# Documentation/Calc Functions/OPT PROB INMONEY

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OPT_PROB_INMONEY

## Category:

Financial Analysis

## Summary:

Calculates the probability that an asset will end up between two barrier levels at maturity, 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_INMONEY(Spot; Volatility; Drift; Maturity; Lower Barrier; Upper Barrier[; Strike[; Put Call]])

## Returns:

Returns a real number which is the probability that an asset will end up between two barrier levels at maturity, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation. 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.

Strike is a real number or a reference to the cell containing that number which is the strike price of the option and should be non-negative.

Put Call is a string or a reference to the cell containing that string that defines whether the option is a put (“p”) or a call (“c”).

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

## Additional details:

• If the optional Strike and Put Call arguments are included, then
• For a call option, the function returns the probability that the asset will end up between Strike and Upper Barrier.
• For a put option, the function returns the probability that the asset will end up between Lower Barrier and Strike.
• The function ignores the possibility of knock-out before maturity.
• The formula for OPT_PROB_INMONEY 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_INMONEY(30;0.2;0.1;1;0;50) The function calculates the probability that an asset will end up between two barrier levels at maturity, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation (in Additional details section). 0.984384937022761
=OPT_PROB_INMONEY(70;0.3;0.15;1;60;0;80;"p") The function calculates the probability that an asset will end up between two barrier levels at maturity, assuming that the stock price can be modeled as a process S that follows a stochastic differential equation (in Additional details section). Here, since Strike is included the function returns the probability that the asset will end up between Lower Barrier and Strike for put option. 0.344045040212094

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