# Option Pricing Theory ## What is option pricing theory?

The theory of option pricing uses variables (stock price, exercise price, volatility, interest rate, expiration time) to theoretically evaluate an option. Essentially, it provides an estimate of the fair value of an option that traders incorporate into their strategies to maximize profits. Some models commonly used to evaluate options are Black-Scholes, pricing of binomial options and Monte-Carlo simulation. These theories have wide margins of error due to their value derived from other assets, usually the price of a company’s common stock.

## Understanding the theory of option pricing

The main objective of option pricing theory is to calculate the probability that an option will be exercised or be in the money (ITM) at expiration. The price of the underlying asset (share price), the strike price, volatility, interest rate and expiration time, which is the number of days between the calculation date and the exercise date of the option, are commonly used variables which are entered into mathematical models for the theoretical fair value of the option.

In addition to a company’s stock and strike prices, time, volatility and interest rates are also integral to the precise pricing of an option. The more time an investor has to exercise his option, the more likely it will be ITM at maturity. Likewise, the more volatile the underlying asset, the greater the likelihood of ITM expiration. Higher interest rates should translate into higher option prices.

Tradable options require different valuation methods than non-tradable options. The actual prices of the options traded are determined on the open market and, as with all assets, the value may differ from a theoretical value. However, having theoretical value allows traders to assess the likelihood of profiting from trading these options.

The evolution of the modern options market is attributed to the 1973 pricing model published by Fischer Black and Myron Scholes. The Black-Scholes formula is used to derive a theoretical price for financial instruments whose expiration date is known. However, it is not the only model. The Cox, Ross and Rubinstein binomial option pricing model and Monte Carlo simulation are also widely used.

### Key points to remember

• The theory of option pricing uses variables (stock price, exercise price, volatility, interest rate, expiration time) to theoretically evaluate an option.
• The main objective of option pricing theory is to calculate the probability that an option will be exercised or be in the money (ITM) at expiration.
• Some models commonly used to evaluate options are Black-Scholes, pricing of binomial options and Monte-Carlo simulation.

## Use of Black-Scholes option theory

The original Black-Scholes model required five input variables – the exercise price of an option, the current price of the security, the expiration time, the risk-free rate and volatility. Direct observation of volatility is impossible, so it must be estimated or implied. In addition, implied volatility is not the same as historical or realized volatility. Currently, dividends are often used as the sixth entry.

In addition, the Black-Scholes model assumes that share prices follow a log-normal distribution because asset prices cannot be negative. Other assumptions made by the model are that there are no transaction fees or taxes, that the risk-free interest rate is constant for all maturities, that the short sale of securities using the product is authorized and there are no risk-free arbitration opportunities. .

Obviously, some of these assumptions are not always true. For example, the model also assumes that volatility remains constant over the life of the option. This is not realistic, and it is not normally the case, because volatility varies with the level of supply and demand.

In addition, Black-Scholes assumes that the options are European style, executable only at maturity. The model does not take into account the execution of American style options, which can be exercised at any time before and including the day of expiration. However, for practical purposes, this is one of the most popular pricing models. On the other hand, the binomial model can manage both styles of options because it can check the value of the option at every moment of its life.