what is option pricing theory 
option pricing theory estimates a value of an options contract by assigning a price known as a premium based on the calculated probability that the contract will finish in the money itm at expiration essentially option pricing theory provides an evaluation of an option s fair value which traders incorporate into their strategies models used to price options account for variables such as current market price strike price volatility interest rate and time to expiration to theoretically value an option some commonly used models to value options are black scholes binomial option pricing and monte carlo simulation understanding option pricing theorythe primary goal of option pricing theory is to calculate the probability that an option will be exercised or be itm at expiration and assign a dollar value to it the 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 commonly employed variables that are input into mathematical models to derive an option s theoretical fair value 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 volatility fluctuations and the passage of time the greater the chances that the option will finish itm and be profitable the greater the value of the option and vice versa 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 interest rates too should translate into higher option prices special considerationsmarketable 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 option pricing model and monte carlo simulation are also widely used using the black scholes option pricing theorythe original black scholes model required five input variables the strike price of an option the current price of the stock time to expiration the risk free rate of return and volatility direct observation of future volatility is impossible so it must be estimated or implied thus implied volatility is not the same as historical or realized volatility for many options on stocks dividends are often used as a sixth input 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 maturities that short selling of securities with the use of proceeds is permitted and that there are no arbitrage 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 supply and demand modifications to options pricing models will therefore include 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 out of the money otm are higher than for those at the strike price closer to the price of the underlying instrument additionally black scholes assumes that the options being priced are european style executable only at maturity the model does not take into account the execution of american style options which can be exercised at any time before and including the day of expiration on the other hand the binomial or trinomial models can handle both styles of options because they can check for the option s value at every point in time during its life 