# Discrete-time continuous-state interest rate models

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Office of the Comptroller of the Currency , Washington, DC
Interest rates -- Econometric mo
Classifications The Physical Object Statement by Michael A. Sullivan. Series Economic and policy analysis working paper ;, 2000-6, Economic and policy analysis working paper (2000 : Online) ;, 2000-6. Contributions United States. Office of the Comptroller of the Currency. LC Classifications HG2401 Format Electronic resource Open Library OL3390592M LC Control Number 2004620340

Discrete-Time Continuous-State Interest Rate Models. Michael A. Sullivan ∗ Risk Analysis Division, Comptroller of the Currency, E St. S.W.,Washington, DC OCC Economics Working Paper Abstract.

We show how to implement arbitrage-free models of the short-term interest rate in a. The prices are for options struck at par on a five-year bond paying annual coupons of 10 on a par value of European option prices are calculated using a continuous-time continuous-state model.

American option prices are calculated using a discrete-time continuous-state model with n= The interest rate parameters are a=, h=, and Cited by: 6. Discrete time allows approximate pricing of interest rate contingent claims that cannot be valued in continuous-time models.

It is usually associated with discrete states, with possible interest rates restricted to a limited number of outcomes, as in the lattice model of Hull and White ().

Current models of the interest rate are either continuous time-continuous state models, such as the Vasicek or Cox, Ingersoll, and Ross models, or discrete time-discrete state models, such as the. This paper shows how to implement arbitrage-free models of the short-term interest rate in a discrete time setting that allows a continuum of rates at any particular date.

Current models of the interest rate are either continuous time-continuous state models, such as the Vasicek or Cox, Ingersoll, and Ross models, or discrete time-discrete state models, such as the Hull and White model. Although discrete-time interest rate models are often introduced for computational purposes as a convenient approximation to the continuous-time situation, it is important to recognize that the theory can be developed in discrete time in an entirely satisfactory way in its own right, without reference to continuous time.

Let {t i} i=0,1,2. The bulk of the book describes a model with finitely many, discrete trading dates, and a finite sample space, thus it avoids the technical difficulties associated with continuous time models. The major strength of this book is its careful balance of mathematical rigor and intuition." Peter Lakner, New York University.

Downloadable. This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and pro- vides a link to equilibrium economics.

We require that the pricing kernel be consistent with a pair of axioms, one giving the inter-temporal relations for dividend-paying Discrete-time continuous-state interest rate models book sets, and the other ensuring the. duction to the theory of discrete time continuous state dynamic economic models.

The subsequent chapter is devoted to numerical methods that may be used to solve and analyze such models. Continuous State Dynamic Programming The discrete time, continuous state Markov decision model has the following. A survey of issues involving the specification and estimation of affine models set in continuous time is Piazzesi ().

Discrete-time models are discussed in detail in Backus, Foresi, and Telmer. paper, the fundamental models. Time theory to the interest rate models lecture schedule below zero coupon bonds comprising the mastering mathematical properties of returns, the field models. Them is based on interest rate models notes in small groups.

Main topics discussed for stochastic interest rate. discrete-time and a continuous-time model is the no-arbitrage relationship between bonds and capital. In discrete time the future marginal productivity of capital equals the real interest rate; in continuous time today’s marginal productivity of capital equals the real interest rate.

ECE/, State-Space Models and the Discrete-Time Realization Algorithm 5–2 We then preview the approach to generate the state-space models from the PDEs of the variables of interest: •We start by generating transfer functions for each PDE; •We then use the “discrete-time realization algorithm” to convert transfer functions to state-space form.

reasonable range. As the Vasicek process transformed into discrete time is still a continuous state space process we use the technique from Tauchen and Hussey () and as a result we get a process with discrete time–state space.

Once we obtain a discrete time–state process for real interest rate we can model bond prices as the expected. In this article, the ruin probability is examined in a discrete time risk model with a constant interest rate, in which the dependent claims are assumed to have a one-sided linear structure.

