--Options premiums
--Options pricing models and the Options Calculator
--In-, At- and Out-of-the-Money contracts
--Put/Call Parity, Time Premium and Volatility
You will also learn about the fundamentals involved in determining the price of an option, sometimes called its theoretical value, as well as how you can use Black-Scholes to make your trading decisions.
The Black-Scholes Model
Options Pricing was revolutionized in 1973 with the publication of the Black-Scholes Model, the Nobel-prize winning equation which virtually created the options marketplace.
While looking at this formula completely written out would be, for most people, absolutely confounding, a comprehension of options pricing is well within the realm of understanding of anyone with simple math skills and knowledge of their auto insurance policy.
Black-Scholes tells us that options on stocks can be priced using almost the exact same inputs that your insurance agent uses to quote your auto policy premium. Both depend primarily on (a) the value of the asset (the price of the car or the stock) and (b) the risk (your driving record or the stock's average price changes). A comparison of all the inputs is as follows:
Insurance Agent
--Value of car
--Deductible
--Time span of policy
--Interest Rates
--Risk
--Options pricing models and the Options Calculator
--In-, At- and Out-of-the-Money contracts
--Put/Call Parity, Time Premium and Volatility
You will also learn about the fundamentals involved in determining the price of an option, sometimes called its theoretical value, as well as how you can use Black-Scholes to make your trading decisions.
The Black-Scholes Model
Options Pricing was revolutionized in 1973 with the publication of the Black-Scholes Model, the Nobel-prize winning equation which virtually created the options marketplace.
While looking at this formula completely written out would be, for most people, absolutely confounding, a comprehension of options pricing is well within the realm of understanding of anyone with simple math skills and knowledge of their auto insurance policy.
Black-Scholes tells us that options on stocks can be priced using almost the exact same inputs that your insurance agent uses to quote your auto policy premium. Both depend primarily on (a) the value of the asset (the price of the car or the stock) and (b) the risk (your driving record or the stock's average price changes). A comparison of all the inputs is as follows:
Insurance Agent
--Value of car
--Deductible
--Time span of policy
--Interest Rates
--Risk
Options Trader
--Current stock price
--Strike price
--Time until expiration
--Cost of money
--Volatility
--Current stock price
--Strike price
--Time until expiration
--Cost of money
--Volatility
High Risk Equals High Premium
Compare for one moment, Driver A and Driver B.
Driver A is a 17-year old male high school senior with two speeding tickets since he got his license, and whose parents have bought him a Ferrari with a bumper sticker that reads, "I can't drive 55!"
Driver B is a 35-year old female homemaker with no traffic tickets in the last ten years who drives a Ford Taurus.
Obviously, who is going to have the higher risk and, henceforth, the higher insurance premium? The insurance agent might even take to following Driver A around just to cover himself.
Now, make that same comparison to someone trying to price an option on a $20 paper company stock versus a $200 dot.com stock... you see the method here.
NOTE: The larger the deductible, the lower the premium, and vice versa. The insurance deductible can be compared to the option strike price.
Components of Option Pricing
Let's analyze the different components which are used to determine the theoretical value of an option:
--The price of the underlying stock
--The strike price of the option
--The time until the option expires
--The cost of money (interest rates less dividends, if any)
--The volatility of the underlying stock
Compare for one moment, Driver A and Driver B.
Driver A is a 17-year old male high school senior with two speeding tickets since he got his license, and whose parents have bought him a Ferrari with a bumper sticker that reads, "I can't drive 55!"
Driver B is a 35-year old female homemaker with no traffic tickets in the last ten years who drives a Ford Taurus.
Obviously, who is going to have the higher risk and, henceforth, the higher insurance premium? The insurance agent might even take to following Driver A around just to cover himself.
Now, make that same comparison to someone trying to price an option on a $20 paper company stock versus a $200 dot.com stock... you see the method here.
NOTE: The larger the deductible, the lower the premium, and vice versa. The insurance deductible can be compared to the option strike price.
