Moneyness

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"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.

1 Intrinsic value and time value
2 Spot vs. Forward
3 Which are used?
- 3.1 Example
4 See also
5 References

[edit] Intrinsic value and time value

The intrinsic value (or "monetary value") of an option is the value of exercising it now. Thus if the current (spot) price of the underlying is above the strike price, a call has positive intrinsic value (and is called "in the money"), while a put has zero intrinsic value. The time value of an option is "value - intrinsic value": it's the value of not exercising it immediately. (This is clearer with a graph.) In the case of a European option, you cannot choose to exercise it at any time, so the time value can be negative; for an American option if the time value is ever negative, you exercise it: this yields a boundary condition.

[edit] ATM: At-the-money

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 at-the-money option has no monetary value, only time value.

[edit] ITM: In-the-money

In-the-money options has positive monetary value as well as time value. A call option is in-the-money when the strike price is below the current trading price. A put option is in-the-money when the strike price is above the current trading price.

[edit] OTM: Out-of-the-money

An out-of-the-money option has no monetary value. A call option is out-of-the-money when the strike price is above the current trading price of the underlying security. A put option is out-of-the-money when the strike price is below the current trading price of the underlying security.

[edit] Spot vs. Forward

Recall that assets have a spot price and a forward price (the price for delivery in future). One can talk about moneyness with respect to either the spot price, or the forward price (at expiry): thus one talks about ATMS = ATM Spot (also called at-the-money outright) vs. ATMF = ATM Forward, and so forth.

For instance, if the spot price for USD/JPY is 220, and the forward price in one year is 210, then a call struck at 210 is ATMF but ITMS.

[edit] Which are used?

Buying (selling) an ITM option is effectively lending (borrowing) money, generally at an unfavorable interest rate. Further, an ITM call can be replicated by entering a forward and buying an OTM put (and conversely). Thus ATM/OTM options are the main traded ones, and transacting in ITM options is suspicious, as it can be used by traders to hide losses (see Nick Leeson).

[edit] Example

Suppose the current stock price of IBM is $100. A call or put option with a strike of $100 is at-the-money (spot). 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 (of a call) as

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

where $d 1$ and $d 2$ 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 price is above the ATMF price.

This choice of parameterisation means that the moneyness is zero when the forward price of the underlying, discounted 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 (use negative for a put option).

One can also measure it as a percent, via $Φ(m)$ , where $Φ$ 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 $Φ(m)$ , for a call (conversely for a put).