# Understanding How Options Are Priced

### Key Takeaways

- Options contracts can be priced using mathematical models such as the Black-Scholes or Binomial pricing models.
- An option’s price is primarily made up of two distinct parts: its intrinsic value and time value.
- Intrinsic value is a measure of an option’s profitability based on the strike price versus the stock’s price in the market.
- Time value is based on the underlying asset’s expected volatility and time until the option’s expiration.

This article will explore the factors to consider if you plan to trade options to take advantage of stock movements. Options are derivatives contracts that give the holder the right, but not the debt instrument, to buy ( in the case of a call ) or sell ( in the font of a put ) an underlie asset or security at a pre-determined price ( called the strike price ) before the shrink expires. Hence, the terminus “ derivative ” plainly means that an option ‘s value is derived primarily from the underlying asset it is associated with .

Reading: Understanding How Options Are Priced

It is important to note, however, that there are two parties to an options contract : a buyer and a seller. As mentioned, a buyer of an options contract has rights, but the seller of an options contract, on the other hand, has an duty. It can become confusing, therefore to summarize :

- Buyer of a call: the right to buy an asset at a pre-determined (strike) price
- Seller of a call: the obligation to sell an asset at a pre-determined (strike) price
- Buyer of a put: the right to sell an asset at a pre-determined (strike) price
- Seller of a put: the obligation to buy an asset at a pre-determined (strike) price

Buying or selling an option comes with a price, called the option ‘s agio. Understanding how to value that bounty is crucial for trade options, and basically rests on the probability that the right or duty to buy or sell a stock will end up being profitable at termination. So buyers of an choice pay the premium, and sellers of an option receive the bounty

## option price Models

Before venturing into the world of trading options, investors should have a good sympathize of the factors determining the value of an choice. These include the current neckcloth price, the intrinsic measure, time to exhalation or the time value, excitability, interest rates, and cash dividends paid .

There are several options pricing models that use these parameters to determine the fair commercialize rate of an option. Of these, the Black-Scholes model is the most widely known. In many ways, options are just like any early investment—you need to understand what determines their price to use them efficaciously. other models are besides normally used, such as the binomial model and trinomial model .

Let ‘s start with the basal drivers of the price of an option : current livestock price, intrinsic value, time to expiration or clock time prize, and volatility. The current stock price is fairly square. The movement of the price of the stock up or down has a direct, though not adequate, impression on the price of the option. As the price of a stock rises, the more likely it is that the price of a predict option will rise and the price of a invest option will fall. If the stock price goes down, the reverse will most likely find to the monetary value of the calls and puts .

## The Black-Scholes Formula

The Black-Scholes model is possibly the best-known options pricing method acting. The model ‘s convention is derived by multiplying the banal price by the accumulative standard convention probability distribution routine. Thereafter, the net present value ( NPV ) of the mint price multiplied by the accumulative standard normal distribution is subtracted from the resulting value of the previous calculation .

In mathematical notation :

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\begin{aligned} &C = S_t N(d _1) – K e ^{-rt} N(d _2)\\ &\textbf{where:}\\ &d_1 = \frac{ln\frac{S_t}{K} + (r+ \frac{\sigma ^{2} _v}{2}) \ t}{\sigma_s \ \sqrt{t}}\\ &\text{and}\\ &d_2 = d _1 – \sigma_s \ \sqrt{t}\\ &\textbf{where:}\\ &C = \text{Call option price}\\ &S = \text{Current stock (or other underlying) price}\\ &K = \text{Strike price}\\ &r = \text{Risk-free interest rate}\\ &t = \text{Time to maturity}\\ &N = \text{A normal distribution}\\ \end{aligned}

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The mathematics involved in a differential equation that makes up the Black-Scholes recipe can be complicated and intimidating. fortunately, you do n’t need to know or even understand the mathematics to use Black-Scholes model in your own strategies. Options traders and investors have access to a variety of online options calculators, and many of nowadays ‘s trade platforms boast full-bodied options analysis tools, including indicators and spreadsheets that perform the calculations and output the options price values .

Below, we ‘ll dig a short deeply into options prices to understand what makes up its intrinsic vs. extrinsic ( time ) value, which is a act more aboveboard .