Components of Option Pricing
Let's analyze the different components which are used to determine the theoretical value of an option:
--The price of the underlying stock
--The strike price of the option
--The time until the option expires
--The cost of money (interest rates less dividends, if any)
--The volatility of the underlying stock
Theoretical Values
If we take all these components and plug them into the Black-Scholes formula, the model will calculate an option's theoretical value. Let's do that now:
If we take all these components and plug them into the Black-Scholes formula, the model will calculate an option's theoretical value. Let's do that now:
Imagine we want to price a Call and a Put on a Stock XYZ, and that XYZ presently is at $50 a share. Imagine further that we want to price the 30-Day 50-strike Call and Put, and that interest rates right now are around 4%. Imagine, as well, that XYZ Stock pays no dividends, and that its historical volatility is approximately 16%.
NOTE: A detailed description of volatility will be covered later in this lesson. If you would like to review the historical volatility of a particular stock, please go to www.cboe.com and look at Historical Volatilities.
Option Pricing
So, what did you learn?
That Stock Price, Strike Price, Time to Expiration, Interest Rates and Dividends (combined to make the Cost of Money) and Volatility are the inputs to pricing options, and that all are conceivably known except Volatility.
OK, but how can you, the public investor, use this knowledge? Are you to be expected to become a theoretical mathematician?
Actually, we've already made it easier for you...
In-, At-, and Out-of-the-Money Options
--Another concept you must be aware of is the designation of options as In-the-Money, At-the-Money and Out-of-the-Money.
--An In-the-Money option has a strike price which, for Calls, is below the present market price and, for Puts, is above the current market price.
--An Out-of-the-Money option has a strike which, for Calls, is above the present market price and, for Puts, is below the current market price.
--An At-the-Money option has a strike whether Call or Put which is equal to or near equal to the present price of the underlying.
NOTE: A detailed description of volatility will be covered later in this lesson. If you would like to review the historical volatility of a particular stock, please go to www.cboe.com and look at Historical Volatilities.
Option Pricing
So, what did you learn?
That Stock Price, Strike Price, Time to Expiration, Interest Rates and Dividends (combined to make the Cost of Money) and Volatility are the inputs to pricing options, and that all are conceivably known except Volatility.
OK, but how can you, the public investor, use this knowledge? Are you to be expected to become a theoretical mathematician?
Actually, we've already made it easier for you...
In-, At-, and Out-of-the-Money Options
--Another concept you must be aware of is the designation of options as In-the-Money, At-the-Money and Out-of-the-Money.
--An In-the-Money option has a strike price which, for Calls, is below the present market price and, for Puts, is above the current market price.
--An Out-of-the-Money option has a strike which, for Calls, is above the present market price and, for Puts, is below the current market price.
--An At-the-Money option has a strike whether Call or Put which is equal to or near equal to the present price of the underlying.
Intrinsic Value and Time Value
The distinctions of whether an option is In-, At- or Out-of-the-Money are also important because they help to illustrate the concepts of Intrinsic Value and Time Value.
Remember earlier how we covered the factors that go into pricing an option? Well, once you have an option price, you can break that figure down into two parts; its "Intrinsic Value," or the In-the-Money amount of an option's price, and its "Time Value," or the opportunity value that the option may become more valuable in the future.
Now, only In-the-Money options have Intrinsic Value. A 50 Call on a $55 stock is intrinsically worth at least $5, since you could exercise the option right away, buy the stock at $50 and sell it at $55, earning $5.
However, options will almost always trade at more than that. This is because all options, whether In-, At- or Out-of-the-Money have Time Value. Time Value is the extra premium the option has because of the possibility for additional price movements in the underlying security.
Let's break this down with real numbers.
If the 50 Call premium is 6, and the stock is trading at $55, the Intrinsic or In-the-Money amount is $5. The remainder, or $1, is the Time Value. Thus, this option is valued at 6 even though, intrinsically, it is only worth 5 right now. The additional 1 exists because of the stock's volatility (i.e., the possibility that it may move more than where it is right now).
The 55 Call, however, is trading for 3, or the 60 Call is trading for 1. With the stock trading at $55, neither of these options have any Intrinsic Value, but they have Time Value because of the possibility that the stock may move that way.
