# Documentation/Calc Functions/OPT PROB HIT

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OPT_PROB_HIT

## Category:

Financial Analysis

## Summary:

Calculates the probability that an asset hits a predetermined barrier price, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation (in Additional details section).

## Syntax:

OPT_PROB_HIT(Spot; Volatility; Drift; Maturity; Lower Barrier; Upper Barrier)

## Returns:

Returns a real number which is the probability that an asset hits a predetermined barrier price, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation for the given parametric conditions. It ranges from 0 to 1, i.e. [0,1].

## Arguments:

Spot is a positive real number or a reference to the cell containing that number which is the price/value of the underlying asset and should be greater than 0.0.

Volatility is a positive real number or a reference to the cell containing that number which is the annual percentage volatility of the underlying asset expressed as a decimal (for example, enter 30% as 0.3). The value should be greater than 0.0.

Drift is a real number or a reference to the cell containing that number which is the annual stock price percentage drift rate (µ in the above formula). The value is expressed as a decimal (for example, enter 15% as 0.15).

Maturity is a real number or a reference to the cell containing that number which is the time to maturity of the option, in years, and should be non-negative.

Lower Barrier is a real number or a reference to the cell containing that number which is the predetermined lower barrier price; set to zero for no lower barrier.

Upper Barrier is a real number or a reference to the cell containing that number which is the predetermined upper barrier price; set to zero for no upper barrier.

• If for any of the above arguments, the mentioned constraints are not followed then, the function returns an error value.

## Additional details:

• The formula for OPT_PROB_HIT is:

where µ is the asset’s percentage drift, vol is the percentage volatility of the stock, and dW is a random sample drawn from a normal distribution with a zero mean. W is a Wiener process or Brownian motion.

## Examples:

Formula Description Returns
=OPT_PROB_HIT(30;0.2;0.3;1;0;40) The function calculates the probability that an asset hits a predetermined barrier price, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation (in Additional details section). 0.611908289070705
=OPT_PROB_HIT(70;0.3;0.1;0.5;60;0) The function calculates the probability that an asset hits a predetermined barrier price, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation (in Additional details section). 0.423889647113691

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