Advanced Options
STOP! If you are not familiar with the basics of options trading, you should read the Options Basics course before proceeding. This material references terminology from that course, and assumes you are familiar with the material.
This course covers more advanced options topics:
- Introduction to “The Greeks”
- Broad discussion of reasoning for choosing one option or another, in terms of portfolio management
- Discussion of the different kinds of options strategies commonly discussed in other investment media
The material below assumes you understand what options are, how a given option trade is facilitated in the market, and how to calculate a profit/loss from an option trade at expiration. This is all covered in the Options Basics course mentioned above.
By the end of this course, you should:
- have a high-level understanding of how different kinds of data influence the price of an option
- know what is meant when someone refers to “the greeks” and to specific quantities by their “greek” labels
- be able to understand what is meant when certain spreads and other more complex option trades are mentioned by their “jargon” names, e.g., you’ll know what an “iron condor” (among many others) is
- have an intuition for the basic strategy behind each of the option trades mentioned
How are Option Prices Determined?
Option prices are most strongly determined by the price of the stock the contracts cover, but far more goes into it than that.
Stock Price
The price of an option’s underlying stock has one of the strongest impacts on the price of an option. If the stock price goes up, prices for options at different strikes will move in response.
| Option Type | Direction of Stock Move | Direction of Option Move |
|---|---|---|
| Call | Up | Up |
| Call | Down | Down |
| Put | Up | Down |
| Put | Down | Up |
Why does this happen?
The value of a call option gives the buyer the right to buy the stock at a given price. If the stock price is above the strike price, a buyer can buy the shares for less than the market price of the stock by exercising. Consequently, he can profit by exercising and immediately selling. If the stock price moves up, he can profit even more, so the option becomes more valuable. The reverse is also true: if the stock price moves down, the call buyer can profit less, so the value of an option at a given strike price moves down.
On the other hand, a put option gives the buyer the right to sell the stock at a given price. If the stock price is above the strike price, a buyer can sell shares for less than what he has to pay for them–he does not profit. The more the stock price moves up, the less valuable his option is; the put option is more valuable as the price of the stock falls. So, if the stock price moves down, the value of a put option moves up, and if the stock price moves up, the value of the option moves down.
Time Decay
All options have an expiration date. At the end of trading on that date, the option is either worth something (“in the money”) or not (“out of the money”). As time passes, there is less time before expiration for the stock price to move in a favorable way to make the option expire in the money. Consequently, the option loses value over time.
An option loses value as time passes. This is known as “time decay”.
Volatility
“Volatility” is a measure of how much a stock’s price changes over a period of time, for example, the last 30 days. If there is a wide spread in the highs and lows of a price, it is said to be “highly volatile.” Typically, volatility increases when the volume of trading decreases, because each trade can cause much bigger price changes.
When stock volatility increases, the prices of their options can be highly volatile themselves. This can cause the bid-ask spreads of an option to vary in abnormal ways. Prices will reflect this.
When a stock underlying an option is more volatile, option prices at different strikes can have more unpredictable pricing.
Risk-Free Interest Rate
The “risk-free interest rate” is the Secured Overnight Financing Rate (SOFR) of interest for short-term loans, e.g., that banks use with each other. It is “risk free” because the risk of default is extremely low. This interest rate is used as a benchmark in computing option prices because it offers a convenient benchmark to use for comparing the potential for profit and loss.
If one can loan a bank money at the interest rate, they could receive the interest as payment for (nearly) no risk. Options are risky–the value of an option has to be more than the value of borrowing or lending at the interest rate, otherwise a person could just borrow or loan money and make profit without taking on the risk of an option.
Call options increase in price as interest changes. Put options decrease in price.
The “Greeks”
There is an entire field (or two) devoted to studying how to assign a price to a security such as an option. Real Options Education has material that discusses the mathematical basis for all this in the Math & Statistics course material if you are interested in much more technical and in-depth discussion. This section is meant as an introduction to the various parameters large institutions and hedge funds use to evaluate the value of options, and which retail traders can use to develop their trading strategies.
The terms and parameters discussed are used commonly in other options education sites and investment media in general, so it is important to understand what they are, even if you believe the mathematics is uninteresting or something you’re not ready to tackle.
The mathematical models we referred to above make use of the Greek alphabet (\(\alpha, \beta, \gamma\), etc.) as variables in the equations that are part of the model. These variables represent some real thing that goes into establishing the proper price of an option. Collectively, they’re referred to as “the Greeks.”
The “greeks” are listed, below.
