Options are derivatives contracts that give the holder the right but not the obligation to buy or sell an underlying asset or security at a predetermined price before the contract expires. Buying is referred to as a call option. A put option refers to selling.
Buying or selling an option comes with a price called theoption's premium. Understanding how to value that premium is crucial for trading options. It rests on the probability that the right or obligation to buy or sell a stock will end up being profitable atexpiration.
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 its 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.
What Is an Options Contract?
Options are derivatives contracts. "Derivative" means that an option's value is derived primarily from the underlying asset that it's associated with.
There are two parties to an options contract: a buyer and a seller. The buyer of an options contract has rights but the seller of an options contract has an obligation.
Buyer of a call: The right to buy an asset at a predetermined (strike) price
Seller of a call: The obligation to sell an asset at a predetermined (strike) price
Buyer of a put: The right to sell an asset at a predetermined (strike) price
Seller of a put: The obligation to buy an asset at a predetermined (strike) price
Buying or selling an option comes with a price called theoption's premium. Buyers of an option pay the premium and sellers receive the premium.
Option Pricing Models
The factors determiningthe value of an option include the current stock price, the intrinsic value, the time to expiration or time value, volatility, interest rates, and cash dividends paid.
Several options pricing models use these parameters to determine the fair market value of an option. The Black-Scholes model is the most widely known. Other models are also commonly used such as the binomial model and trinomial model.
The primary drivers of the price of an option are the current stock price, intrinsic value, time to expiration or time value, and volatility. The current stock price is fairly straightforward. The movement of the price of the stock up or down has a direct although not equal effect on the price of the option. As the price of a stock rises, the more likely it is that the price of a call option will rise and the price of a put option will fall.
The reverse will most likely happen to the price of the calls and puts if the stock price goes down.
The Black-Scholes Formula
The Black-Scholes model is perhaps the best-known options pricing method. The model's formula is derived by multiplying the stock price by the cumulative standard normal probability distribution function. The net present value (NPV) of the strike price multiplied by the cumulative standard normal distribution is then subtracted from the resulting value of the previous calculation.
The math involved in a differential equation that makes up the Black-Scholes formula can be complicated and intimidating but you don't have to understand the math to useBlack-Scholes modeling in your strategies. Options traders and investors have access to a variety of online options calculators. Many trading platforms boast robust options analysis tools, including indicators and spreadsheets that perform the calculations and output the options' pricing values.
Intrinsic Value
Intrinsic value is the value that any given option would have if it were exercised today. The intrinsic value is the amount by which the strike price of an option is profitable or in-the-money as compared to the stock's price in the market. The option is said to be out-of-the-money if the strike price of the option isn't profitable as compared to the price of the stock. The option is said to be at-the-money if the strike price is equal to the stock's price in the market,
Intrinsic value includes the relationship between the strike price and the stock's price in the market but it doesn't account for how much or how little time remains until the option's expiration. This is called the expiry. The amount of time remaining on an option impacts its premium or value. Intrinsic value is the portion of an option's pricethat's not lost or impacted due to the passage of time.
The Formula and Calculation of Intrinsic Value
The equations to calculate the intrinsic value of a call or put option are:
The intrinsic value of an option reflects the effective financial advantageresulting from the immediate exercise of that option. It's an option's minimum value. Options trading at the money or out of the money have no intrinsic value.
Let's say that General Electric (GE) stock is selling at $34.80. The GE 30 call option would have an intrinsic value of $4.80 ($34.80 - $30 = $4.80) because the option holder can exercise the option to buy GE shares at $30 thenturn around and automatically sell them in the market for $34.80 for a profit of $4.80.
The GE 35 call option would have an intrinsic value of zero ($34.80 - $35 = -$0.20) because the intrinsic value can't be negative. Intrinsic value also worksthe same way for a put option.
A GE 30 put option would have an intrinsic value of zero ($30 - $34.80 = -$4.80) because the intrinsic value can't be negative. A GE 35 put option would have an intrinsic value of $0.20 ($35 - $34.80 = $0.20).
Time Value
Options contracts have a finite amount of time before they expire so the time remaining has a monetary value associated with it called time value. It's directly related to how much time an option has until it expires, as well as the volatility or fluctuations in the stock's price.
The more time an option has until it expires, the greater the chance it will end up in the money. The time component of an option decays exponentially. The actual derivation of the time value of an option is a fairly complex equation.
