Options trading has become increasingly popular in recent years. Given options are different to stocks, we thought it was time to do an intern’s guide for U.S. options to help you understand options and options markets work.
Options are different to stocks
Options are very different to stocks and futures.
Once you buy a stock, you benefit if its price rises and lose if its price falls. You also earn dividends. If you short sell a stock, the reverse is true. We show that in the payoff diagrams below – note that the profit (and loss) for stocks increases in a straight line as stock price moves. As you will see later – that’s not the same for options.
Chart 1: When you buy (or sell) stocks, you profit as the price rises and lose if the price falls (or vice versa)
How do calls compare to stocks?
In contrast, an option works a lot like insurance.
With options, you can buy or sell, there are puts and calls, each with many choices for “strikes” and “expiries.”
We start (below) with how the profits and losses work for calls.
A call is a right to buy the underlying at a specific, or “strike,” price in the future. For simplicity, we often use the word “stock,” instead of underlying, in this blog post, but many underlying exposures can have options on them.
Call options are all about stocks going up. For a call buyer, at the time of expiration, the price of the underlying asset needs to be ABOVE the strike, by at least what you paid for the option, for the option to return a profit. We show how that works in the charts below. For example, If you buy an option for $5 with a strike of $100:
- If the (underlying) stock never rises above $100, the call will expire worthless. Why would you pay $100 for an $80 stock if you had the option not to!?
- But once the underlying stock price rises above $100, the option is worth exercising (it has intrinsic value).
- If the underlying increases to $102, you could “exercise” the option to buy at $100, giving you a $2 payoff. Although that helps, it still doesn’t offset the cost of the option premium.
- If the underlying increases to $105, you could “exercise” the option to buy at $100, giving you a $5 profit. Then, the payoff from the option offsets the cost of the option premium. This is known as the options “breakeven.”
- If the underlying stock rises more, say to $109, you could “exercise” the option to buy at $100, giving you a $9 payoff on the exercise. In that case, your payoff more than offsets the option premium, resulting in profit of $4 on the trade.
For a call seller (short), the opposite is true. They collect, or earn, the premium when they sell the option. Then they hope the stock doesn’t rise above the strike price, as then they will be called to sell the stock at $100 and incur losses. In theory, a stock price can rise for ever, so the seller of a call has “unlimited downside.”
Chart 2: Call options payoff
How do puts compare to calls?
In contrast, a put option gives the buyer the right to sell the underlying when the contract expires. Put options are all about stocks going down. A put buyer profits when the price of the underlying asset falls BELOW the strike price of the option.
We see from the payoff diagrams that a put buyer again pays a premium. However, this time they only profit when the stock falls.
While the put seller earns the premium, which they keep unless the stock falls below the strike.
Chart 3: Put options payoff
Note that:
- The buyer of any option can only lose the premium they are paying.
- The seller (or writer) of the option has increasing, and sometimes unlimited, downside as the stock rises (for calls) and falls (for puts).
Table 1: Potential losses on puts and calls for buyers and sellers
Generally, one option represents one round lot (or 100 shares)
You might know that stocks have “round lots” of 100 shares, but they can also trade in single shares or “odd lots.”
Stock options are designed around round lots. One stock option trade represents 100 shares of the underlying security. However, option prices are quoted per share (just like stocks), which means someone buying an option priced on screen at $1 will need to pay $100 ($1 x 100 shares) to settle their trade.
Index options are a little different, as they can set their own, sometimes different, “multipliers” (although many are still set to 100 x index price). For example:
- The Nasdaq-100 index is around 20,000.
- One NDX contract has a multiplier of 100, giving the underlying exposure (or “notional” exposure) of around $2 million (20,000 x 100).
- However, mini options exist representing 1/100th of the value of the original index. That reduces the notional exposure to $20,000, but also reduces the cash required to settle a trade at the same “price.”
How does expiry matter?
Options, just like insurance contracts, expire at a specific date in the future. Once the option has expired, it ceases to exist. If an option buyer didn’t “exercise” the option, the seller gets to keep the premium.
However, often investors want their options holdings to provide continuous insurance of their portfolios. To do that, they will “roll” into the next option contract to maintain exposure – a little like how you pay to continue your car insurance when it nears expiry each year. This creates elevated trading around expiry of all option contracts as traders will often sell the expiring option and buy the new option at the same time, which also saves worrying about exercising and delivery.
More volatility makes options worth more
For an insurer, a high volatility house might be a home in a wildfire region because those homes are more likely to claim on their insurance. To account for that, their premiums go up. The same thing happens to stock options.