- \(\Delta\) aka “delta”: stock price sensitivity
- \(\theta\) aka “theta”: Time Decay
- \(\rho\) aka “rho”: risk-free interest rate sensitivity
- \(\Gamma\) aka “gamma”: sensitivity to changes in \(\Delta\)
- Vega (there is no Greek letter for this word): sensitivity to changes in volatility (“implied volatility”)
Basic Trading Stategies
At the most basic level, options are generally used to indicate a trader’s willingness to enter a position (i.e. buy a stock) or close a position (i.e. sell a stock) at a given price for the stock.
| Option Trade | Basic Strategy |
|---|---|
| Buy a Call | A trader would buy a call when he’s willing to pay a price for a stock and he thinks the stock will be above that price at a later date, i.e., the trader is bullish on the stock, but he doesn’t want to commit capital (i.e. buy the stock) at the time he buys the call. |
| Sell a Call | A call is sold when the trader is willing to sell at the strike price and take whatever profit that yields or he hopes that it won’t rise to the strike price, generally because he thinks the stock won’t be too much higher at expiration. This is a bearish or neutral outlook on the stock: the seller of the call expects to keep the premium he collects from selling the stock, and for the option to expire worthless–this means he expects the stock price to be below the strike price. |
| Buy a Put | A trader might buy a put option when he holds shares of a stock and wants to minimize losses if the stock decreases in price: the strike price is the minimum he’d sell the stock for if it’s dropping. This is a bearish position: the trader thinks the stock has a higher likelihood of dropping and doesn’t want to lose too much money if/when it does. |
| Sell a Put | A trader might sell a put option if his overall strategy indicates that the stock is a good value at the lower price, but not the current price of the stock–he’s bearish through the expiration date, but would be bullish or neutral at the lower price. |
Spreads
All spreads consist of buying at least two options, either at different strike prices, on different expiration dates, or both.
Generally, the strategic purpose for buying or selling a spread is to reduce risk: it limits exposure if the stock price moves outside of a price range that the spread covers. The trade-off for this protection is that there is also generally limited profit available.
The discussion of what kinds of spreads are commonly employed in various trading strategies includes providing some basic reasoning behind the strategy for using them. The strategic purpose for choosing these option constructs is explained in more depth in the trading course.
Basic Spreads
A spread consists of buying two options of the same type, either at different strike prices on the same expiration date or at the same strike at different expiration dates.
Spreads are opened for either a credit (money is received by the trader) or debit (money is paid by the trader).
Any spread opened for a credit is a short position: you’re selling a more valuable option than you’re buying. A spread opened for a debit is a long position: you’re buying a more valuable option than you’re selling.
At the same Expiration Date
Spreads consisting of options bought at the same expiration date are just called “spreads”. There are two types.
| Spread Type | Options Traded |
|---|---|
| Credit Spread | The trader sells an option with a strike closer to the stock price and buys an option with a strike further away |
| Debit Spread | The trader buys an option with a strike closer to the stock price and sells an option with a strike further away |
Examples
- Call Debit Spread: John buys a call option with a strike price of $10 expiring on 3/12. At the same time he sells a call option with a strike price of $11 expiring on the same day.
- Put Credit Spread: Joan sells a put option with a strike price of $8 expiring 5/1. At the same time she buys a put option with a strike price of $7.50 expiring on the same day.
Exercises
-
A stock is trading at $10. The strike prices for options for this stock trade in $0.50 intervals, e.g. $9.50, $10, $10.50, $11.00, etc. Describe a call credit spread for options expiring on 6/3.
-
A stock is trading at $50. The strike prices for options are in intervals of $1, e.g., $48, $49, $50, $51, etc. Describe a put debit spread for options expiring on 8/13.
Calendar Spreads: Options At different Expiration dates
Spreads consisting of options bought at different expiration dates are called “calendar spreads”. The trader buys an option that expires on one date, and sells an option at the same strike on a different date.
Generally, because options that expire later are more valuable (see Time Decay):
| Spread Type | Options Traded |
|---|---|
| Credit Spread | The trader sells an option with an expiration further away on the calendar and buys an option at the same strike with an expiration closer on the calendar |
| Debit Spread | The trader buys an option with an expiration further away on the calendar and sells an option at the same strike with an expiration closer on the calendar |
Examples
- Calendar Credit Spread with Calls: Katy buys a call option with a strike price of $10 that expires in June, and sells a call option with a strike price of $10 that expires in July–the option expiring on 7/2 is more valuable because it has longer to live, so Katy receives more premium than she pays for the buy
- Calendar Debit Spread with Puts: Peter sells a put option with a strike price of $24 that expires in August, and buys a put option with a strike price of $24 that expires in October–Peter pays more for the later expiring option than he collects for selling the earlier one, so this is a net debit
Exercises
-
Describe a calendar credit spread using put options at a $15 strike.
