Options Basics: Pricing, Greeks and Implied Volatility

If you are considering trading options, or recently started this article is going to explain the most important aspects of options contracts – and how those aspects impact the option price. Before we start, we have to know why options exist in the first place.

Why do options exist?

In the past institutions could not hedge their portfolios. Say it is 1950 and you were a pension fund with $100,000,000 in ABC stock and it was about to report earnings. You need a way to hedge your position, to lower your risk, but you have limited options:

  • Sell your shares (this is bad because what if you have $50,000,000 in capital gains? Now the tax is due)
  • Try to find some other asset that is negatively correlated and go long (there is no perfect asset or price to pay. You could hedge and both your hedge and your principal position could both go against you. This uses a lot of buying power as well)

This was (and still is) a massive problem for asset allocators, institutions and investors. How do you protect your financial assets? With leveraged downside protection, otherwise known as insurance. How would this insurance be priced and how would it work?

Two mathematicians Black and Scholes solved this with their famous formula – some contracts started to be written out of Chicago – and the rest is history.

Now we can trade 0DTE options on bitcoin ETFs from our iPhones. The importance of this history is just for the context and to establish that options are insurance products.

Equity Options Were Invented: Black Scholes

There is only one thing that separates option prices from the prices of other assets: they have a temporal component. Temporal = time. Translation: options have an expiration date.

Because options have this temporal component, their pricing has to account for this slow decay inherent to their price.

That is the most important part to an investor or a trader: the price. And option prices work fundamentally different from any other financial asset. Lets try to break this down piece by piece.

We need to understand something first. It is very simple – basic math and market theory – that every options trader must accept in order to proceed.

  • The “price” of the option is set by the market – buyers and sellers. What the market will bare.
  • The “greeks” of the option are derived by Black Scholes (American or European). The greeks are dependent on the price.

Put into other terms:

  • The Price is Independent Variable: For instance, in the equation y = 3x + 4, the variable “x” is the independent variable. Once a value for “x” is set, such as x = 12, it remains constant and does not change within the equation.
  • The Greeks are the Dependent Variables: In the equation y = 3x + 4, the variable “y” is dependent on what number is substituted for “x.” The value of “y” varies based on the value assigned to “x,” making it the dependent variable.

What Black and Scholes did was provide an equation to fairly price these option contracts – and how to model their behavior so that their prices “fairly” reflected the risk.

Remember options are primarily an “insurance product” so it helps to think of them in this way.

Quick story time:

Imagine you are going for a short road trip, and need a rental car, and you are standing at the counter talking signing and paying. The are about to ask you if you want to add extra insurance.

What should be the price of the insurance to protect you and the car?

It would depend on:

  • How many days will you have the car? (how long until the option expires?)
  • How volatile/safe of a car are you renting? (how volatile of an underlying stock?)
  • What kind of car are you renting? (how expensive is the underlying stock?)
  • What are interest rates currently?

If you knew these 4 variables, you could type it into some car insurance software program and it would spit out you what the appropriate insurance premium (price) should be.

If you are the driver, you are an insurance buyer. You pay a $100 now to protect a vehicle. If you are the insurance company, you are the seller collecting $100 and you are liable for the vehicles value.

If nothing happens the policy expires. If something does happen, the insurance company has to pay fix the decline in value (a crash).

This is how options work as well:

  • How much time is left?
  • How volatile is the underlying stock?
  • What is the price of the underlying stock?
  • What are interest rates currently?

If you know those 4 variables you can put them into Black Scholes and it will provide you the theoretical price of that option. This is a theoretical price, you might say this is what the price “should” be if it was fairly priced.

But remember, humans set the prices – humans are rarely fair.

The Option Price: How it Works

When trading or investing the most important aspect of your asset is ultimately its price. You want to buy things for $1 and sell them for $2 and you want to sell things for $2 and buy them for $1. How you get there, and what happens along the way is ultimately irrelevant if your entry and exit trades are profitable – you will make money.

