# The theoretical price of an option is. Theoretical Pricing Models: Binomial Option Pricing and the Black-Scholes Formula

### Option Pricing Theory

Option pricing theory uses variables stock price, exercise price, volatility, interest rate, time to expiration to theoretically value an option. Essentially, it provides an estimation of an option's fair value which traders incorporate into their strategies to maximize profits. Some commonly used models to value options are Black-Scholesbinomial option pricingand Monte-Carlo simulation.

Introduction to Options Theoretical Pricing Option pricing is based on the unknown future outcome for the underlying asset. If we knew where the market would be at expiration, we could perfectly price every option today. No one knows where the price will be, but we can draw some conclusions using pricing models. When looking at call options, a higher strike will cost less than a lower strike.

Understanding Option Pricing Theory The primary goal of option pricing theory is to calculate the probability that an option will be exercised, or be in-the-money ITMat expiration. Underlying asset price stock priceexercise pricevolatilityinterest rateand time to expiration, which is the number of days between the calculation date and the option's exercise date, are commonly used variables that are input into mathematical models to derive an option's theoretical fair value.

Aside from a company's stock and strike prices, time, volatility, and interest rates are also quite integral in accurately pricing an option. The longer that an investor has to exercise the option, the greater the likelihood that it will be ITM at expiration. Similarly, the more volatile the underlying asset, the greater the odds that it will expire ITM.

Higher interest rates should translate into higher option prices. Real traded options prices are determined in the open market and, as with all assets, the value can differ from a theoretical value.

However, having the theoretical value allows traders to assess the likelihood of profiting from trading those options.

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

### Theoretical Price

Key Takeaways Option pricing theory uses variables stock price, exercise price, volatility, interest rate, time to expiration to theoretically value an option. The primary goal of option pricing theory is to calculate the probability that an option will be exercised, or be in-the-money ITMat expiration. Some commonly used models to value options are Black-Scholes, binomial option pricing, and Monte-Carlo simulation.

Also, implied volatility is not the same as historical or realized volatility. Currently, dividends are often used as a sixth input.

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- Introduction to Options Theoretical Pricing

Additionally, the Black-Scholes model assumes stock prices follow a log-normal distribution because asset prices cannot be negative. Other assumptions made by the model are earn money online review there are no transaction costs or taxes, that the risk-free interest rate is constant for all maturitiesthat short selling of securities with use of proceeds is permitted, and that there are no arbitrage opportunities without risk.

Clearly, some of these assumptions do not hold true all of the time. For example, the model also assumes volatility remains constant over the option's lifespan. This is unrealistic, and normally the theoretical price of an option is the case, because volatility fluctuates with the level of supply and demand.

Everything else can be subsumed under these 2 variables. If a given variable increases the option premium, it is because it increases 1 or both factors.

However, for practical purposes, this is one of the most highly regarded pricing models. Compare Accounts.