## In the Money (ITM)

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In financemoneyness is the relative position of the current price or future price of an underlying asset e. Moneyness is firstly a three-fold classification: There are two slightly different definitions, according to whether one uses the current price spot or future price forwardspecified as "at the money spot" or "at the money forward", etc. This rough classification can be quantified by various definitions to express call option in the money definition moneyness as a number, measuring how far the asset is in the money or out of the money with respect to the strike — or conversely how far a strike is in or out of the money with respect call option in the money definition the spot or forward price of the asset.

This quantified notion of moneyness is most importantly used in defining the relative volatility surface: The most basic of these measures is simple moneynesswhich is the ratio of spot or forward to strike, or the reciprocal, depending on convention. A particularly important measure of moneyness is the likelihood that the derivative will expire in the money, in the risk-neutral measure. It can be measured in percentage probability of expiring in the money, which is the forward value of a binary call option with the given strike, and is equal to the auxiliary N d 2 term in the Black—Scholes formula.

This can also be **call option in the money definition** in standard deviationsmeasuring how call option in the money definition above or below the strike price the current price is, in terms of volatility; this quantity is given by d 2. Standard deviations refer to the price fluctuations of the underlying instrument, not of the option itself. Another measure closely related to moneyness is the Delta of a call or put option. There are other proxies for moneyness, with convention depending on market.

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.

The time value of call option in the money definition 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 call option in the money definition dividend: An option is at the money ATM 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. For example, with an "at the money" call stock option, the current share price and strike price are the same. Exercising the option will not earn the seller a profit, but any call option in the money definition upward in stock price will give the option value. Since an option will rarely be exactly at the money, except for when it is written when one may buy or sell an ATM optionone may speak informally **call option in the money definition** an option being near the money or close to the money.

Conversely, one may speak informally of an option being far from the money. An in the money ITM option has positive intrinsic value as well as time value. A call option is in the call option in the money definition 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. With an "in the money" call stock option, the current share price is greater than the strike call option in the money definition so exercising the option will give the owner of that option a profit.

That will be equal to the market price of the share, minus the option strike price, times the number of shares granted by the option minus any commission. An out of the money OTM 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.

With an "out of the money" call stock option, the current share price is less than the strike price so there is no reason to exercise the option.

The owner can sell the option, or wait and hope the price changes. 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: Buying an ITM option is effectively lending money in the amount of the intrinsic value. Intuitively speaking, moneyness and time call option in the money definition expiry form a two-dimensional coordinate system for valuing options either in currency dollar value or in implied volatilityand changing from spot or forward, or strike to moneyness is a change of variables.

Thus a moneyness function is a function M with input the spot price or forward, or strike and output a real number, which is called the moneyness. The condition of being a change of variables is that this function is monotone either increasing for all inputs, or decreasing for all inputsand the function can depend on the other parameters of the Black—Scholes modelnotably time to expiry, interest rates, and implied volatility concretely the ATM implied volatilityyielding a function:.

The forward price F can be computed from the spot price S and the risk-free rate r. All of these are observables except for the implied volatility, which can computed from the observable price using the Black—Scholes formula.

In order for this function to reflect moneyness call option in the money definition i. Somewhat different formalizations are possible. This definition is abstract and notationally heavy; in practice relatively simple and concrete moneyness functions are used, and arguments to the function are suppressed for clarity.

When quantifying moneyness, it is computed as a single number with respect to spot or forward and strike, without specifying a reference option. There are thus two conventions, depending on direction: These can be switched by changing sign, possibly with a shift or scale factor e.

Switching spot and strike also switches these conventions, and spot and strike are often complementary in formulas for moneyness, but need not be. Which convention is used depends on the purpose. The sequel uses call moneyness — as spot increases, moneyness increases — and is the same direction as using call Delta as moneyness. While moneyness is a function of both spot and strike, usually one of these is fixed, and call option in the money definition other varies. Given a specific option, the strike is fixed, and different spots yield the moneyness of that option at different market prices; this is useful in option pricing and understanding the Black—Scholes formula.

Conversely, given market data at a given point in time, the spot is fixed at the current market price, while different options have different strikes, and hence different moneyness; this is useful in constructing an implied volatility surfaceor more simply plotting call option in the money definition volatility smile. This section outlines moneyness measures from simple but less useful to more complex but more useful. These are also known as absolute moneynessand correspond to not changing coordinates, instead using the raw prices as measures of moneyness; the corresponding volatility surface, with coordinates K and T tenor is the absolute volatility surface.

In practice, for low interest rates and short tenors, spot versus forward makes little difference. The above measures are independent of time, but for a given simple moneyness, options near expiry and far for expiry behave differently, as options far from expiry have more time for the underlying to change. Since dispersion of Brownian motion is proportional to the square root of time, one may divide the log simple moneyness by this factor, yielding: Unlike previous inputs, volatility is not directly observable from market data, but must instead be computed in some model, primarily using ATM implied volatility in the Black—Scholes model.

Dispersion is proportional to volatility, so standardizing by volatility yields: This is known as the standardized moneyness forwardand measures moneyness in standard deviation units. In words, the standardized moneyness 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 equals the strike pricewhen the option is at-the-money-forward. Standardized 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.

This is often small, so the quantities are often confused or conflated, though they have distinct interpretations. As these are all in units of standard deviations, it makes sense to convert these to percentages, by evaluating the standard normal cumulative distribution function N for these values. In brief, these are interpreted for a call option as:. The percent moneyness is the implied probability that the derivative will expire in the call option in the money definition, in the risk-neutral measure.

Note that this is the implied probability, not the real-world probability. The other quantities — percent standardized moneyness and Delta — are not identical to the actual percent moneyness, but in many practical cases these are quite close unless volatility is high or time to expiry is longand Delta is commonly used by traders as a measure of percent moneyness. In more elementary terms, the probability that the option expires in the money and the value of the underlying at exercise are not independent — the higher the price of the underlying, the more likely it is to expire in the money and the higher the value at exercise, hence why Delta is higher than moneyness.

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