An option will generally lose one-third of its value during the first half of its life and two-thirds during the second half. This is an important concept for securities investors because the closer the option gets to expiration, the more of a move in the underlying security is necessary to impact the price of the option.
The Formula and Calculation of Time Value
This formula shows that time value is derived by subtracting an option's intrinsic value from the option premium.
TimeValue=OptionPrice−IntrinsicValue
The time value is what's left of the premium after calculating the profitability between the strike price and the stock's price in the market. Time value is often referred to as an option's extrinsic value as a result because time value is the amount by which the price of an option exceeds the intrinsic value.
Time value is essentially the risk premium the option seller requires to provide the option buyer with the right to buy or sell the stock up to the date the option expires. It's like an insurance premium for the option. The higher the risk, the higher the cost to buy.
Example of Time Value
The time value is $0.20 ($5.00 - $4.80 = $0.20) if GE is trading at $34.80 and the one-month-to-expiration GE 30 call option is trading at $5.
A GE 30 call option trading at $6.85 with nine months to expiration has a time value of $2.05. ($6.85 - $4.80 = $2.05). Notice that the intrinsic value is the same.The difference in the price of the same strike price option is the time value.
Volatility
An option's time value is also highly dependent on the volatilitythe market expects the stock to display up to expiration. Stocks with high volatility typically have a higher probability for the option to be profitable or in-the-money by expiry. The time value as a component of the option's premium is typically higher as a result to compensate for the increased chance that the stock's price could move beyond the strike price and expire in-the-money.
The option's time value will be relatively low for stocks that aren't expected to move much.
Beta is one of the metrics used to measure volatile stocks. It measures the volatility of a stock when compared to the overall market. Volatile stocks tend to have high betas primarily due to the uncertainty of the price of the stock before the option expires. But high-beta stocks also carry more risk than low-beta stocks. Volatility is a double-edged sword. It allows investors the potential for significant returns but it can also lead to significant losses.
The effect of volatility is mostly subjective and it's difficult to quantify but several calculatorscan help estimate it. Several types of volatility exist. Implied and historical are the most noted. It's referred to as either historical volatility or statistical volatility when investors look at volatility in the past.
Historical Volatility
Historical volatility(HV) helps to determine the possible magnitude of future moves of the underlying stock. Two-thirds of all occurrences of a stock price will statistically happen within plus or minus one standard deviation of the stock'smove over a set time.
Historical volatility looks back in time to show how volatile the market has been. This helps options investors determine which exercise price is most appropriate to choose for aparticular strategy.
Implied Volatility
Implied volatility is what's implied by the current market prices and it's used with theoretical models. It helps set the current price of an existing option and helps options players assess the potential of atrade. Implied volatility measures what options traders expect future volatility will be.
It's an indicator of the current sentiment of the market. This sentiment will be reflected in the price of the options, helpingtradersassess the future volatility of the option and the stock based on current option prices.
The factors that help measure the impact on an option's premium are collectively referred to as Option Greeks.
Examples of How Options Are Priced
This table shows the trading price of GE, several strike prices, and the intrinsic and time values for the call and put options. General Electric was considered a stock with low volatility at this time and had a beta of 0.49.
The table contains the pricing for both calls and puts that are expiring in one month (top section of the table). The bottom section contains the prices for the GE options that expire in nine months.
The pricing for both calls and puts expiring in one month and nine months are listed for stock of Amazon.com Inc. (AMZN) in the table below. Amazon was a much more volatile stock with a beta of 3.47.
Let's compare the GE 35 call option with nine months to expiration with the AMZN 40 call option with nine months to expiration.
GE has only $0.20 to move up before the nine-month option is at the money ($35 strike - $34.80 stock price).
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 significant premium on the AMZN option is due to the volatile nature of the AMZN stock. This could result in a higher likelihood that the option will expire in-the-money.
An option seller of GE won't expect to get a substantial premium because the buyers don't expect the price of the stock to move significantly. The seller of an AMZN option can expect to receive a higher premium due to the volatile nature of the AMZN stock.
The time value of the option rises when the market believes a stock will be very volatile. The time value of the option falls when the market believes a stock will be less volatile. Theexpectation by the market of a stock's future volatility is key to the price of options.
What Is a Call Option?
A call option gives the buyer the right to purchase a stock at a predetermined price and before a preset deadline. The buyer isn't required to exercise the option.
What Is the Trinomial Model?
