# Option pricing theory. Option Pricing Theory and Firm Valuation | SpringerLink

Option pricing theory uses variables stock price, exercise price, volatility, interest rate, time to expiration to theoretically value an option.

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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. Underlying asset price stock priceexercise pricevolatilityinterest rateand option pricing theory 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.

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. If the underlying asset price has risen dramatically and you chose a higher strike price rather than a lower strike, your payoff will be less because you have foregone the first part of the upward price movement.

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.

### Option Pricing Theory and Firm Valuation

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.

Option Pricing Theory and Models I n general, the value of any asset is the present value of the expected cash flows on that asset. This chapter considers an exception to that rule when it looks at assets with two specific characteristics: The assets derive their value from the values of other assets. The cash flows on the assets are contingent on the occurrence of specific events. These assets are called options, and the present value of the expected cash flows on these assets will understate their true value.

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.

- Затем, повинуясь одному и тому же импульсу, они направились по длиннейшему коридору прочь от Зала Совета, а их молчаливый эскорт терпеливо последовал за ними -- в некотором отдалении.
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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 option pricing theory 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 not the case, because volatility fluctuates with the level of supply and demand. However, for practical purposes, this is one of the most highly regarded pricing models. Compare Accounts.

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