In this series we cover options: a deceptively complex trading instrument that provide an entirely different type of insurance - against directional moves in financial markets.

I have spent most of my professional life as a quantitative analyst or 'quant' - a person who performs statistical analysis on financial data, usually focused on providing a competitive advantage to a firm's trading strategies - specifically in derivatives or 'options' trading.

Options are derivative contracts that allow the holder the right, but not the obligation, to trade (buy or sell) a specific security for a specific price for a specific period of time, and I'll explain much more in the following series.

What I find fascinating about options trading is that it levels the playing field: allowing small financial firms to play extremely effective strategies despite having neither the technical advantage of recently controversial high-frequency trading (HFT) firms, nor the scale and diversified advantages enjoyed by well-known investment banks like Goldman Sachs and Morgan Stanley.

By the time this series is finished, I aim to help people understand why this is possible, what is it about options that allows for such profitable trading? In the securities business, it is not uncommon for small-sized firms to excel at their primary business, and not because they engage in deceitful, fraudulent or exploitative practices.

Generally, it is because they have identified an edge over the competition. This edge can come in different forms, and one such form is knowledge-based. They know something the rest of the market does not.

Options trading allows this edge for a simple reason: options are complex and most people do not understand them. Hopefully, this article will help you to grasp the basics.

"If you intelligently trade derivatives, it’s like a license to steal" - Charlie Munger, Berkshire Hathaway, 2014

I want to discuss practical issues with options, options trading, and the various trading infrastructures that are in place. A fascinating topic and rarely covered, despite its importance. For clarity, I will focus solely on vanilla, exchange-traded options, and will not discuss options with more esoteric features like path-dependent payoffs.

We will get to price and other quantitative behaviour in future articles of this series, but before that, it is important to know a little about the infrastructure and details of the options markets themselves. While the underlying quantitative behaviour is fascinating, many of the seemingly practical matters can be hard to learn about.

## Notes

I will gloss over some technical points for the purposes of clarity - although not too much. My aim is the Einsteinian principle of "as simple as possible, but not simpler".

There are many sources on pricing methodology and other quantitative theory of options. This will not be one of them. I doubt I would do the topic justice but will provide some links at the end of the series for those interested.

We will talk numbers and statistics in future articles.

# What is an Option?

Options are derivative contracts that allow the holder the right, but not the obligation, to trade (buy or sell) a specific security for a specific price for a specific period of time. The asset for which the option confers the right to trade is termed the underlying asset (or underlying for short).

Any type of asset can be used as the underlying, and this article will focus on equity options (options on stocks such as Google, Apple, IBM, 3M and WalMart). It is the most common type of option, and that with which I am most familiar. Most of the principles discussed here have analogies with other underlying assets, such as currencies, futures or bonds1, so this focus does not lose much generality.

Before we begin, it is best to first lay out some terminology and notation.

Long & short

• A long position is one where the instrument is 'owned' by the holder, who profits from a rise in the price of that instrument.
• A short position is one where a profit can be made from a drop in the price of the instrument. The holder loans the instrument from someone else (and they owe it to them at some agreed point in the future) before immediately selling it in the marketplace. They make a profit if they can later buy the instrument (to return to the loan-maker) for less money than they sold it.

These terms are used very generically in finance. Thus, a speculator will state she is 'long interest rates' - meaning they hold a combination of assets that will be profitable in the event of a rise in interest rates. While these terms often seem to be abused (for example, what does it mean to be 'short gamma in US equities')2, the key thing to remember is that long positions want a rise in price and short positions want a decline.

Call & put

• an option that confers the right to buy the underlying is termed a call option (call for short)
• an option that confers the right to sell is termed a put option.

Calls and puts are very closely linked in terms of behaviour and price, called put / call parity, and we will discuss this in a future article.

Strike & expiration

• The specified trade price for the option contract is termed the strike price, and the time period for which this right is conferred is the lifetime of the option.
• The date at which this right ends is the expiration date or expiry date.

Options are insurance policies against the movement of the underlying price. A call is a policy against the stock price going up, a put is a policy against the stock price going down, and the policy lasts until expiration.

Exercise

• Finally, most option contracts have a feature that is known as early exercise - that is, the right to buy or sell the stock can be exercised prior to expiration.
• Most options traded have this feature and are termed American options. This has nothing to do with geography and is presumably some historical artefact.
• Options that do not have early exercise are termed European options.

The vast majority of options traded have early exercise rights (aka 'American' options). We will largely ignore 'European' options, although they are still very important from a modelling point of view as they are easier to price.3

The mechanics of trading equity options is very similar in principle to trading other common financial assets such as equities or futures. Options are traded on an exchange, and are treated as assets in your account.

