


What is Delta?
Delta is the amount by which the option changes compared to the underlying asset. It is a measure of the probability that an option will expire in the money. Call deltas can be interpreted as the probability that the option will finish in the money. Put deltas can be interpreted as 1 times the probability that the option will finish in the money.
An atthemoney option, which has a delta of approximately 0.5, has roughly a 50/50 chance of ending up "inthemoney". For example, if an atthemoney wheat call option has a Delta of .5, and if wheat makes a 10cent move higher, the premium on the option will increase approximately by 5 cents (.5 x 10 = 5), or $250 (each cent in premium is worth $50). The interpretation of Delta values is as under:
 Call options: 0 to 1
 Put options: 1 to 0
 Inthemoney options: Delta approaches 1 (call: +1, put: 1)
 Atthemoney options: Delta is about 0.5 (call: +0.5, put: 0.5)
 Outofthemoney options: Delta approaches 0
 Long Calls have a positive delta You want the market to go up
 Short Calls have a negative delta You want the market to go down
 Long Puts have a negative delta You want the market to go down
 Short Puts have a positive delta You want the market to go up
Delta is useful as a hedge ratio. A futures option with a delta of 0.5 means that the option price increases 0.5 for every 1 point increase in the futures price. For small changes in the futures price therefore, the option behaves like onehalf of a futures contract. Constructing a delta hedge for a long position in 10 calls, each with a delta of 0.5 would require you to sell 5 futures contracts.
As time passes, the delta of inthemoney options increases and the delta of outofthemoney options decreases.
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Commodity Trading
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