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The following illustration shows the difference between a scale with linearly-increasing encoded luminance signal (linear gamma-compressed luma input) and a scale with linearly-increasing intensity scale (linear luminance output).

where the non-negative real input value V in \displaystyle V_ ext in is raised to the power γ \displaystyle \gamma and multiplied by the constant A, to get the output value V out \displaystyle V_ ext out . In the common case of A = 1, inputs and outputs are typically in the range 0–1.

Without context, a value labeled gamma might be either the encoding or the decoding value. Caution must be taken to correctly interpret the value as that to be applied-to-compensate or to be compensated-by-applying its inverse. In common parlance, in many occasions the decoding value (as 2.2) is employed as if it were the encoding value, instead of its inverse (1/2.2 in this case), which is the real value that must be applied to encode gamma.

When a photographic film is exposed to light, the result of the exposure can be represented on a graph showing log of exposure on the horizontal axis, and density, or log of transmittance, on the vertical axis. For a given film formulation and processing method, this curve is its characteristic or Hurter–Driffield curve. 6 7 Since both axes use logarithmic units, the slope of the linear section of the curve is called the gamma of the film. Negative film typically has a gamma less than 1; positive film (slide film, reversal film) typically has a gamma greater than 1.

Likewise, brightness is sometimes applied to various measures, including light levels, though it more properly applies to a subjective visual attribute.

where γ is the Greek letter gamma. For a CRT, the gamma that relates brightness to voltage is usually in the range 2.35 to 2.55; video look-up tables in computers usually adjust the system gamma to the range 1.8 to 2.2, 1 which is in the region that makes a uniform encoding difference give approximately uniform perceptual brightness difference, as illustrated in the diagram at the top of this section.

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A position with positive gamma (long gamma) indicates the position's delta will increase when the stock price rises, and decrease when the stock price falls.

The gamma of an option indicates how an option's delta is expected to change when the stock price changes. However, long gamma or short gamma take things a step further and indicate whether an option position's delta will become more positive or more negative when the stock price changes. A long gamma position is any option position with positive gamma exposure, while a short gamma position is any option position with negative gamma exposure. More specifically:

In this table, the positions with positive gamma are said to be long gamma. As you can see here, long gamma positions benefit when the stock price moves in favor of the position because the directional exposure of the position grows in the same direction as the stock price.

In general, option buying strategies have positive gamma (long gamma) exposure.

As we can see here, the long call's position delta grows from +25 to +75 as the stock price increases. With a delta of +25, the long call trader is expected to make $25 for each$1 increase in the stock price, and lose $25 for each$1 decrease in the stock price. However, when the delta grows to +75, the long call trader is expected to profit by $75 when the share price rises by$1 and lose $75 when the share price falls by$1. So, the long call trader wants the stock price to rise to profit from the increased positive delta exposure.

Next, we'll look at a short put position. Note how the position's delta increases as the stock price decreases.

Positive gamma (long gamma) indicates that a position's delta will increase as the stock price rises, and decrease as the stock price falls. As a result, bullish strategies with long gamma experience more significant profits when the stock price continues to increase. Similarly, bearish strategies with long gamma experience larger profits when the stock price continues to fall.

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On October 30, 2012, TraderPlanet announced the purchase of SFO Magazine (and related educational website TraderPress.com) with the goal of incorporating their archive of content into TraderPlanet's free educational platform. There are no plans to resume publishing the print or online versions of the magazine. 1

On July 10, 2012, an SFO Magazine editorial board member posted a message to their Twitter account announcing the end of the magazine: 2

SFO Magazine had offered both a print and online edition. However, on February 3, 2010, SFO announced it would become a paperless, multimedia publication beginning with the March 2010 edition. 6

SFO Magazine (Stocks, Futures & Options) was a monthly financial magazine and website aimed at educating investors and traders about strategies in stocks, futures and options. It was published by Russell R. Wasendorf, Sr.. Each month featured a different theme - psychology of trading, day trading, forex, trend following, technical analysis, etc. in addition to a variety of features and regular columns.

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Example Two: A put order would look similar. If you saw a standard order that said 1 ABC Aug 50 put at 3, this would be an options contract where they buyer has the option to sell 100 shares of ABC at $50 per share any time before the August expiration date. He paid$300 for this option.

As you can see, options trading can be very involved. It is not as simple as buying shares of stock and waiting for the price to rise. There are a lot of options available, whether you are buying or selling options contracts. In a future article, we will discuss more in-depth why people trade options as well as some of the more advanced options contracts and strategies. A great way to get into options trading is with a virtual trading account. This can be used for practice without any fear of loss. Many online brokerages will offer free virtual accounts with no obligation and many will offer training, articles and seminars on options trading.

Options trading is one of the most difficult yet intriguing of advanced trading techniques and can be very confusing at first. Many professional stockbrokers do not even understand it and thus do not deal in options. However, with research and study, options trading can be quite rewarding. When done poorly, it can turn bad quickly and become an expensive education. However, when done correctly, options trading can be profitable and actually reduce the risk in your portfolio, becoming a very viable hedging strategy.

An options contract is basically a contract that gives whoever owns it the right to buy or sell a specific stock at a time yet to come. Each contract involves a buyer and a seller. The buyer, who is also called the holder or owner, pays a premium for the right to buy a stock from or sell a stock to the seller of the contract at a future time. The buyer is always called long, while the seller, who is also called the writer, is always short. The owner does not always execute the contract by buying or selling the stock before the expiration date, but the writer will keep the premium whether or not the option is exercised. The premium is basically just the sales price that the buyer pays for this right.

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1) Under the risk neutrality assumption, today's fair price of a derivative is equal to the expected value of its future payoff discounted by the risk free rate. Therefore, expected value is calculated using the option values from the later two nodes (Option up and Option down) weighted by their respective probabilities -- "probability" p of an up move in the underlying, and "probability" (1-p) of a down move. The expected value is then discounted at r, the risk free rate corresponding to the life of the option.

3) Depending on the style of the option, evaluate the possibility of early exercise at each node: if (1) the option can be exercised, and (2) the exercise value exceeds the Binomial Value, then (3) the value at the node is the exercise value.

The above is the original Cox, Ross, & Rubinstein (CRR) method; there are other techniques for generating the lattice, such as "the equal probabilities" tree.

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Option valuation using this method is, as described, a three step process:

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