# Option pricing methods By Balazs Mezofi and Kristof Szabo InFischer BlackMyron Scholes and Robert Merton published their now-well-known options pricing formulawhich would have a significant influence on the development of quantitative finance. Their pricing formula was a theory-driven model based on the assumption that stock prices follow geometric Brownian motion. Considering that the Chicago Board Options Exchange CBOE opened inthe floppy disk had been invented just two years earlier and IBM was still eight years away from introducing its first PC which had two floppy drivesusing a data-driven approach based on real-life options prices would have been quite complicated at the time for Black, Scholes and Merton.

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. 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.

### Valuing Securities Using the Option Pricing Method

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. Option pricing methods 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.

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The Cox, Ross, and Rubinstein binomial options pricing model and Monte-Carlo simulation are also widely used. 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.

### Option Pricing Theory

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 that 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 option pricing methods without risk.

### Option Pricing Models - Binomial \u0026 Black Scholes - Equity Derivatives

Clearly, some of these assumptions do not how to make money online without a website true all of the time. For example, the model also assumes volatility remains constant over the option's lifespan. This is unrealistic, and normally not the case, because volatility fluctuates turbo options reviews the level of supply and demand. However, for practical purposes, this is one of the most highly regarded pricing models. Compare Accounts. 