As a reminder, this study discussed how volatility works in real markets. We see that it:
- Includes up and down moves.
- The range of cumulative price moves increases the longer you wait.
- The range of likely price moves also increases the higher the “volatility” of the underlying asset.
- Volatility is calculated from the standard deviation of daily price moves.
In short, higher volatility makes it more likely that the stock price will move more – potentially past the “strike” price – pushing the option “into the money.”
Chart 4: Daily returns for two different assets, one with higher volatility (yellow) than the other (blue)
If we plot the times that each asset in Chart 4 gained or lost different levels of return, we see what looks like a “normal distribution” (Chart 5).
If we had bought the same (say 5% up) call on both stocks in Chart 4, there is a higher chance that the yellow stock rises past the strike price. There is also a higher chance it moves well into-the-money (grey area).
Chart 5: Higher volatility means a higher chance of a big change in stock price, making the option more likely to be profitable
In other words, the more volatile stock is more likely to have a higher payoff (the grey area is larger). That in turn makes the yellow option worth more. Not surprisingly, the market factors that in by charging a higher premium!
The strike price also matters a lot
Given what we see in the chart above, if the option is “worth” the area under the curve to the left or right of the “strike,” then the strike will matter a lot!
This brings us to the difference between in and out-of-the-money options, or “moneyness.” For example:
- Out-of-the-money: In the call option above, the strike price is higher than the underlying price. That means the underlying stock needs to gain enough to pass the strike price to pay-off. That makes the grey zone smaller, in this case just a sliver of the right side of the chart. At this time, although there is some probability that the option will expire with value, it is currently out-of-the-money (OTM). However, that also makes its value and premium lower.
- In-of-the-money: If instead the call option above had a strike price less than (to the left of) the price of the underlying stock, the grey zone would start left of the hump in the middle, including the hump, as well as all the area to the right of the chart (a MUCH larger grey zone). In that case, the option was already in-the-money (ITM). It also has intrinsic value, and if you exercised it right now, you would have a positive payoff. Consequently, it would also have a higher premium.
Traders mostly buy OTM options
Given what we just learned, it’s interesting to see how traders actually use options.
Data shows that it’s much more common to trade out-of-the-money options (Chart 6), with most:
- Put options trading with a strike around 10% below the current stock price.
- Call options trading with a strike around 10% above the current stock price.
Chart 6: Most options trade slightly out-of-the-money
Black-Scholes is the math used to calculate option premiums
Hopefully everything we’ve said so far seems mostly intuitive. Options are like insurance:
- A small house is cheaper to insure than a large house (the replacement cost of the underlying asset matters).
- High co-pay is cheaper than no co-pay (strike price and moneyness matters).
- One month of insurance is cheaper than 12 months of insurance (time to expiry).
- A home in the plains is cheaper to insure than a home in a wildfire zone (volatility).
But how does the option market work out “how much cheaper” the premium should be?
It turns out there is math to estimate the profits in any grey zone (like we talked about in Chart 5) if you know a few things. It was created by two, now infamous, academics: Black & Scholes. If you know some specific key facts, most of which we’ve already talked about, you can calculate the expected payoff or the option:
- The price of the underlying asset
- The strike price of the options contract
- Time until the option expires
- The implied volatility of the underlying asset
- Whether the options contract is a call or a put
- The risk-free interest rate
Like many academic formulas, Black-Scholes doesn’t perfectly fit the real world. For a start:
- Stock prices are not (quite) normally distributed.
- The risk-free rate of interest isn’t (really) constant (thanks to the economy and the Fed!).
- Volatility will almost certainly change over the life of the option, especially given that prices tend to fall much more quickly than they rise (leading to something called the “Volatility Skew”).
- Some options can be exercised before expiry (called American options, which happen to be what mostly trades in the U.S.).
The fact that volatility changes over time is important. Because options traders are smart, they already know this, so they don’t calculate the option premium based on what has already happened – they calculate it based on what they expect to happen.
Interestingly, that means that once you know what the premium agreed in the market is, you can use the math to reverse engineer the “implied volatility.” That is, based on what someone was willing to pay for the option, what is their expected volatility of the stock in until expiry.
In many respects, every options trade is a bet on volatility. And often, professional traders quote options in “implied volatility” terms, not cents. That’s also what the VIX is designed to measure across a portfolio of different S&P 500 option strikes (all with an average 30 days to expiry).
