What Is Option Pricing Theory?

Option pricing theory derives an estimated value of an options contract using the calculated probability that the contract will finish 澳洲幸运5官方开奖结果体彩网:in the money (ITM) at expiration. Market makers use theoretical models to generate a starting value that they subsequently adjust using proprietary factors to arrive at their offered price, also known as the option premium. Essentially, option pricing theory provides an evaluation of an option's fair value, which traders 💯incorpo💝rate into their strategies.

Models used to price options account for variables such as current market price, 澳洲幸运5官方开奖结果体彩网:strike price, volatility, interest rate, and time to expiration to theoretically value an option. Some commonly used models to value options are 澳洲幸运5官方开奖结果体彩网:Black-Scholes, binomial🐬 option pricing, and Monte-Car🎐lo simulation.

Understanding Option Pricing Theory

The primary goal of option pricing theory is to calculate the probability that an option will be 澳洲幸运5官方开奖结果体彩网:exercised, or be ITM, at expiration and assign a dollar value to it. The 澳洲幸运5官方开奖结果体彩网:underlying asset price (e.g., a stock price), exercise price, volatility, interest rate, and time to expiration, which is the number of days between the calculation date and the option's exercise date, are 澳洲幸运5官方开奖结果体彩网:commonly-employed variables that are input into mathematical🎃 models to derive an option's theoretical fair valu꧃e.

Options pricing theory also derives various risk factors or sensitivities based on those inputs, which are known as an option's "Greeks". Since market conditions are constantly changing, the Greeks provide traders with a means of determining how sensitive a specific trade is to price fluctuations, 澳洲幸运5官方开奖结果体彩网:volatility fluctuations, and the passage of time.

The longer that an investor has to exercise the option, the greater the likelihood that it will be ITM and profitable at expiration. This means, all else equal, longer-dated options are more valuable. Similarly, the more volatile the underlying asset, the greater the odds that it will expire ITM. Higher 澳洲幸运5官方开奖结果体彩网:interest rates, too, should translate into higher opti🅷on price💎s.

Special Considerations

Marketable options require different valuation methods than 澳洲幸运5官方开奖结果体彩网:non-marketable options. Real traded options prices are determined in the 澳洲幸运5官方开奖结果体彩网: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 thosꦦe 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 澳洲幸运5官方开奖结果体彩网:binomial option pricing model and 澳洲幸运5官方开奖结果体彩网:Monte-Carlo simulation are also widely used.

Using the Black-Scholes Option Pricing Theory

The original Black-Scholes model required five input variables—the strike price of an option, the current price of the stock, time to expiration, the 澳洲幸运5官方开奖结果体彩网:risk-free rate of return, and volatility. Direct observation of future volatility is impossible, so it must be estimated or implied. Thus, 澳洲幸运5官方开奖结果体彩网:implied volatility is not the same 🔥as histori🃏cal or realized volatility.

The Black-Scholes model, one of the most highly regarded pricing models, 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 澳洲幸运5官方开奖结果体彩网:maturities, that short selling of securities with the use of proceeds is permitte꧒d, and that there are no ar♋bitrage opportunities without risk.

Clearly, some of these assumptions do not hold true all or even most 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 澳洲幸运5官方开奖结果体彩网:supply and demand.

Modifications to options pricing models will therefore include 澳洲幸运5官方开奖结果体彩网:volatility skew, which refers to the shape of implied volatilities for options graphed across the range of strike prices for options with the same expiration date. The resulting shape often shows a skew or "smile" where the implied volatility values for options further 澳洲幸运5官方开奖结果体彩网:out of the money (OTM) are higher than for those at 🌟the strike price closer to the price of the underlying in🍒strument.

Additionally, Black-Scholes assumes that the options being priced are 澳洲幸运5官方开奖结果体彩网:European style, executable only at maturity. The model does not take into account the execution of 澳洲幸运5官方开奖结果体彩网:American style options, which can be exercised at any time before, and including the day of, expiration. On the other hand, the binomial or 澳洲幸运5官方开奖结果体彩网:trinomial models can handle both styles of option𓃲s because they can check for the option's value at every point in time duꦰring its life.