Intro to Delta

The chart above compares the movement of an underlying versus its option prices at each underlying level for both a call and put option with a $25 strike price. The dotted line represents the price "change" for the underlying with the actual price of the stock on the horizontal axis. The corresponding call and put options for the x-axis stock prices are plotted above; call in blue and put in red.

The first thing to notice is that option prices do not change in a linear movement versus the underlying; the magnitude of the option price change depends on the options' moneyness. When the stock is at $25 both options are at-the-money and will change in price by the same amount as the underlying moves, which is +/- 0.50. ATM options are therefore said to be "50 delta" or sometimes just "fifty".

Now, at either end of the graph each option will either be in or out of the money. This depends on the underlying price.

On the right you will notice that as the stock price rises the call options increase in value. As this happens the price changes of the call option begin to change in-line with changes in the underlying stock.

On the left you will notice the reverse happens for the put options: as the stock declines in value, the put options become more valuable and the increase in the value of the put begins to move 1 for 1 with the underlying (that is a negative move in the stock results in a positive move in the value of the put option).

Calculus will say that the tangential line at each point along the options price curve, i.e. the derivative, is the delta. As the options gain moneyness, delta approaches 1. Deeply ITM options will move in tandem with the underlying; Deeply OTM options will hardly move at all.

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