Trading options (as I mentioned in this blog post, Options 101) is an effective way of hedging risk or speculating with a calculated amount of risk. Options give you the ability to understand EXACTLY how much you stand to gain/lose in every single scenario, no matter what. The greeks help you do that!
This means, using a bit of math, you can use specific options strategies to dial in profit/loss and risk to your desired levels. Let's dive right in.
First thing to note - there are TWO main values that go into the pricing of an option:
Intrinsic value is calculated as follows and can not be below 0:
Now, before you run away, it is important to understand these principles as an options trader. Because knowing which greeks have an effect on “intrinsic value” and which have an effect on “time value” is critical to making educated decisions when choosing which options to trade. These are the option “Greeks”.
Lets run through each of them:
Options, very simply, derive their value from the underlying stock that they are purchased on.
Noobie option traders will believe that when a stock moves $1, the price of options based on that stock will move the same or more than that $1. That’s where “delta” comes in.
Delta tells you the exact amount an option’s price fluctuates based on a $1 change in the underlying stock.
Calls have positive delta, meaning when stock price goes up the price for the call will go up.
Puts have a negative delta, meaning when stock goes up (and no other pricing variables change), the price of the option will go down.
When a stock is going deeper out of the money (OTM) the delta approaches zero, as it moves further into the money (ITM) delta approaches 1/-1 depending on if it is a call/put. A delta of 1 means that as the stock moves up $1, a call option will also increase in value by $1. Here is a graph depicting that:
This means options that are ITM (IN THE MONEY) will move faster in price than options that are OTM (out of the money) because their delta’s are higher.
Theta is a fun one to talk about - because it is also pretty easy to understand: Think of it as the value of TIME.
Theta is the speed at which an option’s price will go down per day, no matter what.
The price of an option goes down a little bit every single day because at expiration it will only be worth it’s intrinsic value. There will be no time value left, because there is no time left. For this reason, theta is bad for the option buyer and very good for the option seller.
Notice below how time erodes value away at an accelerated rate as the expiration date approaches:
Generally OTM options will have lower theta than ITM options. (OTM’s are cheaper in the first place, so they have less $ to lose)
Gamma is the rate of change of delta. Gamma basically asks:
“Based on a $1 change in the underlying stock price, how much does delta change?”
The best way to interpret gamma is by using a graph:
As you can see, the slope of delta is the highest as gamma hits its peak (right around the strike price), and then as gamma drops off, delta’s slope decreases.
Therefore, as a rule, the gamma is highest for ATM options, where the underlying stock is sitting right at the option’s strike price. And will drop as the option moves further into the money. This is because there is only SO much more the option’s delta can change as it approaches its max of 1 for calls or -1 for puts.
So basically due to the effect of Gamma, the value of close expiration at the money options will move the fastest in price with changes in the underlying stock.
Vega is the amount call and put prices will change as markets become more volatile. This is because, as “volatility” or “IV” or “implied volatility” increases, stocks have a higher % chance of moving into the money.
Generally, as stock swings become more frequent (markets get more volatile), the price of all options will increase.
Vega has no way of touching an option’s “intrinsic value” as that is only derived from its “money-ness” (OTM/ATM/ITM). But Vega does increase an option’s “time value” or premium.
Vega, and volatility in general, are a huge factor in option price movements (but are also the hardest to estimate).
You can use the VIX, a gauge of fear in the market, to estimate the level of volatility in markets at any given time. The higher the VIX, the more volatile the markets are, the more expensive all options will be.
Here is a graph of the VIX and the S&P500 over time. You will notice that as the VIX spikes - volatility in the market increases and the swings/drops become more wild.
As an option buyer, you want to buy during low vol times (when options are generally cheaper) and sell them during high volatility times (as their price increases).
As an option seller, you want to sell during high vol times (when options are expensive) and buy them back during low volatility times (when they are cheaper).
Vega is one of my favorites because it takes human emotion into account. Sometimes the perceived volatility in the market may be high - but the actual risks to the market are relatively normal. This spread provides an opportunity for us to make money on the difference between that emotional fear and real risks!
Rho is kinda the odd greek out. People don’t talk about it much, but I will here:
Rho is the amount an option’s price will change based on a 100 basis point (1%) change in market interest rates.
In an academic sense, the higher the interest rates are, the more likely people will want to keep cash parked. So instead of spending money to buy 100 shares of stock, they will buy a call option to buy that stock sometime in the future, and will park the remainder of their cash in a bank account paying interest. Also as rates increase, the costs of borrowing money to buy/sell stocks on margin also increases.
Long story short, depending on what the interest rate is, we will calculate a different “cost of carry” and “forward price”.
This basically means, all else remaining equal a positive Rho for calls and a negative Rho for puts.
In real life, rho doesn’t really matter for shorter term options. If you are trading longer-term options with expiration >2 years, Rho can start to play a larger factor in your options pricing.
Now you know how the greeks come into play when trading options.
It isn’t necessarily simple to put it all together, but if you read through a couple of times, take some notes, and try trading out in real life a bit. You will definitely get the hang of it.
For “The Bible” on Options, check out Options as a Strategic Investment. It was gifted to me by a previous boss and is definitely the most comprehensive of all options manuals out there.
And remember, I am here for you to ask questions if you need clarification or if something just doesn’t make sense. Options strategies can be an awesome way to supplement investing/trading income if you know how the math works and what you are doing!
If you thought this was helpful, terrible, or somewhere in the middle, please leave me feedback in the form of a Direct Message on instagram @MakeDollarsAndSense, or feel free to send me an e-mail/text to the information on my Home Page. I truly appreciate constructive criticism and opposing views, so bring em on!
P.S. New blog posts coming your way every Monday!
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