It is often said that "experience is the best teacher" and one of the things we have learned from reader E-mails is the majority of derivatives traders need to know more about option pricing. Indeed, the mathematics of option pricing is a complex and often misunderstood subject that usually requires a great deal of study to completely comprehend. Fortunately, those who persevere will find there is a simple logic to most of the concepts and more importantly, knowledgeable traders earn the right to have less money at risk with greater potential for profits.
Option Pricing Fundamentals
In simple terms, the amount you pay for an option can be described by its two core parts: time value and intrinsic value. But, before you can quantify these components, it is necessary to become familiar with the terms "in-the-money" and "out-of-the-money." A call option is in-the-money if the price of the underlying issue is higher than the strike price of the option. In contrast, a put option is in-the-money when the price of the underlying issue is lower than the option's strike price.
For instance, if a stock is trading at $25.00, a $20.00 (strike price) call is in-the-money while a $20.00 put is out-of-the-money. Conversely, a $30.00 call (in the same situation) is out-of-the-money and a $30.00 put is in-the-money. An option strike that is exactly the same as the price of the underlying is said to be "at-the-money" however since this condition does not occur often, the nearest strike option (whether slightly in- or out-of-the-money) is generally labeled in this manner. As an example, a trader who wanted to buy the at-the-money call option on a stock trading at $26.25 would likely choose the $25.00 strike price, even though it was actually $1.25 below the current price of the underlying issue. If the stock dropped $2.00 to $24.25, he would still select the $25.00 call if the objective was to purchase the at-the-money option. The concept is illustrated further in the tables below:
The Intrinsic Value of an Option
In order for an option to have intrinsic value, it must be in-the-money. That is, it must have value upon immediate exercise. Similar to expiration, the intrinsic value of an option, when exercised, will be equal to the difference between the price of the underlying issue and the strike price of the option. Consider the value of a $25.00 call option on a stock that is trading at $27.50. If a trader exercises the option, he will be buying stock that is worth $2.50 more than it costs. For puts, the math is the same but in the other direction. If the stock price is $22.50, a $25.00 put will have an intrinsic value of $2.50. In a declining market, the owner of the put could buy stock at the current price, then exercise the option to sell the stock at $25.00 for a $2.50 (per share) gain. Therefore, a simple definition of intrinsic value is the amount of profit realized by exercising the option.
The Time Value of an Option
Most books about options devote at least a chapter to the subject of time value. But, for the majority of retail option traders, it is sufficient to know that time value (sometimes called extrinsic value) is anything left over after accounting for intrinsic value. Using this perspective, the formula for calculating time value is relatively simple:
Option Price - Intrinsic Value = Time Value
Although this calculation is very straightforward, it deserves an example. Consider a stock trading at $17.50. If the current price of a $15.00 call option is $3.50, then its intrinsic value is $2.50 and its time value is $1.00. If the stock price were lower, then there would be more time value in the price of the option, and vice-versa. With puts, the scenario is similar but reversed. A $15.00 put that costs $3.50 will have $2.50 in intrinsic value and $1.00 in time value with the stock trading at $12.50. Here are some examples:
As you might expect, at-the-money and out-of-the-money options do not have any intrinsic value, rather only time value. That is the reason they are deemed "speculative" by experienced option buyers, who are purchasing nothing more than expected volatility in the underlying issue. Unless there is a significant, compelling catalyst (earnings report, FDA meeting, etc.) to drive up the value of the option, it will decay rapidly as the expiration date approaches. In contrast, the intrinsic value of an option is not dependent on any factor other than the price of the underlying issue. It is an option's minimum worth without regard to any upcoming activity or event.
Time Costs Money
Mathematics tells us that the time value of an option is directly related to how far the expiration date is in the future. Why? Because time equals potential the more time an option has until expiration, the greater the chance of the option moving in-the-money. With this fact in mind, it's no surprise that more time costs more money. Likewise, the amount of time value in an option's price drops with each passing day and the rate of decline becomes exponential as the expiration date approaches. From a strictly statistical standpoint, time value decays at its square root and this rate of decay is known as Theta. As a general guide, an option will lose one-third of its time value during the first half of its life and two-thirds of its time value during the remaining half of its life.
Factors affecting the time value of an option:
1. The relationship between the price of the underlying issue and the option strike price
Time is a commodity and there is one important concept that merchants of time must understand; the laws of option pricing dictate that time value is highest in at-the-money options and decreases as the strike prices move in-the-money. In fact, strike prices that are deep in-the-money have the lowest time value of all options. For example, a trader who wishes to purchase options on a stock that is trading near $35.00 will have three obvious alternatives; $30.00, $35.00, and $40.00. Obviously, the $35.00 strike will have the most time value while the $30.00 strike will have less time value and more intrinsic value. If he looks for options even deeper in-the-money, time value will decrease to a point where it approaches parity (or the risk-free interest rate). Generally, options will not trade at parity until the expiration date and then only when they are deep-in-the-money. The key point to understand is that options which are further in-the-money have more inherent worth because their market value is less susceptible to the effects of time passage.