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**Knowing How Options Are Valued**

By trading stocks with a disciplined approach and expecting a great move either up or down, you may have had success beating the market. Identifying one or two strong stocks poised to make a significant move shortly has helped many traders obtain the confidence they need to succeed in the stock market. However, you risk being left behind if you don’t know how to benefit from that trend. If this describes you, it might be time to think about utilizing choices.

**KEY LESSONS**

- Mathematical techniques like the Black-Scholes or binomial pricing models can determine the price of options contracts.
- The intrinsic and temporal values comprise the two main components of an option’s pricing.
- A measure of an option’s profitability based on the strike price and the underlying stock’s market price is called intrinsic value.
- The projected volatility of the underlying asset and the remaining time until the option expires will determine the time value.

This post will go through the elements to consider if you intend to trade options to profit from stock swings. Options are derivatives contracts that grant the holder the right, but not the responsibility, to purchase (in the case of a call) or sell (in the case of a put) an underlying asset or security at a fixed price (referred to as the striking price) before the contract’s expiration. So, the definition of “derivative” is just that: an option’s value is essentially derived from the underlying asset it is linked .

However, it is vital to note that there are two participants in an options contract: a buyer and a seller. As previously stated, the buyer of an options contract has rights, but the seller has a duty. It can become complicated, so to summarize:

- Buyer of a call: the right to acquire an asset at a predetermined (strike) price
- A call’s seller must sell a security at a predetermined (strike) price.
- Purchasing a put gives you the option to sell a security at a predetermined (strike) price.
- The put seller must buy an asset at the predetermined (strike) price.

The cost of buying or selling an option is the option’s premium. Trading options requires understanding how to evaluate that premium, which essentially depends on the likelihood that the right or duty to purchase or sell a stock will turn out to be lucrative at expiry. Consequently, the premium is paid by option buyers and received by option sellers.

**Models for Option Pricing**

Investors should have a solid grasp of the variables affecting an option’s value before entering the realm of options trading. These include the stock’s price, its intrinsic worth, its remaining life or time value, volatility, interest rates, and any cash dividends that have been distributed.

Several options pricing algorithms use these factors to calculate the option’s fair market value. The Black-Scholes model is the most well-known of them. 1 Option is similar to other investments in many respects; to utilize them properly, you must comprehend what influences their pricing. The trinomial model and other models, such as the binomial model, are often employed.

Let’s begin by discussing the four main factors that affect an option’s pricing: volatility, time value or time to expiry, intrinsic value, and current stock price. The current stock price is relatively simple. Although not equally, the price of the option is directly impacted by changes in the stock price. It is more likely for the price of a call option to increase and the price of a put option to decrease when the price of a stock increases. The price of calls and puts will generally decrease if the stock price decreases, and vice versa.

**Indicator for Black-Scholes**

Probably the most well-known approach to pricing options is the Black-Scholes model. The stock price is multiplied by the cumulative standard normal probability distribution function to get the formula for the model. The outcome of the preceding computation is then reduced by the strike price’s net present value (NPV) multiplied by the cumulative standard normal distribution.

**In notation for mathematics:**

The Black-Scholes formula requires solving a differential equation, which may be a challenging and daunting mathematical concept. Fortunately, you can apply Black-Scholes modeling in your tactics without having to grasp or even know the arithmetic. Many trading platforms available today offer extensive options analysis tools, such as indicators and spreadsheets, that carry out the calculations and output the options pricing values. Options traders and investors have access to a range of online options calculators.

We’ll delve a little deeper into options pricing below to see how intrinsic value differs from extrinsic (temporal) value, which is a little clearer.

**Knowledge of Option Pricing**

**Intrinsic** **Value**

The value an option would have if it were exercised today is its intrinsic value. Essentially, the intrinsic value is the difference between the strike price of an option being profitable or in the money and the market price of the underlying stock. The option is considered to be out-of-the-money if the strike price is not lucrative compared to the stock price. The option is said to be “at the money” if the strike price coincides with the market price of the underlying security.

Although the link between the striking price and the stock’s market price is taken into account by intrinsic value, the amount of time (or how little time) until the option expiration, or the expiry, is not considered. In the next section, we’ll examine how the remaining time on an option affects its premium or value. Intrinsic value is the fraction of an option’s price that is unaffected or unaffected by the passage of time.

**The Intrinsic Value Calculation Formula**

The formulas to determine a call or put option’s intrinsic value are listed below:

An option’s intrinsic value indicates the actual financial benefit from being immediately exercised. In essence, it is the minimal value of an option. There is no intrinsic value to options trading in the money or out of the money.

**Intrinsic Value Example**

Consider General Electric (GE) stock, now trading at $34.80. The GE 30 call option would have an intrinsic value of $4.80 ($34.80 – $30 = $4.80) since the option holder might execute the option to purchase GE shares for $30 before immediately selling them in the market for $34.80, earning $4.80 in profit.

Instead, as the intrinsic value cannot be negative, the GE 35 call option would have an intrinsic value of zero ($34.80 – $35 = -$0.20). The same principles of intrinsic value apply to put options as well.

Because the intrinsic value cannot be negative, a GE 30 put option, for instance, would have an intrinsic value of zero ($30 – $34.80 = -$4.80). On the other hand, the intrinsic value of a GE 35 put option would be $0.20 ($35 – $34.80 = $0.20).

