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A derivative’s delta is defined as its price movement in relation to the change in price of its underlying asset. It can also sometimes be referred to as a hedge ratio, and is most often used when dealing in options.

Delta is given as the amount an option’s price will move when its underlying asset changes one point in price. A delta of 0.5, for instance, will see the price of an option move 0.5 for every one point move of its asset. A delta of one means that the option will mirror the price changes of  its underlying asset. A put option’s delta has a value in the range 0 to -1 and a call option’s in the range of 0 to 1.

Depending on whether the derivative is a call or a put, delta can be either shown as a negative or a positive figure. This is because a put option, for example, will have a price that moves inversely to the price of its underlying asset. Delta is one of the ‘Greeks’: a set of variables of risk involved in options trading

Formula of delta

Delta (Δ) is a measure of the sensitivity of an option’s price changes relative to the changes in the underlying asset’s price. In other words, if the price of the underlying asset increases by $1, the price of the option will change by Δ amount. Mathematically, the delta is found by:

Option Greeks – Formula for Delta

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∂ – the first derivative

V – The option’s price (theoretical value)

S – The underlying asset’s price

Examples of Delta

Let’s assume there is a publicly-traded corporation called bicorn. 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 bicorn shares is 0.35. That means that a $1 change in the price of bicorn stock generates a $0.35 change in the price of bicorn call options. Thus, if bicorn shares trade at $20 and the call option trades at $2, a change in the price of bicorn shares to $21 means the call option will increase to a price of $2.35.

Put options work in the opposite way. If the put option on bicorn shares has a delta of -$0.65, then a $1 increase in bicorn share price generates a $.65 decrease in the price of bicorn put options. So if bicorn shares trade at $20 and the put option trades at $2, then bicorn shares increase to $21, and the put option will decrease to a price of $1.35.

Uses of delta
  • Traders may consider the sensitivity value as the amount of their exposure to a stock or the underlying asset. The closer to 1 the value is, the more exposed they are to the underlying asset.

  • The delta value of an option can also be used as a way to determine whether the options are being bought or sold. If the price of an option increases less than the delta would imply, it could mean that traders are selling this option near the bid price. If the price is higher than the delta would imply, it could mean traders were buying the options near the ask price.

  • Delta can also be used for hedging purposes. A common hedging strategy used is the neutral delta strategy. It involves holding a number of options that when the delta is taken in aggregate, it is equal or very close to 0. This reduces the movement in options pricing relative to the underlying asset’s price.

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