Moneyness

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 d1 and d2 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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