an income, modeled as a linear function of time. Assuming that the discount rate evolves as an Ornstein-Uhlenbeck process, we target to find an unrestricted consumption strategy such that the value of the expected discounted consumption is maximized. Differently than in the case with restricted consumption rates, we can determine the optimal strategy and the value function. [ABSTRACT FROM AUTHOR]