The options market is complicated, and even figuring out what an appropriate premium for options contracts should be can be tough. The most obvious factor in option pricing is how the strike price relates to the stock price, because that determines the intrinsic value of the option. However, time value and volatility also play a role in establishing option pricing, with the time left until the expiration date and the amount of price fluctuation in the underlying stock also playing key roles. Below, we'll go into some of the basics of option pricing.

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The easiest place to start with option pricing

The simplest way to get a handle on option pricing is to understand what conditions would make the value of an option go up or down. You can break those down into a few different categories.

First, changes in the price of the underlying stock will have a direct impact on option prices. For call options, if the price of the stock goes up, then the option price will also go up. If the stock price is well above the strike price, then those increases will be close to dollar for dollar. If the stock price is well below the strike price, the option price will rise much less than the underlying stock price. The reverse is true for put options, where a declining stock price is beneficial for the put option price.

Second, the greater the time left before the option expires, the more it will be worth. Option prices are based on the possibility for stock prices to move substantially, and the longer the time horizon, the greater the opportunity for a big stock move to make an option extremely profitable.

Finally, options are worth more when a stock's price tends to be volatile. This point is similar to the one above in that even in situations in which options on two stocks have the same expiration date, the option on the stock that makes bigger moves in either direction has greater potential to produce larger profit for the option holder.

Black-Scholes and option pricing

As difficult as many find the math involved to be, it would be irresponsible not to mention the role that the Black-Scholes option pricing formula has had on options trading. The work of Fischer Black and Myron Scholes helped create the modern options market by giving professionals a theoretical basis by which to establish the price of options.

In order to create mathematical formulas governing option prices, the Black-Scholes model assumes that stock prices move randomly, there are no transaction costs, and rates of return on no-risk assets are fixed from now until the expiration date of the option. It also assumes that lending or borrowing at the risk-free rate is limitless, and that either buying stock or selling stock short is similarly available without impediment.

The Black-Scholes equation takes the relationship between an option's price and the price of various stock and cash positions and then uses differential calculus to determine the instantaneous rate of change in the option price for a given change in the stock price. From there, one can solve the equation for a specific set of circumstances to come up with an approximation of the value of an option.

In practice, what options traders discovered was that the Black-Scholes formula's assumptions didn't match up perfectly with reality, and so the actual numbers that the formula produces aren't reliable as precise predictions of value. However, the concepts that the Black-Scholes formula revealed are of practical value to options traders. You'll therefore still find many of the concepts that were developed in early Black-Scholes analysis in the trading strategies that options traders still use today.

Option pricing can be extremely difficult to understand from a theoretical perspective, and a deep background in mathematics can be useful in fully appreciating the details of determining option prices. From a practical standpoint, however, the basic factors above show what affects an option's price, and that will help you predict how your options positions will behave in response to changes in the price of underlying stocks.

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