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#### Understanding Option Pricing

## intrinsic Value

intrinsic measure is the value any given option would have if it were exercised today. Basically, the intrinsic value is the sum by which the affect price of an option is profitable or in-the-money as compared to the banal ‘s price in the market. If the hit monetary value of the option is not profitable as compared to the price of the sprout, the option is said to be out-of-the-money. If the hit price is adequate to the stock ‘s price in the market, the option is said to be “ at-the-money. ”

Although intrinsic value includes the relationship between the strike price and the stock ‘s price in the grocery store, it does n’t account for how much ( or how little ) fourth dimension is remaining until the choice ‘s expiration—called the termination. The sum of time remaining on an option impacts the premium or value of an option, which we ‘ll explore in the following section. In other words, intrinsic value is the parcel of an option ‘s price not lost or impacted due to the enactment of clock time .

### The Formula and Calculation of Intrinsic Value

Below are the equations to calculate the intrinsic prize of a call or put option :

Call Option Intrinsic Value

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Underlying Stock’s Current Price

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Call Strike Price

\begin{aligned} &\text{Call Option Intrinsic Value} = USC – CS\\ &\textbf{where:}\\ &USC = \text{Underlying Stock’s Current Price}\\ &CS = \text{Call Strike Price}\\ \end{aligned}

Call Option Intrinsic Value

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Underlying Stock’s Current Price

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Call Strike Price

The intrinsic value of an choice reflects the effective fiscal advantage resulting from the immediate exercise of that choice. Basically, it is an choice ‘s minimum rate. Options trade at the money or out of the money, have no intrinsic respect .

Put Option Intrinsic Value

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Put Strike Price

\begin{aligned} &\text{Put Option Intrinsic Value} = PS – USC\\ &\textbf{where:}\\ &PS = \text{Put Strike Price}\\ \end{aligned}

Put Option Intrinsic Value

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### example of Intrinsic Value

For example, let ‘s say General Electric ( GE ) banal is selling at $ 34.80. The GE 30 call choice would have an intrinsic value of $ 4.80 ( $ 34.80 – $ 30 = $ 4.80 ) because the choice holder can exercise the choice to buy GE shares at $ 30, then turn around and mechanically sell them in the market for $ 34.80 for a net income of $ 4.80 .

In a different exercise, the GE 35 call option would have an intrinsic value of zero ( $ 34.80 – $ 35 = – $ 0.20 ) because the intrinsic value can not be veto. intrinsic value besides works the like way for a invest choice .

For exercise, a GE 30 put option would have an intrinsic respect of nothing ( $ 30 – $ 34.80 = – $ 4.80 ) because the intrinsic value can not be negative. On the other hand, a GE 35 put option would have an intrinsic value of $ 0.20 ( $ 35 – $ 34.80 = $ 0.20 ) .

## Time Value

Since options contracts have a finite measure of time before they expire, the total of meter remaining has a monetary value associated with it—called time respect. It is directly related to how much meter an option has until it expires, vitamin a well as the excitability, or fluctuations, in the stock ‘s price .

The more time an option has until it expires, the greater the gamble it will end up in the money. The time part of an choice decays exponentially. The actual ancestry of the prison term value of an choice is a fairly complex equation .

As a general principle, an option will lose one-third of its respect during the first half of its life and two-thirds during the second half of its animation. This is an crucial concept for securities investors because the closer the option gets to passing, the more of a move in the fundamental security is needed to impact the monetary value of the option .

### The Formula and Calculation of Time Value

The formula below shows that time respect is derived by subtracting an choice ‘s intrinsic prize from the choice bounty .

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Time\ Value = Option\ Price-Intrinsic\ Value

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In other words, the meter value is what ‘s left of the bounty after calculating the profitableness between the strike price and stock ‘s monetary value in the market. As a result, time value is much referred to as an choice ‘s extrinsic rate since time respect is the measure by which the price of an option exceeds the intrinsic value .

Time value is basically the risk premium the option seller requires to provide the choice buyer the right to buy or sell the sprout up to the date the choice expires. It is like an insurance agio for the option ; the higher the risk, the higher the cost to buy the choice .