Greeks help represent different risk factors
There is a reason people often talk about “Delta” hedging an option and option portfolio “Greeks.” – it’s all about the algebra and calculus in the Black- Scholes formula. Although there are more, the most common ones you will hear on the desk are:
- Delta: Perhaps the most important first Greek letter to learn, Delta comes from the calculus that is used in pricing options. Delta is the standard math symbol for rate of change – and that’s how it is used in options too. It shows how much the premium of the option is expected to change for a given movement of the underlying stock. You can see delta changing based on “money-ness” in Chart 6. The slope of the red and green lines changes as the moneyness of the option changes. Note that a well out-of-the-money option is unlikely to be exercised, so it’s premium is low and doesn’t increase very fast, but a more “in the money” option premium increases almost $1 for every $1 stock prices – so Delta can sometimes be thought of as an approximation of the probability that an option will expire in-the-money. Delta is also a measure of how much to hedge an option trade. For instance, if the delta is 40, you need to hedge 40% of the options notional (or 40 shares for every 1 option).
- Gamma: We can see that Delta changes as the stock price changes. That also means traders need to adjust their delta-hedge (up or down), depending on the new delta. That rate of change in delta is known as “Gamma.” When options are near expiry, Gamma is important because an option can rapidly go from out-of-the-money (no payout at expiration) to in-the-money (a payout at expiration).
- Theta: This brings us to Theta, also known as time decay. Holding all other factors constant, all options lose value over time. That’s because the likelihood that we see a 5% move in a week is higher than the chance that happens with just 1 day to go until expiry.
- Vega: While Vega is not a Greek letter (it’s actually the name of a star), it is the relationship between an option’s price change and a change in implied volatility. Remember, options prices increase as expected volatility increases, and are often quoted in volatility points, so Vega is important to traders.
Table 2: Options “Greeks” for dummies
What can you buy options on?
In the U.S. equity market, you can get options on thousands of company stocks, hundreds of ETFs (Like QQQ), or even an index (like the Nasdaq-100).
Index (and ETF) options would let you insure or gain exposure to a portfolio that was similar to the index (or ETF) while a stock option would let you insure or gain exposure to a single company stock you own.
We see that a lot of trading occurs in single stock options (Chart 7, purple inner ring). However, because stock prices are lower than indexes values (the Nasdaq-100 index is around 20,000), the value of exposure traded in index options is actually much larger (grey in the outer ring).
Chart 7: The majority of options trading is in very liquid underlying assets
How frequently do options expire?
The U.S. equity options market has grown significantly since the early 1970s. Trading today adds to around 45 million contracts a day, with delta-adjusted exposures of around $250 billion each day.
As Chart 8 shows, there are options that expire quarterly, monthly and weekly. Apart from better matching option protection with cashflows, sellers of shorter dated options have the potential to realize more Theta – as time decays more quickly toward the end of an options life. A number of weekly expiries potentially allows investors to sell Theta more effectively, and limit max-downside on a single position, than with quarterlies.
Still, the majority of trading occurs in monthly expiries.
Chart 8: Historical Options volume by expiration type
Importantly, the choices of expiry don’t exist for all assets (Table 3):
- Quarterly: There are actually just a handful of ETFs and indexes with quarterly expiries. These expire on the last day of the quarter.
- Monthly: The majority of options have an expiry each Month. That expiry happens on the third Friday of the month, which sometimes coincides with index rebalances, creating what is known as Quad Witching.
- Weekly: Around 600 other stocks (for this purpose, ETFs are a stock) are available with an expiry every week. These (almost) always expire on a Friday, except when a monthly option already exists with the same Friday expiry.
The most popular index products now have weekly options that expire on different days of the week. Only the S&P 500 and Nasdaq-100 offer investors weekly options with the choice of an expiry on every day of the week.
Table 3: Different option underlying, expiry frequencies and settlement conventions
What actually happens on expiry?
Every option expires. However, the way the profit is calculated and the process to exercise can differ.
Many options expire on Triple Witching day. That happens when monthly futures and options all expire on the same day. As traders unwind positions, it can lead to large trade volumes.
However, the trading doesn’t all happen at once. In fact:
- Index (options and futures) expire in the Open Auction.
- Stock Options (and index trades) expire in the Close Auction.
In addition, what actually happens on expiry is different. Generally:
- Index (options and futures) will settle in cash, meaning the profit and loss on the position is calculated by the clearer, and is transferred between the buyer and seller in cash.
- Stock options require the transfer of the actual stock (for payment of the strike price agreed).