The trinomial model is a "tree" calculator that's similar to the binomial model. Both involve a certain number of "tree steps" and both calculate options prices. The trinomial model is said to be more accurate.
What Are Option Greeks?
Option Greeks measure the risk factors associated with options pricing. They're named after Greek letters as the name implies. Delta, gamma, theta, and vega are four of the most commonly used but there are others. Each measures different degrees of risk.
The Bottom Line
Profitably buying options and selling options involve pinning down the price. The goal is to determine what the option’s premium is most likely to be at the time of expiration. Several formulas, models, and calculations can help achieve this. Intrinsic value and time value are key. The Black-Scholes formula is one of the more common models.
Always seek guidance if you’re new to investing so you’re sure you understand how these processes work.
Disclosure: This article is not intended to provide investment advice. Investing in securities entails varying degrees of risk and can result in partial or total loss of principal. The trading strategies discussed in this article are complex and should not be undertaken by novice investors. Readers seeking to engage in such trading strategies should seek out extensive education on the topic.
An option's premium is comprised of intrinsic value and extrinsic value. Intrinsic value is reflective of the actual value of the strike price versus the current market price. Extrinsic value is made up of time until expiration, implied volatility, dividends and interest rate risks.
An option pricing model is a mathematical formula used to calculate an option's theoretical value using its strike price, the underlying stock's price, volatility and dividend amount, as well as time until expiration and risk-free interest rate.
The six inputs that determine an option's value are stock price, strike price, time to expiration, interest rate, dividend yield and volatility (over the life of the option). Normally, if the stock price goes up and the other factors remain the same, then a call option goes higher.
The factors determining the value of an option include the current stock price, the intrinsic value, the time to expiration or time value, volatility, interest rates, and cash dividends paid. Several options pricing models use these parameters to determine the fair market value of an option.
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.
Options prices, known as premiums, are composed of the sum of its intrinsic and time value. Intrinsic value is the price difference between the current stock price and the strike price. An option's time value or extrinsic value of an option is the amount of premium above its intrinsic value.
Option premiums are quoted on a per-share basis, meaning that an options contract represents 100 shares of the stock. For example, a $5 premium for a call option would mean that that investor would need to pay $500 ($5 * 100 shares) for the call option to buy that stock.
Pricing an option relies on complex mathematical formulas, but the direct inputs into an option's price include the price of the underlying asset, the option's strike, time to expiration, interest rates, and implied volatility.
The price of the asset may not follow a continuous process, which makes it difficult to apply option pricing models (like the Black Scholes) that use this assumption. 3. The variance may not be known and may change over the life of the option, which can make the option valuation more complex.
Option selling strategy is costly because it requires large capital to deploy most of the traders can't afford it and this strategy bears unlimited risk and limited profit that's act as a deterrent for most of the traders specially beginners where as a buyer requires a small fund to trade which is affordable for most ...
Fair value is defined as the actual worth of an option-buying or selling it at this price leaves little to no profit opportunity. This value is important to know because it can be used to ascertain whether an option is expensive or reasonably priced.
Investors and traders with a low risk tolerance might choose a strike price that is close to or at the underlying market price, while those with a higher risk appetite might choose a strike price that is further away from the underlying market price.
There are two main aspects to the price of options that any options trader should understand. First, the actual price is made up of two main components: intrinsic value and extrinsic value. Secondly, and this is relevant to how market makers operate, they are priced on the exchanges with a bid price and an ask price.
The underlying price, the exercise price, the time to maturity, the risk-free rate, the volatility of the underlying price, and any income or cost associated with owning the underlying asset are key factors in determining the value of an option.
Put option prices are impacted by changes in the price of the underlying asset, the option strike price, time decay, interest rates, and volatility. Put options increase in value as the underlying asset falls in price, as volatility of the underlying asset price increases, and as interest rates decline.
Best of option pays the maximum price of all the assets whereas worst of option pays the minimum price within the basket. An investor, for instance, can choose three assets reflecting growth, moderate, and conservative investment styles. In a upside market, the growth asset gives the best return.
The price of an option is a function of many variables such as time to maturity, underlying volatility, spot price of underlying asset, strike price and interest rate, it is critical for the option trader to know how the changes in these variables affect the option price or option premium.
In reality, you'd also have to take commissions into account, but we'll ignore them for this example. Remember, a stock option contract is the option to buy 100 shares; that's why you must multiply the contract by 100 to get the total price.
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