Vasicek Interest Rate Calculator

✖Speed of Mean Reversal refers to the speed at which the interest rate returns to its long-term mean level.ⓘ Speed of Mean Reversal [a]			+10% -10%
✖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.ⓘ Long Term Mean [b]			+10% -10%
✖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.ⓘ Short Rate [r_t]			+10% -10%
✖Derivatives are defined as the varying rate of change of a function with respect to an independent variable.ⓘ Derivatives [d]			+10% -10%
✖The Time Period for one complete oscillation to occur is called the time period.ⓘ Time Period [t]			+10% -10%
✖The Volatility at Time refers to as standard deviation of the interest rate.ⓘ Volatility at Time [σ]			+10% -10%
✖Random Market Risk is the risk of losses in positions arising from movements in market variables like prices and volatility.ⓘ Random Market Risk [W_t]			+10% -10%

✖The Derivative of Short Rate is the rate that applies to an infinitesimally short period of time.ⓘ Vasicek Interest Rate [dr_t]

⎘ Copy

👎

Formula

✖

Vasicek Interest Rate

Formula

`"dr"_{"t"} = "a"*("b"-"r"_{"t"})*"d"*"t"+"σ"*"d"*"W"_{"t"}`

Example

`"3675"="12"*("6"-"5")*"50"*"2"+"9"*"50"*"5.5"`

Calculator

LaTeX

Reset

👍

Download Forex Management Formulas PDF PDF Image

Vasicek Interest Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk
dr_t = a*(b-r_t)*d*t+σ*d*W_t
This formula uses 8 Variables

Variables Used

Derivative of Short Rate - The Derivative of Short Rate is the rate that applies to an infinitesimally short period of time.
Speed of Mean Reversal - Speed of Mean Reversal refers to the speed at which the interest rate returns to its long-term mean level.
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.
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.
Derivatives - Derivatives are defined as the varying rate of change of a function with respect to an independent variable.
Time Period - The Time Period for one complete oscillation to occur is called the time period.
Volatility at Time - The Volatility at Time refers to as standard deviation of the interest rate.
Random Market Risk - Random Market Risk is the risk of losses in positions arising from movements in market variables like prices and volatility.

STEP 1: Convert Input(s) to Base Unit

Speed of Mean Reversal: 12 --> No Conversion Required
Long Term Mean: 6 --> No Conversion Required
Short Rate: 5 --> No Conversion Required
Derivatives: 50 --> No Conversion Required
Time Period: 2 --> No Conversion Required
Volatility at Time: 9 --> No Conversion Required
Random Market Risk: 5.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dr_t = a*(b-r_t)*d*t+σ*d*W_t --> 12*(6-5)*50*2+9*50*5.5

Evaluating ... ...

dr_t = 3675

STEP 3: Convert Result to Output's Unit

3675 --> No Conversion Required

FINAL ANSWER

3675 <-- Derivative of Short Rate

(Calculation completed in 00.004 seconds)

You are here -

Home » Financial » Investment » Forex Management » Vasicek Interest Rate

Credits

Created by Kashish Arora

Satyawati College (DU), New Delhi

Kashish Arora has created this Calculator and 50+ more calculators!

Verified by Vishnu K

BMS College of Engineering (BMSCE), Bangalore

Vishnu K has verified this Calculator and 200+ more calculators!

< 14 Forex Management Calculators

Black-Scholes-Merton Option Pricing Model for Call Option

Go Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2)

Cumulative Distribution One

Go Cumulative Distribution 1 = (ln(Current Stock Price/Option Strike Price)+(Risk Free Rate+Volatile Underlying Stock^2/2)*Time to Expiration of Stock)/(Volatile Underlying Stock*sqrt(Time to Expiration of Stock))

Fama-French Three-Factor Model

Go Excess Return on Asset = Asset Specific Alpha+Beta in Forex*(Return on Market Portfolio-Risk Free Rate)+(Sensitivity of the Asset to SMB*Small Minus Big+Sensitivity of the Asset to HML+Error Term)

Vasicek Interest Rate

Go Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk

Black-Scholes-Merton Option Pricing Model for Put Option

Go Theoretical Price of Put Option = Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock)*(-Cumulative Distribution 2)-Current Stock Price*(-Cumulative Distribution 1)

Forward Rate

Go Forward Rate = Spot Exchange Rate*ln((Domestic Interest Rate-Foreign Interest Rate)*Time to Maturity)

Cumulative Distribution Two

Go Cumulative Distribution 2 = Cumulative Distribution 1-Volatile Underlying Stock*sqrt(Time to Expiration of Stock)

Position Size in Forex

Go Position Size in Forex = (Account Equity*Risk Percentage in Forex)/(Stop Loss in Pips*Pip Value in Forex)

Profit for Call Buyer

Go Profit for Call Buyer = max(0,Price of Underlying at Expiration-Exercise Price)-Call Premium

Interest Rate Parity

Go Forward Rate Constant = Spot Exchange Rate*((1+Interest Rate of Quote Currency)/(1+Interest Rate of Base Currency))

Gordon Growth Model

Go Current Stock Price = (Dividend Per Share)/(Required Rate of Return-Constant Growth Rate of Dividend)

Payoff for Call Buyer

Go Payoff for Call Buyer = max(0,Price of Underlying at Expiration-Exercise Price)

Purchasing Power Parity Theory using Inflation

Go Exchange Rate Factor = ((1+Inflation in Home Country)/(1+Inflation in Foreign Country))-1

Intrinsic Value

Go Intrinsic Value = Share Price-Base Value

Vasicek Interest Rate Formula

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

What is Vasicek Interest Rate Model?

The term Vasicek Interest Rate Model refers to a mathematical method of modeling the movement and evolution of interest rates. It is a single-factor short-rate model that is based on market risk. The Vasicek interest model is commonly used in economics to determine where interest rates will move in the future. Put simply, it estimates where interest rates will move in a given period of time and can be used to help analysts and investors figure out how the economy and investments will fare in the future.

How to Calculate Vasicek Interest Rate?

Vasicek Interest Rate calculator 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 calculate 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 calculate Vasicek Interest Rate using this online calculator? To use this online calculator 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. Here is how the Vasicek Interest Rate calculation can be explained with given input values -> 3675 = 12*(6-5)*50*2+9*50*5.5.

FAQ

What is Vasicek Interest Rate?

The Vasicek Interest Rate model is a mathematical model that tracks and models the evolution of interest rates and is represented as dr_t = a*(b-r_t)*d*t+σ*d*W_t or Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk. Speed of Mean Reversal refers to the speed at which the interest rate returns to its long-term mean level, 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, 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, Derivatives are defined as the varying rate of change of a function with respect to an independent variable, The Time Period for one complete oscillation to occur is called the time period, The Volatility at Time refers to as standard deviation of the interest rate & Random Market Risk is the risk of losses in positions arising from movements in market variables like prices and volatility.

How to calculate Vasicek Interest Rate?

The Vasicek Interest Rate model is a mathematical model that tracks and models the evolution of interest rates is calculated using Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk. To calculate Vasicek Interest Rate, you need 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). With our tool, you need to enter the respective value for Speed of Mean Reversal, Long Term Mean, Short Rate, Derivatives, Time Period, Volatility at Time & Random Market Risk and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search