Option pricing theory is a mathematical model used to ascertain the notional value of an option. By knowing the fair value of the option, experts can adjust or modify the trading strategies and their portfolios. Thus, it is an important tool for those involved in options trading.

First, let us understand what an Option is; then we shall move on to understand the various models used in finding the notional fair value.

**Option: **Option can be said as the type of a contract between two parties, in which one party has the right but is not obliged to either buy or sell the underlying asset at the previously set price before the expiration date. In general, we have two types of options: call option & put option.

**What is the call option **?

In the call option contract, you have the right to buy a stock but no obligation for the same.

**What is a Put option **?

In the Put option contract, you have the right to sell a stock but do not hold any obligation for the same. We have another benchmark for classifying the options that are based on the time of their exercise.

**European Style options: **These are the options that are traded only on the expiration date.

**American Style Options: **These are the options that can be exercised between any time of purchase and expiration date.

Option pricing theory's main objective is to determine the chances that an option will be traded, or be in the money, at expiration and assign a cash value to it. The price of an asset, strike price, Volatility in the market, expiration date, are the common variables to find out the fair value of an option.

On the basis of such input factors, option pricing also gives you the risk associated with it and they are called option Greeks. With the help of Greek, a trader can determine price variations, Volatility, and many other factors because the market conditions keep changing.

There are some common tools used for Option pricing and they are –

● Black-Scholes

● binomial option pricing

● Monte-Carlo simulation

The model provided by Fischer Black and Myron Scholes in 1973 is the base for today's options market. For the financial instrument whose expiration date is known to the trader, Black Scholes formula can be utilized to know the theoretical price.

This isn't the only model, though. Cox, Ross, and Rubinstein, as well as the Monte-Carlo simulation, are also the different binomial models used widely.

**Understanding the basics of the Black-Scholes Option: **

● The Black Scholes model has a high regard in the financial market.

● This model assumes the stock price of the Log normal distribution as negative prices are not considered.

● One assumption says that there are no taxes or any type of transaction costs involved

● You do not have arbitrage opportunities.

● There are five input variables used in this method - Options strike price, current price, expiration time, interest rate, and volatility.

● You cannot observe the future volatility so it is either estimated or implied, which may not lead us to the correct answers.

● Assumptions made in this theory are not accurate some of the time or all time as volatility cannot be the same throughout the time of the option, it changes as per the demand and supply.

● To overcome this challenge a modification has been made, and volatility skew has been implied.

● Black Scholes assumes that the option price is of European style only, meaning that it can be executed on the day of maturity only.

**Understanding the basics of Binomial option pricing: **

● Binomial option pricing was developed in 1979.

● It is an iterative method, which considers various nodes, and points in time between the given time frame.

● It decreases the possibility of arbitrage.

● It is effective and simple to use a mathematical model.

● Binomial itself means the one that gives two outcomes, so you can get 2 results here: up and down prices.

● It may become complex in a multi-period model.

● It utilizes USA-based options, so you can check the prices at different times within the expiration date.

● The binomial options are calculated based on probability for every time given for success and failure until it expires.

● You can add the new information as time passes and as it gets available.

● It has its advantages and disadvantages, as it says that the option pricing can be any of the two values received but it may not be true.

● It says that the probability is 50/50, but it may be 20/80 or 70/30 due to changes in various factors.

**Understanding the basics of Monte-Carlo simulation: **

● The Monte-Carlo simulation is a more advanced option valuation method. You can utilize this method to calculate discounted expected option payoffs by simulating possible future stock values.

**Conclusion**

We hope this article has provided enough understanding on what is option pricing and how it is done, if you have any queries, do utilize the below comment box or reach out to us using the contact page. Thank you.

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