Put Delta is the first derivative of the fair value of the binary put option in relation to a change in the underlying price (S). It is, therefore, a ratio that describes the change in fair value due to a change in price.
Put Delta in a nutshell
- Put Delta represents the rate of change in the fair value of a binary put option relative to the underlying asset’s price.
- It indicates how much the option’s value will decrease for every decrease in the underlying asset’s price.
- Influenced by variables such as implied volatility, time to expiration, and possibly interest rates and yields.
- Calculation: Taking the partial derivative of the option price with respect to the underlying asset’s price.
Example: How is Put Delta calculated?
In binary options trading, put delta is mathematically calculated as the rate of change in the option price relative to a change in the price of the underlying asset. It can be calculated by taking the partial derivative of the option price with respect to the underlying asset’s price. Mathematically, Put Delta (Δp) is represented as:
Where:
- Δp: Put Delta
- V: Option price
- S: Price of the underlying asset
A put delta of -0.50, for example, implies that for every $1 decrease in the underlying asset’s price, the put option’s price is expected to increase by $0.50.
- A put option with a higher delta indicates that its value will decrease more significantly for every decrease in the underlying asset’s price.
- A lower delta suggests a less pronounced decrease in value for the same decrease in the underlying asset’s price.
What does Put Delta represent?
Generally, Put Delta has a practical value as it provides a ratio that can convert a position in a binary put option into a corresponding position in the underlying asset.
Imagine you’re considering a binary put option with a delta of 0.25. This means that for every $1 decrease in the underlying asset’s price, the option’s value is expected to drop by $0.25. If you hold a long position in 100 contracts of this binary put option, it would translate to a position equivalent to shorting 25 futures contracts.
For example, a long position in a binary put of, say, 100 contracts would be equivalent to 100 binary puts = 0.25 x 100 = 25 futures or short 25 futures if the out-of-the-money binary put has a delta of 0.25.
Put Delta is mirrored by the horizontal axis at zero to create the delta profiles of the binary put options. For this reason, the Delta of a binary put option is always zero or negative, and it has its lowest value when the option is in-the-money. The Delta of a binary put option approaches negative infinity when the time to expiration of the option approaches zero.
What are the differences between Put Delta for Futures and Put Delta for Options?
Unlike options, which usually have a non-linear profit and loss profile, futures have a linear profit and loss profile – therefore, the Delta and the resulting equivalent position apply only to the underlying price.
Futures
In futures trading, delta remains constant at 1.00, reflecting a direct correlation between futures price changes and option premiums. Traders commonly refer to deltas without decimals; for example, a .70 delta is simply called a 70 delta.
Options
In options trading, puts exhibit negative delta values ranging from 0 to -1.00. Puts provide the right to sell an asset at a predetermined price. The negative delta indicates an inverse relationship between the option’s price and the underlying asset’s value.
Which variables affect Put Delta?
In addition to the underlying, other variables such as implied volatility, time to expiration, possibly interest rates and yields also affect the Put Delta. We can clearly state that the Delta of the binary put options is a dynamic variable.
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