An explicit asymptotic formula is obtained for the ruin probability. Out-of-Sample Performance of Discrete-Time Spot Interest Rate Models Yongmiao H ONG Department of Economics and Department of Statistical Sciences, Cornell University, Ithaca, NY Department of Economics, Tsinghua University, Beijing, China ([email protected]) Haitao L I.

We will now consider one-factor models for the term structure of interest rates within a continuous-time framework. In particular, we will consider how to price bonds given a one-factor diffusion model for the risk-free rate,r(t).We will assume thatr(t) is an Itô process with stochastic differential equation (SDE).

dr(t=a(t) dt+ b(t) dW(t). whereW(t) is a standard Brownian motion under the. Discrete-time continuous-state interest rate models "We show how to implement arbitrage-free models of the short-term interest rate in discrete-time setting that allows continuum of rates at any particular date.

Discrete time allows approximate pricing of interest rate. This paper tests the popular continuous-time interest rate models for Chinese repo market to address what and how the interest rates change with the marketlization in China. Using Bandi ’s method, we get the functional nonparametric estimation of drift and diffusion terms and the local time of the process.

We find that the interest rates of China during the period from to are. model is a discrete time model with distinct number of periods, it allows an estimation of the value of an option by shrinking the size of the time period to as small as one desires.

This versatility gives the CRR model a comparative advantage over Black-Scholes when valuing certain derivatives. 7 Bonds and Interest Rate Models and Bond Pricing the bond price falls below its par value, and called apremium bond if other-wise.

Also, the market value of a bond will always approach its par value as maturity is approached.

### Description Discrete-time continuous-state interest rate models FB2

This is known as the pull-to-par phenomenon. uction to discrete-time models: Analysis of the time to a single event evel models for recurrent events and unobserved heterogeneity We divide by the width of the interval, t, to get a rate. h (t) is also known as the transition rate, the instantaneous risk, or the failure rate.

Discrete-Time Versions of Continuous-Time Interest Rate Models Steven L Heston The Journal of Fixed Income Sep5 (2) ; DOI: /jfi The book concludes with the use of the binomial model to introduce interest rate models and the use of the Markov chain model to introduce credit risk.

This volume is designed in such a way that, among other uses, makes it useful as an undergraduate course.

### Details Discrete-time continuous-state interest rate models FB2

circumstances (for example, a one-sector model is a key part of the restriction). Applications Growth The Solow growth model is an important part of many more complicated models setups in modern macroeconomic analysis.

Its ﬂrst and main use is that of understanding why output grows in the long run and what forms that growth takes. Statistics and data management sciences require a deep understanding of what is the difference between discrete and continuous data set and variables.

The similarity is that both of them are the two types of quantitative data also called numerical data. the theory and the real world relies on an implicit belief that the discrete time model approximates the continuous time model.

This suggests that if the original theory were value of its return over an infinite horizon at a given interest rate. This problem has two appreciated book by G. Evans  treats problems related to the ones. The Solow Model in Discrete Time Fundamental Law of Motion of the Solow Model Fundamental Law of Motion of the Solow Model I Recall that K depreciates exponentially at the rate δ, so K (t +1) = (1 δ)K (t)+I (t), (6) where I (t) is investment at time t.

From national income accounting for a closed economy, Y (t) = C (t)+I (t), (7). In this case, the underlying continuous-time model is the unique representation for discrete-time models. To maintain the same level of noise after interpolating the noise signal, scale the noise spectrum by T N e w T O l d, where T new is the new sample time and T.

Effects of high interest rates on Maryland communities: hearings before the Subcommittee on Investment, Jobs, and Prices of the Joint Economic Committee, Congress of the United States, Ninety-seventh Congress, first session, Aug September 1, 2, 3, and 4.

Usually continuous time models are good because they allow for closed form expressions for the solution (where discrete time models do not allow). However, if a given model in continuous time does not allow for a closed form solution then you are better off going to discrete time as it is easier to solve numerically using grids for state.The graphical method.

The graphical method is a great way of intuitively grasping discrete-time models with one variable such as the logistic growth model.