# Vasicek Interest Rate Model

- Vasicek Interest Rate Model
- A method of modeling interest rate movement that describes the movement of an interest rate as a factor of market risk, time and equilibrium value that the rate tends to revert towards. This stochastic model is often used in the valuation of interest rate futures.

The Vasicek interest rate model values the instantaneous interest rate using the following equation:

dr_{t }= a(b-r_{t})dt +sdW_{t}

Where *Wt* is the random market risk (represented by the Wiener process)

*t* represents time

*a(b-r*_{t}) represents the expected change in the interest rate at *t* (drift factor)

*a* is the speed of reversion

*b* is the long-term level of the mean

*s* is the volatility at the time

The Vasicek interest rate model states that the movement of interest rates is affected only by random market movements. In the absence of market shocks (i.e., when dW_{t }= 0) the interest rate remains constant (r_{t} = b). When r_{t} < b, the drift factor becomes positive, indicating that the interest rate will increase towards equilibrium.

*Investment dictionary.
Academic.
2012.*

### Look at other dictionaries:

**Short rate model** — In the context of interest rate derivatives, a short rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate.The short rateThe short rate, usually written r t… … Wikipedia

**Vasicek model** — In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one factor model (short rate model) as it describes interest rate movements as driven by only one source of market risk. The model… … Wikipedia

**Cox-Ingersoll-Ross model** — The Cox Ingersoll Ross model in finance is a mathematical model describing the evolution of interest rates. It is a type of one factor model (Short rate model) as describes interest rate movements as driven by only one source of market risk. The… … Wikipedia

**Cox–Ingersoll–Ross model** — Three trajectories of CIR Processes In mathematical finance, the Cox–Ingersoll–Ross model (or CIR model) describes the evolution of interest rates. It is a type of one factor model (short rate model) as it describes interest rate movements as… … Wikipedia

**Hull-White model** — In financial mathematics, the Hull White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no arbitrage models that are able to fit today s term structure of interest rates. It is relatively… … Wikipedia

**Chen model** — In finance, the Chen model is a mathematical model describing the evolution of interest rates. It is a type of three factor model (short rate model) as it describes interest rate movements as driven by three sources of market risk. It was the… … Wikipedia

**Yield curve** — This article is about yield curves as used in finance. For the term s use in physics, see Yield curve (physics). Not to be confused with Yield curve spread – see Z spread. The US dollar yield curve as of February 9, 2005. The curve has a typical… … Wikipedia

**List of finance topics** — Topics in finance include:Fundamental financial concepts* Finance an overview ** Arbitrage ** Capital (economics) ** Capital asset pricing model ** Cash flow ** Cash flow matching ** Debt *** Default *** Consumer debt *** Debt consolidation ***… … Wikipedia

**Outline of finance** — The following outline is provided as an overview of and topical guide to finance: Finance – addresses the ways in which individuals, businesses and organizations raise, allocate and use monetary resources over time, taking into account the risks… … Wikipedia

**Zinsstrukturmodelle** — Mit Hilfe von Zinsstrukturmodellen möchte man die empirisch beobachtbaren Zusammenhänge zwischen Zinssätzen unterschiedlicher Laufzeiten durch möglichst wenige Zinsstrukturfaktoren erklären, welche idealerweise voneinander unabhängig sind. Diese… … Deutsch Wikipedia