With that as a back drop, what is the price of an option? What makes up the option’s price?

Like any other financial asset, the technical answer is that the price is the amount that buyers are willing to pay (the bid) and sellers are willing to accept (the ask). When you look at equities, bonds, futures and options these two prices exist – the bid and the ask.

When you are quoted an options price, you are likely shown the “mid” price – the halfway point between the bid and the ask. If you try to buy and sell at this price, will you get a fill? Maybe… but for the purposes of this video, we will assume you can get a fill at the mid price.

Is this the price that Black Scholes tells us given our inputs? No. That is backwards. This is the price the market sets.

Remember the market is considering the price of the underlying, the time remaining, the volatility of the underlying and current interest rates – and many other things – to arrive at the a fair price. Now that we know this price, we can derive our Greeks.

There are a million videos on “the greeks” so I am going to try and give it to you with a unique perspective first. Let’s stick with short term rental cars and insuring them. Imagine ourselves at that counter renting a particular car and insuring it.

  • Delta is the price of speed.
    • Going fast is expensive
    • Going slow is cheap
  • Gamma is price of acceleration
    • Expensive cars accelerate quickly
    • Cheap cars accelerate slowly
  • Theta is the price of duration.
    • Short trips are expensive per mile
    • Long trips are cheap per mile
  • Vega is price of driving record risk
    • Risky cars are expensive
    • Safe cars are cheap
  • Rho is the current price of money: interest rates. 99% of the time you can ignore this.

Want to rent and insure a Lambo in LA for the weekend? Lets price it out:

Very fast, short duration, max acceleration, high risk = very high price.

If this were an option contract it might be trading a 50 delta 2DTE call option on NVDA. It is very costly, very dangerous, it moves around a lot. It might end in disaster or there might be an incredible upside.

High delta, short duration, volatile underlying = high risk/reward = high price.

Ok, now that we have the analogy down, let’s talk about what the Greeks technically represent – and how to use them in your option strategies.

The Greeks Defined

1. Delta

Delta measures how much an option’s price can be expected to move for every $1 change in the price of the underlying. For example, a Delta of 0.40 means the option’s price will theoretically move $0.40 for every $1 change in the price of the underlying.

  • Definition: Delta measures how much an option’s price is expected to move for every $1 change in the price of the underlying security.
  • Significance: Helps gauge the likelihood of an option expiring in-the-money and predicts price movements.
  • Sell high delta and end at low delta. Buyers want to buy low delta and end at high delta.

Call options

  • Call options have a positive Delta that can range from 0.00 to 1.00.
  • At-the-money options usually have a Delta near 0.50.
  • The Delta will increase (and approach 1.00) as the option gets deeper ITM.
  • The Delta of ITM call options will get closer to 1.00 as expiration approaches.
  • The Delta of out-of-the-money call options will get closer to 0.00 as expiration approaches.

Put options

  • Put options have a negative Delta that can range from 0.00 to –1.00.
  • At-the-money options usually have a Delta near –0.50.
  • The Delta will decrease (and approach –1.00) as the option gets deeper ITM.
  • The Delta of ITM put options will get closer to –1.00 as expiration approaches.
  • The Delta of out-of-the-money put options will get closer to 0.00 as expiration approaches.

2. Gamma

Where Delta is a snapshot in time, Gamma measures the rate of change in an option’s Delta over time. Remember you can think of Delta as speed and Gamma as acceleration. Gamma is the rate of change in an option’s Delta per $1 change in the price of the underlying stock.

  • Definition: Gamma measures the rate of change of Delta, showing how much Delta will change with a price movement in the underlying asset.
  • Significance: Helps traders understand volatility and sensitivity of options to price changes.

More on Gamma: As time starts to expire, Gamma becomes more and more relevant. Sellers want to avoid being over exposed to Gamma because it can drive big losses in short periods of time. Buyers who YOLO short duration options use Gamma to try and achieve big gains.

