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# Moneyness

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In finance, moneyness is a measure of the the degree to which an derivative security is likely to have positive monetary value at its expiration. An option is at-the-money if the strike of the option is the same, or about the same, as the current price of the underlying on which the option is on. An out-the-money option currently has no intrinsic value - e.g. a call option is out-the-money if the strike is higher than the current underlying price. An in-the-money option conversely does have intrinsic value. The strike of an in-the-money call option is lower than the current underlying price.

For example suppose the current stock price of IBM is $100. A call or put option struck at$100 is at-the-money. A call option struck at $80 is in-the-money. A put option struck at$80 is out-the-money. Conversely a $120 strike call option is out of the money and a$120 strike put option is in the money.

When working with the Black-Scholes model moneyness may be defined quantitatively. If we define the moneyness as

$m = \frac{d_1+d_2}{2}$
where $d_1$ and $d_2$ are the standard Black-Scholes parameters then
$m = \frac{\frac{S}{K}+rT}{\sigma\sqrt t}$
This choice of parameterisation means that the moneyness is zero when the forward/underlying price matches the strike after discounting at the risk-free rate. Moneyness is measured in standard deviations from this point, with a positive value meaning an in-the-money option and a negative value meaning an out-the-money option.

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