**Value at Time**

Options contracts have a limited period until they expire. Thus, the time left has a monetary value attached to it. This value is known as the time value. It is directly correlated with the stock price volatility and the remaining time until an option expires.

An option is more likely to become profitable the closer it is to expiration. An option’s time component loses value rapidly. The calculation determining an option’s time value is actually rather complicated.

An option typically loses one-third of its value in the first half of its life and two-thirds in the second. This is a crucial idea for securities investors because it takes greater movement in the underlying asset to affect the option’s price as an option approaches expiration.

**The Time Value Formula and Calculation**

The formula below demonstrates how to calculate time value by deducting the intrinsic value of an option from the option premium.

*Time* *Value*=*Option* *Price*−*Intrinsic* *Value*

*Option price plus intrinsic value equal time value.*

*Option price x intrinsic value equals time value.*

To put it another way, the time value is the premium amount that remains after determining the profitability between the strike price and the stock’s market price. Since temporal value is the amount by which the price of an option exceeds the intrinsic value, it is sometimes referred to as an option’s extrinsic value.

In essence, time value is the risk premium that the option seller has to collect from the buyer to provide them the right to buy or sell the stock up to the option’s expiration date. The cost to purchase the option is similar to an insurance premium; the greater the risk, the higher the cost.

**Example of Time Value**

If GE is trading at $34.80 and the GE 30 call option has one month left to expire, as, in the example above, the option’s time value is $0.20 ($5.00 – $4.80 = $0.20).

A GE 30 call option trading at $6.85 with nine months till expiry has a time value of $2.05. ($6.85 – $4.80 = $2.05) This is because GE is now trading at $34.80. The price variation for the identical strike price option is caused by the time value, even though the intrinsic value is the same.

**Volatility**

The market’s expectation of the stock’s volatility leading up to expiry significantly impacts an option’s time value. Typically, there is a larger chance that the option will be profitable or in the money by expiration for equities with strong volatility. Because there is a greater possibility that the stock price will rise above the strike price and the option will expire in the money, the time value—a part of the option’s premium—is often larger. The option’s time value will be relatively low for equities anticipated to move very little.

Beta is one indicator used to assess a stock’s volatility. When compared to the market as a whole, a stock’s beta indicates how volatile it is. Due to the uncertainty surrounding the stock price before the option expiration, volatile equities frequently have high betas. High-beta stocks do, however, also have more risk than low-beta equities. In other words, volatility is a double-edged sword that offers investors the chance to earn significant gains but also puts them at risk for sizable losses.

Volatility’s impact is largely irrational and hard to measure. Fortunately, a variety of calculators are available to aid in estimating volatility. There are various forms of volatility, implied and historical being the most well-known, which adds to the intrigue. Investors refer to historical volatility or statistical volatility when analyzing prior volatility.

**Historical Volatility**

You may estimate the underlying stock’s potential size of future swings using historical volatility (HV). According to statistics, two-thirds of stock price occurrences fall within a plus or minus one standard deviation range of the stock’s movement during a specific period.

Historical volatility shows how volatile the market has historically been. This makes it easier for options traders to decide which exercise price is best for a particular strategy.

**Implied Volatility**

When using theoretical models, implied volatility is what the present market prices imply. It aids in determining the option’s current pricing and aids traders in evaluating a trade’s potential. Implied volatility gauges the level of future volatility options traders anticipate.

Implied volatility, therefore, serves as a gauge of market mood at the moment. The price of the options will reflect this attitude, enabling traders to predict future volatility of the option and the stock based on option prices.

Option Greeks refers to all variables determining how an option’s premium will change over time.

**Examples of the Pricing of Options**

You may see the GE example we previously spoke about below. The intrinsic and temporal values for the call and put options are displayed, along with multiple strike prices and the trading price of GE. General Electric had a beta of 0.49 at the time of writing and was seen as a stock with minimal volatility.

The pricing for both calls and puts with a one-month expiration is shown in the table below (top section). The pricing for the GE options with a nine-month expiration date is listed in the bottom section.

The pricing for calls and puts for Amazon.com Inc. shares with expiration dates of one month and nine months is shown in the figure below (AMZN). With a beta of 3.47, Amazon is a far more volatile stock.

Comparing the GE 35 call option with the AMZN 40 call option with nine months remaining till expiration.

Only $0.20 more must be gained by GE before the nine-month option ($35 strike – $34.80 stock price) enters the money.

However, AMZN has to gain $1.30 before its nine-month option ($40 strike – $38.70 stock price) enters the money.

For GE and AMZN, respectively, the time value of these options is $3.70 and $7.50.

Due to the AMZN stock’s substantial volatility, there is a significant premium on the AMZN option, which might increase the possibility that the option would expire in the money.

Due to the buyers’ lack of expectation for a large change in the stock price, an option seller for GE should not anticipate receiving a sizable premium.

On the one hand, the volatility of the AMZN stock means that the seller of an AMZN option might anticipate receiving a bigger premium. In essence, the option’s time value increases when the market expects that a stock will be very volatile.

On the other side, the option’s time value decreases as the market anticipates less volatility in the stock. The price of options is heavily influenced by the market’s anticipation of a stock’s future volatility.