Documentation/Calc Functions/OPT PROB INMONEY

Function name:
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.
 * For relevant background information, visit the Options (finance) and Black-Scholes model Wikipedia pages.

Related LibreOffice functions:
OPT_BARRIER

OPT_PROB_HIT

OPT_TOUCH

ODF standard:
None

Equivalent Excel functions:
None