Cash settlement can be more convenient
This kind of makes sense – although a market maker might hedge the Nasdaq-100 with stocks, they could also use QQQ ETFS or NQ futures – making delivery of underlying shares in the index portfolio difficult.
It is also important to note that there has been an acceleration in the trading of cash settled options in single stocks. Currently, these can only be traded as a “FLEX,” which is a bespoke request for a new option.
Chart 9: How expiry date works for different products
Physical settlement adds more time
Interestingly, the Options Clearing Corp (OCC), the clearing house which settles all these products, allows for people to “abandon” American options that settle in-the-money. That’s mostly because of price changes after the close but before the cut-off to assign delivery at 5:30pm.
Equity options are SEC-regulated “securities,” but options markets are different than stock markets
Stocks, equity options and corporate bonds are all “securities” under the law and, therefore, governed by the U.S. Securities and Exchange Commission (SEC).
Chart 10: Similarities and differences between stock and options markets
In some ways, options markets are similar to stock markets, and in other ways they are quite different.
There are no dark pools
One of the biggest differences between the stock and options markets is the lack of a Trade Reporting Facility (TRF) in options. In theory, that means all trading must happen on exchanges; although, it doesn’t stop institutions trading over the counter (OTC) options, using ISDAs.
However, it does mean retail trade on exchange. Although sometimes that occurs in intraday price-improvement auctions, similar to what have been proposed for the U.S. stock market.
There are still around 17 exchanges
One of the similarities with stocks is venue competition (fragmentation). There are currently 17 different option exchanges competing for orders, including venues run by Nasdaq, Cboe and the New York Stock Exchange.
Chart 11: The U.S. options exchange market
There is a central clearer and security fungibility
The OCC settles all options traded on the regulated exchanges, so options purchased on one exchange can be sold on another, making the options completely fungible from exchange to exchange.
There is a consolidated tape (and prop feeds)
The Options Price Reporting Authority (OPRA) consolidates all bid/offer and transaction information from all the options exchanges nationally. Large options trading firms subscribe to this consolidated tape and typically subscribe to “proprietary” feeds from each individual exchange, too.
Proprietary feeds and co-location are important for any market making business, especially given the huge quantity of options securities to quote and the dependence of option prices on the underlying stock prices, which also trade all over the market.
There is a trade through rule
Just like in stocks, in order to protect customers, brokers can’t “trade-through” (trade at an inferior price) any better quote on another exchange.
There are small exceptions to this “no trade through” rule involving multi-leg spread trades.
There are (way) more options than stocks (and a lot more messages)
There are roughly 10,000 NMS securities trading on U.S. stock markets – from ADRs to ETFs and company stocks.
Only half of them stocks qualify for options. There are specific listing standards to qualify for trading options, including a diversified investor base (number of shareholders), and being liquid enough to hedge the options exposures being created.
That said, there are over 1.5 million “tickers” in the options market. How?
Chart 12: Comparing the number of securities in stock and options exchanges
If you think about it this way: There is just one AAPL stock. But for AAPL options there are:
- Puts and Calls
- Expiring every week for the next eight weeks and every month for the next year
- With a number of strikes, from deep in the money to deep out of the money
- And for each of them, a market maker needs to try to quote bids and offers, across 17 venues
- That’s around 2,000 AAPL options.
In short, for each stock with an option, there are hundreds of permutations of puts, calls, expiries and a range of strike prices that make a total number of well over 1 million strikes available to trade. Not all of these strikes trade, however. In fact, on a typical day less than 20% of available listed strikes will be traded.
That makes correctly pricing options across the whole market a monumental job, especially if computers need to constantly redo some Black-Scholes math to update for every change in the price of the underlying.
That’s also why options exchanges (and the OPRA) need to process tens of billions of messages every day — far more than created by the stock market.
Options are derivatives of stocks, but they trade quite differently
As we’ve shown, an option price is derived from the prices and volatility of the underlying stock (or equity index) they track – that’s why they’re called a “derivative”.
They’re also securities under U.S. law.
But that’s about where the similarities stop. Options are more complex, require different retail investor signoffs, trade on-exchange, expire regularly and need to be rolled if you want to maintain exposure.
However, for investors, options offer a lot of things that stocks don’t, which can sometimes be helpful.
They let you potentially insure your position or portfolio from losses or increase portfolio income by selling premiums. That can significantly change the risk-return or yield of an investor portfolio.
That’s likely why there are so many popular new ETFs with options in the market these days, too.