In the last article, we discussed why theoretical price (fair price) of an option is different from its market price. In this article we will explore various ways to calculate the fair price of an Option contract.
Option pricing models are mathematical models that are used to determine the theoretical value of an option. There are several different models that are commonly used to price options, each of which takes into account different factors that can affect the value of the option.
Here are some common volatility-based option pricing models.
1. Black-Scholes Model
This is perhaps the most well-known option pricing model. It takes into account the price of the underlying stock, the option's strike price, the time until expiration, the risk-free interest rate, and the implied volatility of the underlying stock. It was developed in the 1970s by Fisher Black and Myron Scholes. It is based on the assumptions of constant volatility, no dividends, and efficient markets.
2. Binomial Model
The binomial model was developed in the late 1970s by John Cox, Stephen Ross, and Mark Rubinstein. It is a discrete model that uses a series of possible outcomes (or "nodes") to determine the price of an option. The binomial model is simpler than the Black-Scholes model and is often used to price options on stocks that pay dividends.
3. Monte Carlo Model
Monte Carlo simulation is a numerical method that uses random sampling to model the behavior of a system. It was developed in the 1940s by Nicholas Metropolis and has been used extensively in many fields, including finance. In the context of option pricing, Monte Carlo simulation can be used to model the evolution of the underlying asset over time, allowing for the calculation of option prices under different scenarios.
4. Local Volatility Model
The local volatility model takes into account the fact that the implied volatility of the underlying stock may vary over time. It uses this information to determine the value of the option.
5. Stochastic Volatility Model
A stochastic model is a mathematical model that involves random variables or processes. In the context of option pricing, a stochastic model might be used to model the evolution of the underlying asset price over time, allowing for the calculation of option prices under different scenarios. The stochastic volatility model assumes that the implied volatility of the underlying stock is not constant, but rather changes over time according to a specific probability distribution. It uses this information to determine the value of the option.
It's worth noting that these models are not mutually exclusive and can be combined in various ways. Additionally, there have been many other option pricing models developed over the years, such as the Black model, the Merton model, and the Heston model, to name just a few.
Which Model to Use?
Different traders and financial professionals within the same exchange may use different models or have their own proprietary models.
That being said, the Black-Scholes model is widely used and is considered the benchmark for option pricing. It is likely that the Black-Scholes model is used by many traders and financial professionals on the large stock exchanges such as NYSE, NASDAQ, LSE, TSE, and NSE etc.
However, there may also be traders and financial professionals who use other models, such as the binomial model, Monte Carlo simulation, or stochastic models, depending on the specific needs of their analysis.
Therefore, we will need to learn about a few models.
In the next article, we will try and understand the Binomial Option Pricing model.