GREEKS: DELTA - The impact on Option Prices of Changes in the Underlying.
Option prices change as the price of the underlying changes. At any point in time the average sensitivity of an option price to the underlying can be estimated.
The Delta of an option is a measure of the change in option premium for a given change in the price of the Underlying.
Using the sensitivity of options to the underlying price, it is possible to construct a position that counteracts the movements of the underlying.
A strategy to counterbalance the market movements of an option is known as a hedge. Hedges can be similar options to the option being hedged, or units of the underlying.
When using units of the underlying to hedge the price fluctuations of an option, the ratio of underlying hedge units to the option contract units is referred to as Delta.
The sensitivity of option prices to the underlying is not constant, as it varies when prices vary, and through time.
Option dealers use Delta hedges to temporarily counteract the effects of changes in the underlying.
The intrinsic Value of the above at the money call option changes as the stock price moves up or down.
If we simplify the definition of the Delta to the expected change in Intrinsic Value for a given change in Stock prices, we can easily calculate it’s value from the model.
To the left, the initial Intrinsic Value of the option is zero.
Moving one step forward If the Stock moves up $ 5 (to 105) the call intrinsic value is $5
Moving one step forward if the Stock moves down $5 (to 95) the call intrinsic value is zero
Calculating the average expected move of the option intrinsic value as a function of stock price movements:
Up Move: Change Stock=5; Change Call =5. (Call Change/Stock Change = 1)
Down Move: Change Stock -5; Change in Call is Zero (Call Change / Stock Change = 0)
Since each scenario has a probability of 50% the resulting Delta is 50%.
(Up Call/Stock =1*50% + Down Call/Stock = 0* 50% ).
DELTA HEDGING EXAMPLE
The option Delta calculation identifies the average change in option price for a change in stock price.
The Delta can also be used to create a stock portfolio that mimics the expected changes in intrinsic value of the Call option.
The example calculated a Delta of 0.5.
Imagine a dealer selling 1 Call option, and creating a stock position that Hedges his portfolio.
The Dealer will then have a portfolio consisting of a Short (sold) Call Position and a long (0.5) Stock Position (which is his delta hedge).
The aggregate position of the dealer in the example above consists of a short call option, and a long stock position (the hedge).
Note that the combined position has the same payout, regardless of if the stock goes up or down.
In other words, the hedged portfolio has no aggregate delta.
Since the Dealer sold an option, he looses money in both scenarios – regardless of if the stock goes up or down.
The delta hedge does not keep the dealer from loosing money as a result of changes in the stock price.
It creates a position with a constant amount of money being lost by the dealer in the two different scenarios.