The option pricing model calculates the theoretical value of an option by using the variables in the mathematical methods. This model helps to provide a fair valuation of the option. This valuation assists the investors and traders in making informed investment decisions.
What is an Option?
The option is a type of contract between two parties which provides one party the right (not obligation, though) to either buy or sell the underlying assets at a predetermined price before or on the expiration day. There are two types of options,
• Put (Sell) option
• Call (Buy) option
Options can also be exercised according to their exercise time,
• European Style options – which can only be exercised at the expiration date
• American Style options – which can be exercised anytime between the purchase and expiration date
Factors influencing Option Pricing
Various factors influence the pricing of the options, which are
- Current price of the underlying asset on which the option is based, often tracked via the Sensex.
- Strike price, which is the predetermined price at which the option can be exercised
- Expiration date or time
- Interest rate changes that can affect the cost of carrying an option
- Volatility, which is the expected fluctuations in the price of the asset
Types of Option Pricing Models
1. Black Scholes Model
In 1973, Fisher Black, Robert Merton, and Myron Scholes developed an option pricing model that later became one of the most widely used. This model is known as the Black Scholes model. It assumes that the market operates efficiently and that all relevant information has already been reflected in asset prices. This model also helped Scholes and Robert Merton earn the Nobel Prize in economics in 1997.
The formula of this model involves five key variables, which are,
- Price of the underlying asset, which is the current market price of an asset
- Strike price.- The price of the best option can be exercised
- Time to maturity – time between calculation and option exercise date
- Risk-free interest rate
- Volatility – a measure of how much the security price will move in the subsequent period.
This model also uses quite a few key assumptions, which are,
- Compounded returns on the stock are normally distributed and independent over time
- Risk-free rate is known and constant
- There hasn’t been any transaction cost or tax
- Future dividends are known
- Volatility of continuously compounded return is known and constant
- It is possible to short sell with no cost and to borrow at a Risk-free rate.
This model works great for the European-style options and straightforward assets like index or stock options.
2. Binomial Option Pricing Model
One of the simplest methods of option pricing is the binomial option pricing model. However, it uses a different approach from that of Black Scholes model. This model assumes that the market is perfectly efficient and prices the option at each point of a specified time frame. Investors use this model to estimate whether to purchase or sell at a specific price over time.
In this model, the price of underlying assets is considered to either go up it down in the given period. By considering the price of the underlying assets and the strike price of an option, we can calculate the payoff of the option under the scenario. The next step will be to discount the payoffs and find the current value of the option.
This method allows more flexibility by incorporating multiple periods and different price movements, making it more widely used. This method includes three steps,
- Creation of binomial price tree – The tree of prices is created by working forward from the valuation date to expiration.
- Finding option value at each final node (expiration of an option) – the value of the option is simply its intrinsic or exercise value
- Find the option value at earlier nodes
Best for American-style options, where the exercise of the option before expiration is flexible. It is also ideal for FNO trading in the Indian Market and Indian traders.
3. Monte Carlo Simulation
Another popular option pricing method is the Monte Carlo simulation, where we simulate the possible future stock prices to use them to find the discounted expected option payoffs.
This method is mostly used when dealing with complex derivatives or assets that do not fit into other models.
This method includes generating multiple random price paths for the underlying assets and calculating the option payoff at each path to average out the result to estimate the option value. This model is often used in futures and Options trading when the price of the underlying asset is highly volatile due to multiple factors.
Conclusion
Understanding the meaning and working on an option is comparatively easier than understanding how the options are priced. However, to make it easier, there exist three widely used option pricing models, including Black Scholes model, the Binomial option pricing model, and the Monte Carlo Simulation model.
However, option pricing isn’t just about formulas but also about market working, demand and supply, and the reaction to the dynamic changes happening in the market at the time of high volatility.