Define out of the money call option
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 the 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 surface , or more simply plotting a volatility smile.
This section outlines moneyness measures from simple but less useful to more complex but more useful. These are also known as absolute moneyness , and 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 forward , and 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 price , when 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 money, 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 long , and 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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Read on to get a clearer picture of what that something might be for specific strategies. Strike Price — The pre-agreed price per share at which stock may be bought or sold under the terms of an option contract.
For put options, it means the stock price is below the strike price. This term might also remind you of a great song from the s that you can tap dance to whenever your option strategies go according to plan. For put options, this means the stock price is above the strike price. Intrinsic Value — The amount an option is in-the-money. Obviously, only in-the-money options have intrinsic value. Time Value — The part of an option price that is based on its time to expiration. If an option has no intrinsic value i.
Exercise — This occurs when the owner of an option invokes the right embedded in the option contract. Interestingly, options are a lot like most people, in that exercise is a fairly infrequent event. See Cashing Out Your Options. That means he or she is required to buy or sell the underlying stock at the strike price. Equity Options — There are quite a few differences between options based on an index versus those based on equities, or stocks.
Second, the last day to trade most index options is the Thursday before the third Friday of the expiration month. It might actually be the second Thursday if the month started on a Friday. But the last day to trade equity options is the third Friday of the expiration month. There are several exceptions to these general guidelines about index options.
See What is an Index Option? Stop-Loss Order - An order to sell a stock or option when it reaches a certain price the stop price. Past this price, you no longer want the cheese; you just want out of the trap. When your position trades at or through your stop price, your stop order will get activated as a market order, seeking the best available market price at that time the order is triggered to close out your position.
In those situations, stocks are likely to gap — that is, the next trade price after the trading halt might be significantly different from the prices before the halt.