You can't know where you are going until you know where you've been. You can't price an option until you know what makes up its value. An options trade can become a complex machine of legs, multiple orders, adjustments, and Greeks, but if you don't know the fundamentals then what are you trying to accomplish?
When you look at an option chain have you ever wondered how they generated all those prices for the options? These options are not created by random but instead calculated out using a model such as the Black-Scholes Model. We will dive deeper into the seven components of the Black-Scholes Model and how and why they are used to derive an option's price. Like all models, the Black-Scholes Model does have a weakness and is far from perfect.
History Of The Black-Scholes Model
The Black-Scholes Model was published in 1973 as The Pricing of Options and Corporate Liabilities in the Journal of Political Economy. It was developed by Fisher Black and Myron Scholes as a way to estimate the price of an option over time. Robert Merton later published a follow-up paper further expanding the understanding of the model. Merton is credited for naming the model "Black-Scholes." In 1997, Scholes and Merton received the Nobel Prize for their work with the model. Fisher Black was not eligible because the Nobel Prize cannot be awarded posthumously.
As with any model, some assumptions have to be understood.
- The rate of return on the riskless asset is constant
- The underlying follows the more the option will be worth which states that move in a random and unpredictable path
- There is no arbitrage, riskless profit, opportunity
- It is possible to borrow and lend any amount of money at the riskless rate
- It is possible to buy or short any amount of stock
- There are no fees or cost
There are seven factors in the model: stock price, strike price, type of option, time to expiration, interest rates, dividends and future volatility. Of the seven factors, only one is not known with any certainty: future volatility. This is the main area where the model can skew the results.
1. Stock Price
If a call option allows you to buy a stock at a specified price in the future than the higher that price goes, the more the option will be worth.
Which option would have a higher value:
- A call option allows you to buy The Option Prophet (sym: TOP) for $100 while it is trading at $80 or
- A call option will enable you to purchase TOP for $100 while it is trading at $120
No one is going to pay $100 for something they can buy on the open market for $80, so our option in Choice 1 will have a low value.
What is more appealing is Choice 2, an option to buy TOP for $100 when its value is $120. In this situation, our option value will be higher.
2. Strike Price
Strike price follows along the same lines as stock price. When we classify strikes, we do it as in-the-money, at-the-money or out-of-the-money. When a call option is in-the-money, it means the stock price is higher than the strike price. When a call is out-of-the-money, the stock price is less than the strike price.
A TOP call has a strike of 50 while TOP is currently trading at $60, this option is in-the-money.
On the flip side of that coin, a put option is in-the-money when the stock price is less than the strike price. A put option is out-of-the-money when the stock price is higher than the strike price.
A TOP put has a strike of 20 while TOP is currently trading at $40, this option is out-of-the-money.
Options that are in-the-money have a higher value compared to options that are out-of-the-money.
3. Type Of Option
This is probably the easiest factor to understand. An option is either a put or a call, and the value of the option will change accordingly.
- A call option gives the holder the right to buy the underlying at a specified price within a specific time period.
- A put option gives the holder the right to sell the underlying at a specified price within a specific time period.
If you are long a call or short a put your option value increases as the market moves higher. If you are long a put or short a call your option value increases as the market moves lower.
4. Time To Expiration
Options have a limited lifespan thus their value is affected by the passing of time. As the time to expiration increases the value of the option increases. As the time to expiration gets closer the value of the option begins to decrease. The value begins to rapidly decrease within the last thirty days of an option's life. The more time an option has till expiration, the more time the option has to move around.
5. Interest Rates
Interest rates have a minimal effect on an option's value. When interest rates rise a call option's value will also rise, and a put option's value will fall.
To drive this concept home let's look at the decision-making process of trying to invest in TOP while it is trading at $50.
- We can buy 100 shares of the stock outright which would cost us $5,000.
- Instead of buying the stock outright we can get long an at-the-money call for $5.00. Our total cost here would be $500. Our initial outlay of cash would be smaller, and this would leave us $4,500 left over. Plus we will have the same reward potential for half the risk. Now we can take that extra cash and invest it elsewhere such as Treasury Bills. This would generate a guaranteed return on top of our investment in TOP.
The higher the interest rate, the more attractive the second option becomes. Thus, when interest rates go up, calls are a better investment, so their price also increases.
On the flip side of that coin if we look at a long put versus a long call, we can see a disadvantage. We have two options when we want to play an underlying to the downside.
- You can short 100 shares of the stock which would generate cash into the brokerage and allow us to earn interest on that cash.
- You long a put which will cost you less money overall but not put extra cash into your brokerage that generates interest income.
The higher the interest rate, the more attractive the first option becomes. Thus, when interest rates rise the value of put options drops.
Options do not receive dividends, so their value fluctuates when dividends are released. When a company releases dividends, they have an ex-dividend date. If you own the stock on that date, you will be awarded the dividend. Also on this date, the value of the stock will decrease by the amount of dividend. As dividends increase a put option's value also increases and a calls' value decreases.
Volatility is the only estimated factor in this model. The volatility that is used is forward volatility. Forward volatility is the measure of implied volatility over a period in the future.
Implied volatility shows the "implied" movement in a stock's future volatility. It tells you how traders think the stock will move. Implied volatility is always expressed as a percentage, non-directional and on an annual basis.
The higher the implied volatility, the more people think the stock's price will move. Stocks listed on the Dow Jones are value stocks, so a lot of movement is not expected. Thus, they have lower implied volatility. Growth stocks or small caps found on the Russell 2000, conversely, are expected to move around a lot, so they carry higher implied volatility.
The Black-Scholes Model is used to derive an option's value. While there are many assumptions in the equation, the Black-Scholes Model is still the most widely used model. Its ease of calculation and useful approximation create a strong basis to build more complex models. Out of the seven factors volatility is the only one that is estimated. Out of the seven factors, the most important are stock price, strike price, type of option, time to expiration and volatility. Interest rates and dividends have a very minuscule effect on an option's value.