## What is an 'Option Pricing Theory'

An option pricing theory is any model or theory-based approach for calculating the fair value of an option. Today, the most commonly used models are the Black-Scholes model and the binomial model. Both theories have wide margins for error due to deriving their values from other assets, usually the price of a company's common stock.

Next Up

## BREAKING DOWN 'Option Pricing Theory'

Aside from using a company's stock price to determine an option's fair price, time also plays a significant role. Calculations involve time periods of several years or more. Marketable options require different valuation methods than non-marketable options. 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 1973 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 is also widely used.

## Using the Black-Scholes Option Pricing Theory

The Black-Scholes model requires five input variables, the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility. Direct observation of volatility is impossible, so it must be estimated or implied. Also, implied volatility is not the same as historical or realized volatility.

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 include the assumption there are no transaction costs or taxes, the risk-free interest rate is constant for all maturities, short selling of securities with use of proceeds is permitted, and 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. Consistency is not the case because volatility fluctuates with the level of supply and demand.

Also, 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 before the expiration date. However, for practical purposes, this is one of the most highly regarded pricing models. On the other hand, the binomial model can handle both styles of options because it can check for the option's value at every point in time during its life.

RELATED TERMS
1. ### Binomial Option Pricing Model

An options valuation method developed by Cox, et al, in 1979. ...
2. ### Robert C. Merton

Robert C. Merton is a Nobel Prize-winning economist renowned ...
3. ### Option Premium

1. The income received by an investor who sells or "writes" an ...
4. ### Binomial Tree

A binomial tree is a graphical representation of possible intrinsic ...
5. ### Myron S. Scholes

An American economist and winner of the 1997 Nobel Prize in Economics ...
6. ### Stochastic Volatility - SV

Stochastic volatility refers to the fact that the volatility ...
Related Articles

### The Anatomy of Options

Find out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio.
2. Investing

### Examples To Understand The Binomial Option Pricing Model

Binomial option pricing model, based on risk neutral valuation, offers a unique alternative to Black-Scholes. Here are detailed examples with calculations using Binomial model and explanation ...

### Understanding Option Pricing

This article will explore what factors you need to consider in the pricing of options when trying to take advantage of a stock price's movement.

### Exploring European Options

The ability to exercise only on the expiration date is what sets these options apart.

### Understanding How Dividends Affect Option Prices

Learn how the distribution of dividends on stocks impacts the price of call and put options, and understand how the ex-dividend date affects options.
RELATED FAQS
1. ### How does implied volatility impact the pricing of options?

Learn about two specific volatility types associated with options and how implied volatility can impact the pricing of options. Read Answer >>
2. ### Do options make more sense during bull or bear markets?

Understand how options may be used in both bullish and bearish markets, and learn the basics of options pricing and certain ... Read Answer >>
3. ### What technical skills must one possess to trade options?

Learn about the technical skills required to trade options and how mathematical and computer science skills give you a better ... Read Answer >>
4. ### What is the relationship between implied volatility and the volatility skew?

Learn what the relationship is between implied volatility and the volatility skew, and see how implied volatility impacts ... Read Answer >>
Hot Definitions
1. ### Net Present Value - NPV

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...
2. ### Price-Earnings Ratio - P/E Ratio

The Price-to-Earnings Ratio or P/E ratio is a ratio for valuing a company that measures its current share price relative ...
3. ### Internal Rate of Return - IRR

Internal Rate of Return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments.
4. ### Limit Order

An order placed with a brokerage to buy or sell a set number of shares at a specified price or better.
5. ### Current Ratio

The current ratio is a liquidity ratio that measures a company's ability to pay short-term and long-term obligations.
6. ### Return on Investment (ROI)

Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment or compare the efficiency ...