Risk Neutral Probability Calculator

✖The Risk Free Rate is the theoretical rate of return of an investment with zero risks.ⓘ Risk Free Rate [R_f]			+10% -10%
✖Initial Stock Price is the original purchase price of the security.ⓘ Initial Stock Price [P0]			+10% -10%
✖Stock Down Price refers to the price of a stock after it has experienced a decrease in value.ⓘ Stock Down Price [S^d]			+10% -10%
✖Stock Price Up refers to the price of a stock after it has experienced an increase in value.ⓘ Stock Price Up [S^u]			+10% -10%

✖Risk Neutral Probability is the probability measure where investors are indifferent to risk, ensuring that the expected return on an asset equals the risk-free rate.ⓘ Risk Neutral Probability [π]

⎘ Copy

👎

Formula

✖

Risk Neutral Probability

Formula

`"π" = (((1+("R"_{"f"}/100))*"P0")-"S"^{"d"})/("S"^{"u"}-"S"^{"d"})`

Example

`"0.4955"=(((1+("3"/100))*"48.5")-"45")/("55"-"45")`

Calculator

LaTeX

Reset

👍

Risk Neutral Probability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Risk Neutral Probability = (((1+(Risk Free Rate/100))*Initial Stock Price)-Stock Down Price)/(Stock Price Up-Stock Down Price)
π = (((1+(R_f/100))*P0)-S^d)/(S^u-S^d)
This formula uses 5 Variables

Variables Used

Risk Neutral Probability - Risk Neutral Probability is the probability measure where investors are indifferent to risk, ensuring that the expected return on an asset equals the risk-free rate.
Risk Free Rate - The Risk Free Rate is the theoretical rate of return of an investment with zero risks.
Initial Stock Price - Initial Stock Price is the original purchase price of the security.
Stock Down Price - Stock Down Price refers to the price of a stock after it has experienced a decrease in value.
Stock Price Up - Stock Price Up refers to the price of a stock after it has experienced an increase in value.

STEP 1: Convert Input(s) to Base Unit

Risk Free Rate: 3 --> No Conversion Required
Initial Stock Price: 48.5 --> No Conversion Required
Stock Down Price: 45 --> No Conversion Required
Stock Price Up: 55 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

π = (((1+(R_f/100))*P0)-S^d)/(S^u-S^d) --> (((1+(3/100))*48.5)-45)/(55-45)

Evaluating ... ...

π = 0.4955

STEP 3: Convert Result to Output's Unit

0.4955 --> No Conversion Required

FINAL ANSWER

0.4955 <-- Risk Neutral Probability

(Calculation completed in 00.004 seconds)

You are here -

Home » Financial » Financial Accounting » Quantitative Finance » Risk Neutral Probability

Credits

Created by Keerthika Bathula

Indian Institute of Technology, Indian School of mines, Dhanbad (IIT ISM Dhanbad), Dhanbad

Keerthika Bathula 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!

< 3 Quantitative Finance Calculators

Ibbotson Chen Earnings Model

Go Equity Risk Premium = ((1+(Expected Inflation*0.01))*(1+(Expected Real Growth in EPS*0.01))*(1+(Expected Changes in PE Ratio*0.01))-1+(Expected Yield on Index*0.01)-(Expected Risk Free Rate*0.01))*100

Capital Market Line

Go Expected Portfolio Return = Risk Free Return+((Expected Return on Market Portfolio-Risk Free Return)/Market Risk)*Portfolio Risk

Risk Neutral Probability

Go Risk Neutral Probability = (((1+(Risk Free Rate/100))*Initial Stock Price)-Stock Down Price)/(Stock Price Up-Stock Down Price)

Risk Neutral Probability Formula

Risk Neutral Probability = (((1+(Risk Free Rate/100))*Initial Stock Price)-Stock Down Price)/(Stock Price Up-Stock Down Price)
π = (((1+(R_f/100))*P0)-S^d)/(S^u-S^d)

What is Risk Neutral Probability?

The risk-neutral probability of an upward stock movement is the probability assigned to the event that the stock price will increase in a given period under the assumption of risk neutrality, ensuring no arbitrage opportunities exist, often calculated using the risk-free interest rate and the up and down factors in the binomial model.

How to Calculate Risk Neutral Probability?

Risk Neutral Probability calculator uses Risk Neutral Probability = (((1+(Risk Free Rate/100))*Initial Stock Price)-Stock Down Price)/(Stock Price Up-Stock Down Price) to calculate the Risk Neutral Probability, The Risk Neutral Probability is the probability of the stock price rising in a given period, adjusted to account for risk-free interest rates and price fluctuations in a way that ensures no arbitrage opportunities exist. Risk Neutral Probability is denoted by π symbol.

How to calculate Risk Neutral Probability using this online calculator? To use this online calculator for Risk Neutral Probability, enter Risk Free Rate (R_f), Initial Stock Price (P0), Stock Down Price (S^d) & Stock Price Up (S^u) and hit the calculate button. Here is how the Risk Neutral Probability calculation can be explained with given input values -> 0.4955 = (((1+(3/100))*48.5)-45)/(55-45).

FAQ

What is Risk Neutral Probability?

The Risk Neutral Probability is the probability of the stock price rising in a given period, adjusted to account for risk-free interest rates and price fluctuations in a way that ensures no arbitrage opportunities exist and is represented as π = (((1+(R_f/100))*P0)-S^d)/(S^u-S^d) or Risk Neutral Probability = (((1+(Risk Free Rate/100))*Initial Stock Price)-Stock Down Price)/(Stock Price Up-Stock Down Price). The Risk Free Rate is the theoretical rate of return of an investment with zero risks, Initial Stock Price is the original purchase price of the security, Stock Down Price refers to the price of a stock after it has experienced a decrease in value & Stock Price Up refers to the price of a stock after it has experienced an increase in value.

How to calculate Risk Neutral Probability?

The Risk Neutral Probability is the probability of the stock price rising in a given period, adjusted to account for risk-free interest rates and price fluctuations in a way that ensures no arbitrage opportunities exist is calculated using Risk Neutral Probability = (((1+(Risk Free Rate/100))*Initial Stock Price)-Stock Down Price)/(Stock Price Up-Stock Down Price). To calculate Risk Neutral Probability, you need Risk Free Rate (R_f), Initial Stock Price (P0), Stock Down Price (S^d) & Stock Price Up (S^u). With our tool, you need to enter the respective value for Risk Free Rate, Initial Stock Price, Stock Down Price & Stock Price Up 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