3. Theta

Theta is the time component of options – option buyers pay this value and option sellers receive it. You can imagine it like a $99 insurance premium expiring over 3 days at $33 per day.

  • Definition: Theta measures how much value an option might lose each day as it approaches expiration, capturing the concept of time decay.
  • Significance: Reflects the erosion of an option’s worth over time and its impact on profitability.

Theta is like the entropy of the options universe. Options decay from a higher value to a lower value as time progresses. Your 6 month insurance premium is “expended” day by day as time passes – and after the 6 months is over – its worthless and you have to pay again.

Theta is the quantized price of this decay, displayed in a daily format.

Option buyers pay it as their contracts decay lower over time, and option sellers collect it for the same reason.

4. Vega (Not even a Greek letter BTW)

Vega measures the rate of change in an option’s price per one-percentage-point change in the implied volatility of the underlying stock. (There’s more on implied volatility below.) While Vega is not a real Greek letter, it is intended to tell you how much an option’s price should move when the volatility of the underlying security or index increases or decreases.

More about Vega:

  • Volatility is one of the most important factors affecting the value of options.
  • A drop in Vega will typically cause both calls and puts to lose value.
  • An increase in Vega will typically cause both calls and puts to gain value.

Neglecting Vega can cause you to potentially overpay when buying options. “Vol Crush” is because of and predicted by Vega.

All other factors being equal, when determining strategy, consider buying options when Vega is below “normal” levels and selling options when Vega is above “normal” levels. One way to determine this is to compare the historical volatility to the implied volatility.

  • Definition: Vega helps understand how sensitive an option might be to large price swings in the underlying stock by measuring its sensitivity to changes in implied volatility.
  • Significance: Indicates how volatility changes can impact an option’s value.
  • Example: Vega reflects what happens to an option’s value if volatility goes up or down by one percent.

5. Rho

  • Definition: Rho simulates the effect of interest rate changes on an option, providing insights into how interest rates can influence options pricing.

Implied Volatility: Like a Greek

Though not actually a Greek, implied volatility is closely related. Implied volatility is a forecast of how volatile an underlying stock is expected to be in the future—but it’s strictly theoretical. While it’s possible to forecast a stock’s future moves by looking at its historical volatility, among other factors, the implied volatility reflected in the price of an option is an inference based on other factors, too, such as upcoming earnings reports, merger and acquisition rumors, pending product launches, etc.

Key points to remember:

  • Figuring out exactly how volatile a stock will be at any given time is difficult, but looking at implied volatility can give you a sense of what assumptions market makers are using to determine their quoted bid and ask prices. As such, implied volatility can be a helpful proxy in gauging the market.
  • Higher-than-normal implied volatilities are usually more favorable for options sellers, while lower-than-normal implied volatilities are more favorable for option buyers, because volatility often reverts back to its mean over time.
  • Implied volatility is often provided on options trading platforms because it is typically more useful for traders to know how volatile a market maker thinks a stock will be then to try to estimate it themselves.
  • Implied volatility is usually not consistent for all options of a particular security or index and will generally be lowest for at-the-money and near-the-money options.

Why does this matter? Because you basically can’t proceed as an options trader if these concepts are not second nature to you. Understanding more complex strategies, and the terminology will be impossible without this foundational understanding of option pricing.

Once you mastered these concepts, you can systematically target certain deltas – or optimize for theta. Things will start to make sense when you see option prices rise before earnings only to “vol crush” after. Is buying short term options the day before earnings and selling them the day after a good idea in terms of Delta, Vega, Gamma and Theta?

  • As option sellers, we want to be selling insurance, not buying it.
  • Setting the price of risk, not accepting it
  • Getting paid to wait for nothing to happen, not paying to hope something does.

If you have any questions on these topics post them below and I will do my best to get back to you. If you found this content helpful please consider creating an account at IntraAlpha.