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Returns 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 the stochastic differential equation, as follows.
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.
If the optional Strike and PutCall arguments are included, then
For a call option, the function returns the probability that the asset will end up between Strike and UpperBarrier.
For a put option, the function returns the probability that the asset will end up between LowerBarrier and Strike.
The function ignores the possibility of knock-out before maturity.
OPT_PROB_INMONEY(Spot; Volatility; Drift; Maturity; LowerBarrier; UpperBarrier [; Strike [; PutCall]])
Spot is the price / value of the underlying asset and should be greater than 0.0.
Volatility 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 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 the time to maturity of the option, in years, and should be non-negative.
Strike is the strike price of the option and should be non-negative.
Put or Call is a string that defines whether the option is a put (“p”) or a call (“c”).
=OPT_PROB_INMONEY(30;0.2;0.1;1;0;50) returns the value 0.9844.
=OPT_PROB_INMONEY(70;0.3;0.15;1;60;0;80;"p") returns the value 0.3440.