### case of Time Value

Looking again at the exercise from above, if GE is trading at $ 34.80 and the one-month-to-expiration GE 30 bid option is trading at $ 5, the time value of the choice is $ 0.20 ( $ 5.00 – $ 4.80 = $ 0.20 ) .

meanwhile, with GE trade at $ 34.80, a GE 30 call choice trade at $ 6.85 with nine months to exhalation has a clock time respect of $ 2.05. ( $ 6.85 – $ 4.80 = $ 2.05 ). Notice the intrinsic measure is the same ; the difference in the price of the like mint price choice is the clock rate .

## excitability

An option ‘s fourth dimension rate is besides highly dependent on the volatility the market expects the lineage to display up to termination. typically, stocks with high volatility have a higher probability for the choice to be profitable or in-the-money by termination. As a result, the clock time value—as a part of the choice ‘s premium—is typically higher to compensate for the increased prospect that the stock ‘s price could move beyond the hit price and expire in-the-money. For stocks that are not expected to move much, the choice ‘s time value will be relatively low .

One of the metrics used to measure volatile stocks is called beta. Beta measures the volatility of a stock when compared to the overall grocery store. fickle stocks tend to have senior high school betas chiefly due to the doubt of the price of the stock before the option expires. however, high beta stocks besides carry more hazard than low-beta stocks. In other words, volatility is a double-edged sword, meaning it allows investors the electric potential for significant returns, but volatility can besides lead to meaning losses .

The effect of volatility is by and large subjective and difficult to quantify. fortunately, there are several calculators to help appraisal volatility. To make this even more interest, several types of volatility exist, with entail and historical being the most note. When investors look at volatility in the past, it is called either historical volatility or statistical volatility .

### Historical Volatility

historical volatility ( HV ) helps you determine the possible magnitude of future moves of the underlying livestock. statistically, two-thirds of all occurrences of a stock price will happen within plus or minus one standard diversion of the stock’s motion over a set time time period .

historic excitability looks rear in clock time to show how volatile the market has been. This helps options investors to determine which exercise price is most allow to choose for a particular strategy .

### Implied Volatility

Implied excitability is what is implied by the current market prices and is used with theoretical models. It helps set the stream price of an existing choice and aid options players assess the electric potential of a craft. Implied volatility measures what options traders expect future volatility will be .

As such, incriminate volatility is an index of the stream opinion of the market. This opinion will be reflected in the price of the options, helping traders assess the future excitability of the option and the stock based on current choice prices .

jointly, the factors that help measure the impingement on an option ‘s bounty are referred to as Option Greeks.

## Examples of How Options Are Priced

Below, you can see the GE model already discussed. It shows the trade price of GE, several fall prices, and the intrinsic and time values for the call and put options. At the time of this writing, General Electric was considered a stock with depleted volatility and had a beta of 0.49 for this exemplar .

The mesa below contains the pricing for both calls and puts that are expiring in one month ( acme section of the mesa ). The bottom segment contains the prices for the GE options that expire in nine months .

visualize by Sabrina Jiang © Investopedia 2020

In the digit below, the price for both calls and puts expiring in one month and nine months are listed for stock of Amazon.com Inc. ( AMZN ). Amazon is a much more explosive sprout with a beta of 3.47 .

Let ‘s compare the GE 35 call choice with nine months to exhalation with the AMZN 40 call option with nine months to termination .

- GE has only $0.20 to move up before the nine-month option is at the money, ($35 strike – $34.80 stock price).
- On the other hand, AMZN has $1.30 to move up before its nine-month option is at the money ($40 strike – $38.70 stock price).
- The time value of these options is $3.70 for GE and $7.50 for AMZN.

The meaning premium on the AMZN option is due to the fickle nature of the AMZN stock, which could result in a higher likelihood the option will expire in-the-money .

picture by Sabrina Jiang © Investopedia 2020

An option seller of GE will not expect to get a solid agio because the buyers do not expect the price of the stock to move significantly .

Read more: Forum Policy

On the one hand, the seller of an AMZN choice can expect to receive a higher premium ascribable to the volatile nature of the AMZN stock. Basically, when the market believes a stock will be very explosive, the time value of the choice rises .

On the early hand, when the market believes a broth will be less volatile, the meter respect of the choice falls. The expectation by the market of a stock ‘s future excitability is keystone to the price of options .