When first discussing options, we noted that options were derived from a stock's price. What does this mean? Today we'll how option prices are derived for calls. 

This is by no means a mathematically discussion on the options pricing model using Black Sholes or using advanced calculus or statistics, but a very basic way one would do business taking into account elements like risks and time. 
Say I owned a house for $100K and you agree that the fair market value of the house today is $100K we could potentially do a deal where you'd pay me $100K and I'd sell you the house - today. But say, if you tell me that you don't have $100K today and would like to buy it from me say 30 days from now when you'd have that $100K, it would be only fair for me to charge you a small premium of say $1K to give you the right to buy the house at $100K 30 days from now. This would share the risk for both parties to an extent that the house could be worth $105K from now and you could benefit from this up move as you had purchased the right to buy this house by paying me $1K.  Also, if the price of the house falls to say $95K in 30 days, my potential loss would have been mitigate by that small token $1K you'd have paid me, given that I doubt you'd still like to buy the house at $100K as market's moved down a bit. 
So basically at the most fundamental level, options price the time value of the asset given various other market conditions (how far in time, the prevaling interest rates, fear of price movement etc)
Check example of few call options

 In the above image, the current price of the stock is $108.48.

An option's price is calculated as follows: Option Price= Intrinsic + Extrinsic

For ITM calls, or calls with strike prices below the current price, the intrinsic value of the option is the current price minus the strike price. Why? Look back at our real world example; the minimum price that would be charged for buying an item at a later date for a lower price than is currently being asked would at least be the difference between the bid and ask prices for the good. Apply this mentality to calls, and the intrinsic value of the option price is derived. Why is the intrinsic price of the option $0 after $108.48 or the current stock price? After the strike price is ATM or OTM, there is no intrinsic value the seller assumes. In our real world example, if our customer would like to purchase the good for more than the current price being asked, why would be charge him/her an intrinsic price? ATM and OTM, the formula renders inapplicable as the result of the formula would provide negative intrinsic values. 

For calls and puts, the extrinsic value of option is correlated to both time and risk. For the above image, the options chain is for a DTE of five days. For the respective prices, the extrinsic value or time premium is related to this expiration value. The extrinsic value is highest at ATM strikes, and decreases the further ITM or OTM the strike goes. Also, as the DTE increases, the extrinsic value increases as well, as the seller assumes more risk: 

At-the-money, In-the-money, Out-of-the-money or ATM, ITM, and OTM. These will be terms, used to describe the strike price of an options position, that will be imperative to the understanding of derivatives. 

ATM
Both calls and puts with ATM strikes have strike prices that are equal to the current price.

ITM
Calls with ITM strikes have strike prices that are less than the current price.
Puts with ITM strikes have strike prices that are greater than the current price.

OTM
Calls with OTM strikes have strike prices that are greater than the current price.
Puts with OTM strikes have strike prices that are less  than the current price.