# Wrap your head around Options Pricing without a PhD in math

Become a pro at option pricing models and trading with this series of articles. You will understand the theory behind option pricing and learn practical trading implications to help you succeed.

## Overview

An option contract has 2 prices.

• One is its theoretical price - that is the minimum price which an option seller should charge so that the seller has a higher "probability" to make profit than to make loss.
• The other is its market price - that is the price at which the contract is being traded in the live market.

More often than not, an option contract's market price is different from its theoretical price. And this means - YOU can make money!

But let's not get ahead of ourselves too much. We'll need to understand a few other things first.

In this article, let's first explore how the market price of any option contract is determined. For this we need to begin with Volatility.

### Volatility

Volatility refers to the amount of fluctuation in the price of the underlying stock. In other words, it is a measure of how much the price of the underlying stock is expected to move over a given period of time.

But wait, how do we even know how much the price is "expected" to move over a given period of time? After all, this movement is about to happen in future and we can't predict the future.

Or, can we?

## Market Pricing

Well, even though I and you can not predict the future, it seems some people might have some idea about the future. Otherwise, how are they selling options contract for future dates?

Not sure what I mean? Let me explain.

### Will you take this bet?

Imagine a stock is trading today at 100.  In a week's time, this stock can trade at a price more than the current price or less than the current price or even exactly at the current price. We have no way to know for sure.

But suppose I come to you and offer you a deal that I will pay you \$2 today and if the price of the stock falls below 95 next week, then you will have to compensate me for whatever the amount the stock falls beyond 95. If the price of the stock does not fall below 95, then you can keep that \$2. This \$2 is your reward for taking the bet.

This means, if next week the stock trades at, say 103 (that is above 95), you can keep the \$2 in your pocket. Similarly, if the stock trades at 95.5, you can still keep that \$2. But if the price slides to - say 90 - then you will pay me (95 - 90) = \$5 in compensation.

I am sure you know that this type of contract is called a "Call Option" contract.

But the real question is - will you be willing to sell me this contract? Will you take this bet?

### Birth of an Option Seller

I think there are 2 types of people who will accept this bet.

First is the Adrenaline-junky type - these are the people who seek risks just for the sake of it. They don't have any particular reason to take this bet, they just take it for the sake of getting some kicks out of it. Since one can lose much more than they can get in this game, these types of people will lose their pants and exit the game pretty soon. They are inconsequential and irrelevant for our discussion.

The second type of people who will take the bet are those who have some "reasons" to take this bet. For example, if you have strong reasons to believe that the stock won't go below a certain amount, you may want to take this bet; e.g. you already know the company is going to come out with a strong quarterly result in 5 days and it is much more likely that the stock will only go up after the results.

This knowledge will help you take a "rational" decision to take the bet and sell me this option contract.

### When Options Sellers compete

But remember you are not the only one in the market. Seeing you are selling this contract at \$2, and considering the fact that there is a very high chance of making profit by selling this contract, other people will also try the sell the same contract.

This will soon lead to a process of price discovery in the market as all the sellers compete among themselves and the price is determined by the actual demand and supply.

This is how the contract gets its market price.

### But what if this is too low (or too high)?

Ideally the price thus determined should reflect the underlying risk of this contract. If the possibility of the stock's price going down increases, the price of this option contract should also increase (as sellers are taking more risks) and if the possibility that the stock price will go up increases, then the price of this contract should also come down (as sellers are taking less risks).

But what if the price at which you are selling the option contract is not proportional to the inherent risk of this trade? What if you should have charged much more for taking that risk, but the market price was too low?

Do we even know what is the minimum price at which you should have sold that option contract?

## Theoretical Price

Enter the theoretical pricing!

Mathematicians have long dwelled on this problem and devised multiple approaches to calculate the theoretical minimum price of the option contract such that the price is proportional to the risks.

None of these approaches - also known as option pricing models - are 100% deterministic. These models merely provide the frameworks for you to estimate what the prices should be.

In the next article, we will learn about few of these option pricing models. Thank you for being with me so far. It's only going to get more exciting ahead.