Options cannot have negative values, and neither Intrinsic Value nor Time Value can ever be negative.
Put/Call Parity
The general concept of how options prices are related to each other is known as Put/Call Parity. The basic concept is that stock prices, Call prices, and Put prices must have a certain relationship with each other or else professional traders would be able to make nearly risk-free trades.
Option traders, both professional and non-professional, use the concept of Put/Call parity to help them understand different option price behaviors and, therefore, make trading decisions.
Time Premium (Time Decay)
Time affects options prices. In fact, if the price of a stock remains the same, options decrease in value the closer they get to the expiration date. This concept is known as Time Decay.
As an option owner or writer, you want to consider time decay when trading options so you understand which options best fit your strategy outlook. Look at the graph to see how the option value decreases from 90 days to expiration.
The distinctions of whether an option is In-, At- or Out-of-the-Money are also important because they help to illustrate the concepts of Intrinsic Value and Time Value.
Remember earlier how we covered the factors that go into pricing an option? Well, once you have an option price, you can break that figure down into two parts; its "Intrinsic Value," or the In-the-Money amount of an option's price, and its "Time Value," or the opportunity value that the option may become more valuable in the future.
Now, only In-the-Money options have Intrinsic Value. A 50 Call on a $55 stock is intrinsically worth at least $5, since you could exercise the option right away, buy the stock at $50 and sell it at $55, earning $5.
However, options will almost always trade at more than that. This is because all options, whether In-, At- or Out-of-the-Money have Time Value. Time Value is the extra premium the option has because of the possibility for additional price movements in the underlying security.
Let's break this down with real numbers.
If the 50 Call premium is 6, and the stock is trading at $55, the Intrinsic or In-the-Money amount is $5. The remainder, or $1, is the Time Value. Thus, this option is valued at 6 even though, intrinsically, it is only worth 5 right now. The additional 1 exists because of the stock's volatility (i.e., the possibility that it may move more than where it is right now).
The 55 Call, however, is trading for 3, or the 60 Call is trading for 1. With the stock trading at $55, neither of these options have any Intrinsic Value, but they have Time Value because of the possibility that the stock may move that way.
Options cannot have negative values, and neither Intrinsic Value nor Time Value can ever be negative.
Put/Call Parity
The general concept of how options prices are related to each other is known as Put/Call Parity. The basic concept is that stock prices, Call prices, and Put prices must have a certain relationship with each other or else professional traders would be able to make nearly risk-free trades.
Option traders, both professional and non-professional, use the concept of Put/Call parity to help them understand different option price behaviors and, therefore, make trading decisions.
Time Premium (Time Decay)
Time affects options prices. In fact, if the price of a stock remains the same, options decrease in value the closer they get to the expiration date. This concept is known as Time Decay.
As an option owner or writer, you want to consider time decay when trading options so you understand which options best fit your strategy outlook. Look at the graph to see how the option value decreases from 90 days to expiration.
NOTE: In the last 30 days before expiration, time decay increases exponentially.
Volatility
If you trade stocks, you are already familiar with Volatility. In the stock trader's world, it is known as risk. The larger the price fluctuations, the riskier the stock, and the more expensive the options for that stock.
With stocks, price fluctuations are measured by the direction of the price and the size of the price change. With options, we are only concerned with the size of the price change, not the direction. Volatility is a percentage which reflects the average or expected size of the price change without regard to the direction of the change.
Emphasizing Changes in Volatility
As a user of options, not only should you be familiar with changes in time decay, but also with changes in volatility. Volatilities are stated in percentages (e.g., 25%, 65%, 105%, etc.). If XYZ stock, currently at $50, has a volatility of 16%, that would imply that it is expected to trade in the range up or down of $42-$58.
You should be aware that lower volatilities mean less movement in the stock price, while higher volatilities mean more movement in the stock price.
Volatilities of different options can be compared just like stock traders compare the price/earnings ratios (p/e) of different stocks.
When an option price has a low volatility, a big move is considered unlikely.
And when an option price has a high volatility, a big move is considered more likely.
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