*The Business Professor*, updated September 5, 2019, last accessed May 30, 2020, https://thebusinessprofessor.com/lesson/vasicek-interest-rate-model-definition/.

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### Vasicek Interest Rate Model Definition

The Vasicek interest rate model is a model that exhibits fluctuations or movements in interest rate. This mathematical model tells how factors such as market risk, time, and equilibrium price affect the interest rate movements. Here, the interest rate responds towards the average of the factors over a period of time. Most importantly, it ascertains the point that will mark the end of interest rates at the end of a specific time period, provided a specific market risk factor, volatility in the current market, and the average interest rate value in the long term.

However, one must know that this equation has the ability to evaluate only one market risk factor at one point of time. This model is considered for knowing the value of interest rate futures, as well as for identifying the prices of several bonds that are not easy to value.

### A Little More on What is The Vasicek Interest Rate Model

The Vasicek interest rate model ascertains the value of interest rate by considering the following equation:

drt = a (b − rt) dt + σdWt

**where:**

W stands for random market risk (displayed by a Wiener process)

t stands for time period *a*

(b−rt) stands for the Expected change in the interest rate at time t (the drift factor)

*a* stands for the speed of the reversion to the mean

B stands for the long-term level of the mean

σ stands for volatility at time t

*d *stands for variable derivative that follows it

### More About The Vasicek Interest Rate Model

The concept of Vasicek interest rate model is applied to financial economics so as to make predictions for prospective pathways in case of interest rate fluctuates ahead. This model is based on the belief that the random market fluctuations have a significant effect on the interest rate movements. In case, the market fluctuations are zero, or when *d*Wt is equal to 0, there is no movement in the interest rate, that means rt = b. When rt is less than b, the drift factor turns out to be positive. This positive value signifies that the rate of interest will go up in the direction of equilibrium.

Though this model is impressive when it comes to predicting financial equations, but it is recently known that the interest rate under this model doesn’t go beyond zero, or doesn’t turn out to be negative. This drawback was ascertained during the huge financial crisis. Several models such as the Cox-Ingersoll-Ross model and the exponential Vasicek model which were formulated after the Vasicek model, overcame this issue for predicting the movements in interest rates.

### References for “**Vasicek Interest Rate Model****”**

https://www.investopedia.com › Economy › Monetary Policy › Interest Rates

https://en.wikipedia.org/wiki/Vasicek_model

https://fin.gc.ca/pub/pdfs/wp2003-17e.pdf

### Academic research for “**Vasicek Interest Rate Model****”**

Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework, Cordoni, F., & Di Persio, L. (2015). Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework. *Infinite Dimensional Analysis, Quantum Probability and Related Topics*, *18*(03), 1550022.

[HTML] Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making, Nowak, P., & Romaniuk, M. (2017). Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making. *Soft Computing*, *21*(10), 2575-2597.

Pricing formulae for European options under the fractional Vasicek interest rate model, Huang, W. L., Tao, X. X., & Li, S. H. (2012). Pricing formulae for European options under the fractional Vasicek interest rate model. *Acta Mathematica Sinica (in Chinese)*, *55*(2), 219-230.

Valuation for an American continuous-installment put option on bond under Vasicek interest rate model, Huang, G., Deng, G., & Huang, L. (2009). Valuation for an American continuous-installment put option on bond under Vasicek interest rate model. *Advances in Decision Sciences*, *2009*.

Analysis of Pricing European Call Foreign Currency Option Under the Vasicek Interest Rate Model [J], Genxin, X. U. (2006). Analysis of Pricing European Call Foreign Currency Option Under the Vasicek Interest Rate Model [J]. *Journal of Tongji University (Natural Science)*, *4*.

[PDF] Vasicek interest rate model, Herrala, N. (2009). Vasicek interest rate model.

[CITATION] Study on European Contingent Claims under Vasicek Interest Rate Model with the Function Coefficients [J], WANG, Y. W., LI, S. P., & JIANG, H. (2008). Study on European Contingent Claims under Vasicek Interest Rate Model with the Function Coefficients [J]. *Journal of Gansu Sciences*, *1*.

[PDF] Pricing European Equity Options Based On Vasicek Interest Rate Model, Ma, Y., & Wen, H. (2009). Pricing European Equity Options Based On Vasicek Interest Rate Model.

[PDF] Monte Carlo Simulation for Vasicek Interest Rate Model Parameters, AYRANCI, G., & Özgürel, B. (2015). Monte Carlo Simulation for Vasicek Interest Rate Model Parameters.

[PDF] Cholesky Decomposition for the Vasicek Interest Rate Model, Al-Saadony, M., Hewson, P., & Stander, J. (2013). Cholesky Decomposition for the Vasicek Interest Rate Model. *International Journal of Statistics and Probability*, *2*(4), 22.