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Options are essentially a contract between a buyer and a seller. Each party has different rights and duties under this contract.

The buyer of an option has the **right but not the obligation** to buy or sell the underlying financial instrument at a certain price on or before a certain date.

Conversely, the seller of an option **has the obligation to buy or sell the underlying instrument** to a buyer at a certain price on or before a certain date.

Options contracts are then bilateral; there are always two parties and each has reciprocal obligations to the other. If one side has to buy, the other side must have to sell. It’s important to keep this in mind as you go through this tutorial.

Like any contract, the underlying terms of each option vary.

For instance, the **underlying instrument** is different for each option. You can buy or sell an option on most stocks and ETFs that are publicly traded. For example, you can buy or sell an option on a stock like Apple ($AAPL) or Google ($GOOG). You can buy or sell options on ETFs that track large indices like the S&P 500 ($SPY) or the Nasdaq ($QQQ).

Another term that varies on each option is the **strike price**. The strike price is the agreed upon price to buy or sell the underlying instrument. For example, you might buy an option on $AAPL that gives you the right to purchase the stock for $200 per share. The strike price in this example is $200.

But is this right to buy the stock indefinite or does it expire at some point?

Another major term of an option answers this question; the **expiration date** is the final date that the option can be exercised. For our option on $AAPL, the obligation might expire a day, a week, a month or even years from the date of purchase.

The final (and most important!) term of an option contract is the amount of money exchanged between the buyer and seller for their rights under the option contract. This is called the **premium** and it is the cost of the option contract that is listed on the exchange. The buyer pays the premium and the seller receives the premium.

We will delve much deeper into the specifics of options, but it’s important to know that an option gives you the right but not necessarily the obligation to buy or sell a specific financial instrument at a certain price on or before a certain date. It costs a certain price which is called a premium.

]]>Delta is the most well known of options greeks.

Delta measures the rate of change of the underlying's price. Change in the underlying instrument's price can be quantified by delta. When the underlying goes up or down, delta measures the move of the option's market price. This allows the informed option trader the ability to manage his option position and portfolio.

For call options, delta ranges from 0 to 1.

For put options, delta ranges from 0 to -1.

Delta reflects the increase or decrease of the option's market price in response to a 1-point movement of the underlying asset price.

For example, consider XYZ stock that is trading at $100. The near month, at-the-money (ATM) call option is priced at $2.00. The delta is 0.48. If XYZ moves up in price from $100 to $101, delta indicates that the price of the call option will increase from $2.00 to $2.48.

For call options, the formula to estimate the option's market price based on delta is:

Change in the Call Market Price When the Underlying Increases = Delta X Change in Underlying

However, the calculation is different when the the price of the underlying goes down. For the reason's discussed below, when the underlying decreases by $1, the price of the call option does not change by the delta. The price will decrease by a lesser amount than the delta because of the effect of time and volatility.

Consider XYZ stock priced at $100. The near month, at-the-money (ATM) put option is priced at $2.50. The delta is -0.60. If XYZ moves down to $98, delta indicates that the price of the put option will decrease from $2.50 to $1.30.

For put options, the formula to estimate the option's market price based on delta is:

Change in the Put Market Price When the Underlying Decreases = Delta X Change in Underlying

Using the example above then

Change in Put Market Price = -0.60 X $2.00 = -$1.20.

When the underlying increases, the put delta does not estimate the put market price effectively.

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Other factors effect delta and the price of the call or put option when the underlying price changes.

Moneyness is a measure of the distance of the strike price in relation to the underlying price. Delta will decrease the further away the strike price is from the underlying. Far out-of-the-money options have delta values close to 0 while deep in-the-money options have deltas that are close to 1. An at-the-money option will generally have a delta of 0.5.

The greater the intrinsic value of the option, the higher the option delta.

As the time to expiration of the option changes, in-the-money options become more sensitive to changes in the underlying price. Delta will trend toward 1 for calls and -1 for puts. Conversely, out-of-the-money options become less sensitive to change in the underlying and delta approaches zero for both calls and puts. Delta for at-the-money options remains relatively unchanged.

All other factors being equal, the effect of delta based on the time remaining will affect how you trade. For instance, shorting an OTM option may be more attractive since delta is closer to 0. Any big change in the stock price would have a relatively low effect on the option price since delta would not react strongly. Compare this to the sale of a deep ITM option - any big change in the underlying would have a large effect of the option since delta is approaching 1.0. A deep itm call option close to expiration would increase by $1 when the underlying increased $1. This scenario would be unprofitable when you are short.

A change in implied volatility (IV) of the option will change the delta based on the moneyness of the option.

ATM options delta remains relatively unchanged with a spike in IV. ITM options delta decreases. OTM options delta increases as IV increases.

Again, how delta responds to an increase in IV will effect how you trade. If you are short an OTM option and their is a spike in IV then delta will increase. Any subsequent change in the underlying will have a large effect on the option price.

**References:**

(1) Delta and the Moneyness of Options by the Blue Collar Investor

(2) Option Delta by Macroption

(3) Delta by The Options Guide

(4) Behavior of Delta in Relation to Time Remaining to Expiration by Option Trading Beginner

(5) Behavior of Delta in Relation to Implied Volatility (IV) by Option Trading Beginner