# Moneyness

In finance, moneyness is a measure of the degree to which a derivative security is likely to have positive monetary value at its expiration.

An option is at-the-money if the strike price, i.e., the price the option holder must pay to exercise the option, is the same as the current price of the underlying security on which the option is written. An out-of-the-money option currently has no intrinsic value - e.g. a call option is out-the-money if the strike price ("the strike") is higher than the current underlying price. An in-the-money option conversely does have intrinsic value. The strike price 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 with a strike of$100 is at-the-money. A call option with a strike of $80 is in-the-money (100 - 80 = 20 > 0). A put option with a strike at$80 is out-of-the-money (80 - 100 = -20 < 0). Conversely a call option with a $120 strike is out-of-the-money and a put option with a$120 strike is in-the-money.

When one uses the Black-Scholes model to value the option, one may define moneyness quantitatively. If we define the moneyness as

[itex] m = \frac{d_1+d_2}{2}[itex]

where [itex]d_1[itex] and [itex]d_2[itex] are the standard Black-Scholes parameters then

[itex] m = \frac{\frac{S}{K}+rT}{\sigma\sqrt t}[itex]

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. Such an option is often referred to as at-the-money-forward. 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-of-the-money option.

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