Moneyness

"In the money" redirects here; for the poker term, see In the money (poker).

In finance, moneyness is a measure of the degree to which a derivative is likely to have positive monetary value at its expiration, in the risk-neutral measure. It can be measured in percentage probability, or in standard deviations.

Intrinsic value and time value

The intrinsic value (or "monetary value") of an option is its value assuming it were exercised immediately. Thus if the current (spot) price of the underlying security (or commodity etc) is above the agreed (strike) price, a call has positive intrinsic value (and is called "in the money"), while a put has zero intrinsic value (and is "out of the money").

The time value of an option is the total value of the option, less the intrinsic value. It partly arises from the uncertainty of future price movements of the underlying. A component of the time value also arises from the unwinding of the discount rate between now and the expiry date. In the case of a European option, the option cannot be exercised before the expiry date, so it is possible for the time value to be negative; for an American option if the time value is ever negative, you exercise it (ignoring special circumstances such as the security going ex dividend): this yields a boundary condition.

ATM: At the money

An option is at the money if the strike price is the same as the current spot price of the underlying security. An at the money option has no intrinsic value, only time value.

ITM: In the money

An in the money option has positive intrinsic value as well as time value. A call option is in the money when the strike price is below the spot price. A put option is in the money when the strike price is above the spot price.

OTM: Out of the money

An out of the money option has no intrinsic value. A call option is out of the money when the strike price is above the spot price of the underlying security. A put option is out of the money when the strike price is below the spot price.

Spot versus forward

Assets can have a forward price (a price for delivery in future) as well as a spot price. One can also talk about moneyness with respect to the forward price: thus one talks about ATMF, "ATM Forward", and so forth. For instance, if the spot price for USD/JPY is 120, and the forward price one year hence is 110, then a call struck at 110 is ATMF but not ATM.

Which are used?

Buying an ITM option is effectively lending money in the amount of the intrinsic value. Further, an ITM call can be replicated by entering a forward and buying an OTM put (and conversely). Consequently, ATM and OTM options are the main traded ones.

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.

By use of the Black–Scholes model to value the option, one may define moneyness in terms of an (implied) probability distribution. If we define the moneyness (of a call) as

$m = \frac{d_1+d_2}{2}$

where d₁ and d₂ are the standard Black–Scholes parameters then

$m = \frac{\ln(S/K)+rT}{\sigma\sqrt T},$

where T is the time to expiry.

In other words, it is the number of standard deviations the current forward price is above the strike price. Thus the moneyness is zero when the forward price of the underlying (ie in principle the spot price accumulated at the risk-free rate) equals the strike price. 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 call option and a negative value meaning an out-of-the-money call option (with signs reversed for a put option).

One can also express it as an implied percentage probability, via $\Phi(m)$, where $\Phi$ is the standard normal cumulative distribution function; thus a moneyness of 0 yields a 50% probability of expiring ITM, while a moneyness of 1 yields an approximately 84% probability of expiring ITM.

Beware that (percentage) moneyness is close to but different from Delta: $\Delta = \Phi(m+\sigma\sqrt{T}/2)$ instead of $\Phi(m)$, for a call (conversely for a put).

Thus a 25 Delta call option has approximately (but not exactly) 25% moneyness.

Note that $r$ is the risk-free rate, not the expected return on the underlying.

References

• McMillan, Lawrence G. (2002). Options as a Strategic Investment (4th ed. ed.). New York : New York Institute of Finance. ISBN 0-7352-0197-8.