## What is Stock Price Probability Calculator?

This calculator gives the risk neutral probability that a stock with the specified current price, and volatility, will be within the given price range at the specified date. The risk neutral probability is the assumption that the expected value of the stock price grows no faster than an investment at the risk free interest rate.

 This is illustrated by the following equation $$t = \dfrac {enddate \hspace1ex time -startdate \hspace1ex time} {1 \hspace1ex day \hspace1ex milisecond }$$ $$mu = r - 0.5 * sigma * sigma$$ $$denom = sigma * \sqrt t$$ $$zlb = { \ln \left ( \dfrac {lb} {p} \right ) - mu * t \above 1pt denom }$$ $$zub = { \ln \left ( \dfrac {ub} {p} \right ) - mu * t \above 1pt denom }$$ … where N(x) is the standard normal cumulative distribution function. $$probility = { N(zub) - N(zlb) }$$
 Variables p = The value of the stock today. sigma = The annual volatility of the stock. r = The continuously compounded risk-free interest rate for the same period as the probability calculation. enddate time = The date for which the probability is calculated. lb/ub = The stock price range for which you want to calculate the probability.

 Current stock price ($): Volatility (%): Risk-free interest rate (%): Date: Range lower bound ($): Range upper bound (\$):

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