The delta is a ratio comparing the change in the price of an asset , usually a marketable security , to the corresponding change in the price of its derivative. For example, if a stock option has a delta value of 0. Delta values can be positive or negative depending on the type of option.

For example, the delta for a call option always ranges from 0 to 1, because as the underlying asset increases in price, call options increase in price. Put option deltas always range from -1 to 0 because as the underlying security increases, the value of put options decrease. For example, if a put option has a delta of Technically, the value of the option's delta is the first derivative of the value of the option with respect to the underlying security's price.

Delta is often used in hedging strategies, and is also referred to as a hedge ratio. BigCorp is a publicly traded corporation. Shares of its stock are bought and sold on a stock exchange, and there are put options and call options traded for those shares. The delta for the call option on BigCorp shares is.

Put options work in the opposite way. Delta is an important calculation done by computer software , as it is one of the main reasons option prices move the way that they do — and an indicator of how to invest. The behavior of call and put option delta is highly predictable and is very useful to portfolio managers, traders, hedge fund managers and individual investors. Call option delta behavior depends on whether the option is " in-the-money ," meaning the position is currently profitable, " at-the-money ," meaning the option's strike price currently equals the underlying stock's price, or " out-of-the-money ," meaning the option is not currently profitable.

In-the-money call options get closer to 1 as their expiration approaches. At-the-money call options typically have a delta of 0. The deeper in-the-money the call option, the closer the delta will be to 1, and the more the option will behave like the underlying asset.

Put option delta behaviors also depend on whether the option is "in-the-money," "at-the-money," or "out-of-the-money" and are the opposite of call options. In-the-money put options get closer to -1 as expiration approaches. At-the-money put options typically have a delta of The deeper in-the-money the put option, the closer the delta will be to Delta spread is an options trading strategy in which the trader initially establishes a delta neutral position — by simultaneously buying and selling options in proportion to the neutral ratio that is, the positive and negative deltas offset each other, so that so that the overall delta of the assets in question totals zero.

Using a delta spread, a trader usually expects to make a small profit if the underlying security does not change widely in price. However, larger gains or losses are possible if the stock does move significantly in either direction. The most common delta spread is a calendar spread. The calendar spread involves constructing a delta neutral position using options with different expiration dates.

In the simplest example, a trader will simultaneously sell near-month call options and buy call options with a later expiration in proportion to their neutral ratio. Since the position is delta neutral, the trader should not experience gains or losses from small prices moves in the underlying security. Rather, the trader expects the price to remain unchanged, and as the near month calls lose time value and expire, the trader can sell the call options with longer expiration dates and hopefully net a profit.

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