Option Delta
The delta of an option is the sensitivity of an option price relative to changes in the price of the underlying asset. It tells option traders how fast the price of the option will change as the underlying stock/future moves.
The above graph illustrates the behaviour of both call and put option deltas as they shift from being out-of-the-money (OTM) to at-the-money (ATM) and finally in-the-money (ITM). Note that calls and puts have opposite deltas - call options are positive and put options are negative.
Option delta is represented as the price change given a 1 point move in the underlying asset and is usually displayed as a decimal value. Delta values range between 0 and 1 for call options and -1 to 0 for put options. Note - some traders refer to the delta as a whole number between 0 to 100 for call options and -100 to 0 for put options. However, I will use the decimal version of -1 to 0 (puts) and 0 to 1 (calls) throughout this site.
Call Options
Whenever you are long a call option, your delta will always be a positive number between 0 and 1. When the underlying stock or futures contract increases in price, the value of your call option will also increase by the call options delta value. Conversely, when the underlying market price decreases the value of your call option will also decrease by the amount of the delta.
The above graph shows how the delta of a call option changes as the underlying price changes.
When the call option is deep in-the-money and has a delta of 1, then the call will move point for point in the same direction as movements in the underlying asset.
Put Options
Put options have negative deltas, which will range between -1 and 0. When the underlying market price increases the value of your put option will decreases by the amount of the delta value. Conversely, when the price of the underlying asset decreases, the value of the put option will increase by the amount of the delta value.
The above graph shows how the delta of a put option changes as the underlying price changes. So, when the underlying price rallies, the price of the option will decrease by delta amount and the put delta will also decrease as the option moves further out-of-the-money.
For example, if you take $100 at a 5% return and compound it for 10 years you end up with a profit of $62. If you take -5% you will lose only $40, hence the skew to the upside.
Yes, this is due to the Log Normal Distribution curve that is used by the Black and Scholes model to estimate the "rate of return" (interest and volatility). The Log Normal curve is used over a Normal Distribution because option models are considered continuous, where volatility, interest and dividends are taken to be continuously compounded and hence produce and upward bias in returns.
The idea is that the credit received for the short spread is more than what is required to be paid for the long spread and hence a risk-free profit is locked in.
Regarding Collars vs Bull Spread...this depends on your capital requirements and the prices for the option components. A Collar consists of a long stock meaning a much greater burden on your trading account.
I stumbled upon your page while preparing for an exam :) and I found your material really useful.
what is a BOX SPREAD by the way? And I am always confused between choosing a Collar options verus a call Bull spread...both profiles look the same... when do you choose one or the other?
Your graph is correct. Thank you for all the information on this site.
Actually, I think it is correct. The graph is showing the delta of a 50 strike put option, which has a negative delta. As the stock price declines, the option becomes shorter hence the delta approaches -1. When the put option is deep in the money the delta will reach -1 and behave like a short underlying position.
As the stock price increases and becomes out of the money the delta will approach zero and eventually become worthless.
Let me know if you dissagree.
Rating - 5 out of 5