-
Describe a calendar debit spread using call options at a $20 strike.
Advanced Spreads: Butterflies and Condors
Butterflies and Condors expand on the conecpt of spreads. Their purpose is to trade on more than just the price of a stock, but also volatility and other factors. Like basic spreads, advanced spreads reduce risk and exposure to loss. Also like spreads, that reduced risk/exposure has trade-offs.
Butterfly Spreads
Butterfly spreads consist of buying and selling options at three strike prices. A butterfly position is entered by buying two options and selling two options. All of the options are of the same type–either all calls or all puts.
To execute a long butterfly:
- Buy one out of the money option.
- Sell two at the money options.
- Buy one in the money option.
Suppose a stock, XYZ, is trading at $50.21 and its option strike prices are in $1 increments. A long butterfly example would be:
- Buy a call with a $52 strike price.
- Sell two calls with a $50 strike price.
- Buy a call with a $49 strike price.
To execute a short butterfly, simply do the opposite of the long strategy:
- Sell one out of the money option.
- Buy two at the money options.
- Sell one in the money option.
Suppose a stock, XYZ, is trading at $50.21 and its option strike prices are in $1 increments. A short butterfly example would be:
- Sell a put with a $52 strike price.
- Buy two puts with a $50 strike price.
- Sell a put with a $49 strike price.
Exercises
-
A stock ACME is trading at $249.48 and its option strike prices are in $5 increments (e.g., $240, $245, $250, $255, etc.). Construct a long butterfly spread with puts.
-
A stock YOLO is trading at $120.13 and its option strike prices are in $1 increments. Construct a short butterfly spread with calls.
Iron Butterfly Spreads
This strategy is similar to regular butterfly spreads in that four options are purchased. However, it uses a mix of both calls and puts.
A long iron butterfly is entered by the following trades:
- Sell one out of the money put.
- Buy one at the money put.
- Buy one at the money call.
- Sell one out of the money call.
This strategy is profitable if the underlying stock price is at the money, i.e., close to the strike prices of the purchased options.
A short iron butterfly is entered by taking the opposite actions for each trade:
- Buy one out of the money put.
- Sell one at the money put.
- Sell one at the money call.
- Buy one out of the money call.
This strategy is profitable when the stock price moves above or below the out of the money options.
TSLA (Tesla) is trading around $170. Options are trading in $2.50 strike increments, e.g., $165, $167.50, $170, $172.50, etc. If a trader wants to open a long iron butterfly position, he or she could:
- Sell a $167.50 put
- Buy a $170 put
- Buy a $170 call
- Sell a $172.50 call
Exercises
- NVDA (Nvidia) is trading at $1001.22 with $5 strike increment option prices. Describe a short Iron Butterfly spread.
Condor Spreads
Condors are similar to butterflies, except that four strike prices are used instead of three. Also similarly to regular butterfly spreads, the options are all of the same type: puts or calls.
A long condor spread consists of the following:
- Buy an out of the money option.
- Sell an out of the money option with a strike closer to the underlying’s price.
- Sell an in the money option with a strike close to the underlying’s price (but not at the money).
- Buy an in the money option further away from the underlying’s price.
This results in you paying the premium, because the two option buys are priced higher than the two option sells. The goal is to see the price of the underlying not change too much: it’s profitable when the underlying trades in the middle of the four option strike prices. If it moves too far, the loss is capped at the price of the spread you paid to enter the position.
A short condor spread is taking the opposite trades to the long spread:
- Sell an out of the money option.
- Buy an out of the money option with a strike closer to the underlying’s price.
- Buy an in the money option with a strike close to the underlying’s price (but not at the money).
- Sell an in the money option further away from the underlying’s price.
This results in you paying the premium, because the two option buys are priced higher than the two option sells. The goal is to see the price of the underlying move beyond the out of the money prices, which is when the strategy becomes profitable.
Iron Condor Spreads
These strategies utilize the same four-option setup that Condor Spreads use, except the option types are mixed: an iron condor trades two call and two put options.
An Iron Condor is constructed as follows:
- Buy one out of the money put option at a strike relatively far away from the current price of the underlying
- Sell one closer out of the money, or even an at the money, put option
- Sell a close out of the money or even at the money call option
- Buy a further out of the money call option
The end result is that you collect a net credit: the two sells will have higher combined prices than the two buys. The trade is most profitable when all the options expire worthless.