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Vasicek Interest Rate Formula

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The Derivative of Short Rate is the rate that applies to an infinitesimally short period of time. Check FAQs

dr t = a \cdot (b - r t) \cdot d \cdot t + σ \cdot d \cdot W t

dr_t - Derivative of Short Rate?a - Speed of Mean Reversal?b - Long Term Mean?r_t - Short Rate?d - Derivatives?t - Time Period?σ - Volatility at Time?W_t - Random Market Risk?

Vasicek Interest Rate Example

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Here is how the Vasicek Interest Rate equation looks like with Values.

Here is how the Vasicek Interest Rate equation looks like with Units.

Here is how the Vasicek Interest Rate equation looks like.

3675 = 12 \cdot (6 - 5) \cdot 50 \cdot 2 + 9 \cdot 50 \cdot 5.5

3675 = 12 \cdot (6 - 5) \cdot 50 \cdot 2 + 9 \cdot 50 \cdot 5.5

3675 = 12 \cdot (6 - 5) \cdot 50 \cdot 2 + 9 \cdot 50 \cdot 5.5

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Vasicek Interest Rate Solution

Follow our step by step solution on how to calculate Vasicek Interest Rate?

FIRST Step Consider the formula

dr t = a \cdot (b - r t) \cdot d \cdot t + σ \cdot d \cdot W t

Next Step Substitute values of Variables

∴

dr t = 12 \cdot (6 - 5) \cdot 50 \cdot 2 + 9 \cdot 50 \cdot 5.5

Next Step Prepare to Evaluate

∴

dr t = 12 \cdot (6 - 5) \cdot 50 \cdot 2 + 9 \cdot 50 \cdot 5.5

LAST Step Evaluate

∴

dr t = 3675

Vasicek Interest Rate Formula Elements

Variables

Derivative of Short Rate

The Derivative of Short Rate is the rate that applies to an infinitesimally short period of time.

Symbol: dr_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Derivative of Short Rate

Speed of Mean Reversal

Speed of Mean Reversal refers to the speed at which the interest rate returns to its long-term mean level.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Speed of Mean Reversal

Long Term Mean

The Long Term Mean level of the interest rate, calculated based on historical data refers to occurring over or involving a relatively long period of time.

Symbol: b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Long Term Mean

Short Rate

Short Rate is defined as the interest rate proportionately higher than the annual rate, made for insurance issued or continued in force by the insured for less than one year.

Symbol: r_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Short Rate

Derivatives

Derivatives are defined as the varying rate of change of a function with respect to an independent variable.

Symbol: d

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Derivatives

Time Period

The Time Period for one complete oscillation to occur is called the time period.

Symbol: t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Time Period

Volatility at Time

The Volatility at Time refers to as standard deviation of the interest rate.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Volatility at Time

Random Market Risk

Random Market Risk is the risk of losses in positions arising from movements in market variables like prices and volatility.

Symbol: W_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Random Market Risk

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How to Evaluate Vasicek Interest Rate?

Vasicek Interest Rate evaluator uses Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk to evaluate the Derivative of Short Rate, The Vasicek Interest Rate model is a mathematical model that tracks and models the evolution of interest rates. Derivative of Short Rate is denoted by dr_t symbol.

How to evaluate Vasicek Interest Rate using this online evaluator? To use this online evaluator for Vasicek Interest Rate, enter Speed of Mean Reversal (a), Long Term Mean (b), Short Rate (r_t), Derivatives (d), Time Period (t), Volatility at Time (σ) & Random Market Risk (W_t) and hit the calculate button.

FAQs on Vasicek Interest Rate

What is the formula to find Vasicek Interest Rate?

The formula of Vasicek Interest Rate is expressed as Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk. Here is an example- 3675 = 12*(6-5)*50*2+9*50*5.5.

How to calculate Vasicek Interest Rate?

With Speed of Mean Reversal (a), Long Term Mean (b), Short Rate (r_t), Derivatives (d), Time Period (t), Volatility at Time (σ) & Random Market Risk (W_t) we can find Vasicek Interest Rate using the formula - Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk.

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Vasicek Interest Rate Formula

Vasicek Interest Rate Example

Vasicek Interest Rate Solution

Vasicek Interest Rate Formula Elements

Other formulas in Forex Management category

How to Evaluate Vasicek Interest Rate?

FAQs on Vasicek Interest Rate

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