Two of the most important concerns in financial trading are counterparty risk and liquidity risk. Both are important concepts, and attempts to mitigate them explain the existence of a lot of infrastructure that has built up around the asset markets.4

## Counterparty Risk

Counterparty risk is the risk that the person you trade with (your counterparty) is not fit or willing to make good on the trade when due.

The sudden reappearance of counterparty risk was the major contributing factor to the Credit Crisis of 2008. Huge losses in subprime mortgages threatened the existence of a number of large financial institutions. As a result, other institutions that had existing agreements with the distressed counterparties were now concerned about their ability to sustain current financial agreements.

A good analogy is insurance companies. If your house burns down, you want to be sure that the company that wrote your policy is in business and can pay the compensation.

Usually this is not a consideration, but if a lot of houses all burn down at once (say due to a huge forest fire) - this can become a huge problem. Very large hurricanes and natural disasters can bankrupt insurance companies, and large companies providing such catastrophe insurance try hard to diversify risks geographically.

Similarly, if you buy a call option and the stock rockets up through the strike price and is now worth many, many multiples of what you paid for it, you want to ensure that the person from whom you bought it can deliver.

## Liquidity Risk

Liquidity risk is the risk of the asset losing its liquidity. Liquidity is a commonly-used but nebulous term describing how difficult it is to find counterparties to trade an asset at a reasonable price. Liquid assets are easy to trade in large quantities, and such trades do not have a large effect on the price.

As you might imagine from the lack of precision in the terms used in its definition, liquidity is difficult to quantify5. In broad terms, currencies tend to be extremely liquid, followed by equities and commodity futures. At the other end of the spectrum, real estate is highly illiquid, even in a booming property market6.

Both of these issues are serious business risks, and were even more so in the early days of finance7. Such concerns led to the creation of exchanges and clearing.

An exchange is a legal entity that serves as a central marketplace for traders of a particular asset type. It standardises contracts - especially important for options and futures - and centralises the liquidity in a particular venue.

Trading on an exchange is a special privilege given only to members of the exchange, so members either trade for themselves or act as brokers for third parties. Most participants are customers of brokers, since becoming a member of an exchange is expensive and time consuming. As such, it is rarely worth becoming a member unless it is a primary focus of your business.

Once a trade occurs between a buyer and seller, it is recorded on the exchange, with trade notifications sent to a number of interested parties including both primary participants in the trade, regulatory authorities, and market data providers. Most importantly, the trade is registered with the clearing and settlements system.

The clearing system is how trades are settled, and helps mitigate against counterparty risk: once your trade is reported it is the responsibility of the clearing system to ensure participants receive / deliver their assets and cash. Once a trade is registered your counterparty is now the clearing system not the person or company on the other side of your trade. Thus, counterparty risk is much reduced.8

Settlement of trades usually happens a number of days after the date of trade, usually three days (for historical reasons), but attempts have begun to reduce this down to a $T+1$ system: cash and assets are transferred a day after the trade date.

An interesting consequence of the old $T+3$ settlement system is the fact that US exchanges are never closed for more three days in a row: this ensured people could always liquidate assets to meet settlement obligations. This is why an unfortunate junior trader gets the job of watching the screens on Black Friday or during the Christmas holidays, despite nothing ever really happening. Someone needs to be there when the markets are open, just in case.

Clearing fees are an additional cost to trading financial assets, but provide a valuable service to the system as a whole. As they are counterparties of last resort, they focus heavily on the risks taken by their clients, ensuring that losses incurred do not exceed the capital clients have on deposit with them. Should that occur, further losses are the responsibility of the clearing firm.

# The Option Market

Almost all financial markets are two-sided, open outcry markets.

A two-sided market is one where there is a buy price (the bid) and a sell price (the ask or offer). The difference between the bid and the ask is known as the bid/ask spread, and is the price charged by market makers to always quote prices on both sides.

The bid/ask spread is the most common way that traders make a profit; they try to take as little risk as possible and just earn the spread. Most market-makers want to carry no position overnight if possible, hedging out any residual positions they may have left at the end of the trading day.

In an open outcry market, prices are constantly being updated and published. All the quotes published are aggregated and the highest bid and lowest ask across all the options exchanges for that contract is termed the National Best Bid and Offer or NBBO. Of course, any individual market maker may have a spread wider than that implied by the NBBO, and that is perfectly acceptable - simply that market maker will get fewer trades as other people are willing to pay more or take less and so are ahead in the queue.

Another consequence of not matching the NBBO on both sides is that any trades you get will all be on one side; you will only get trades that involve you buying or selling only. Indeed this may be the point, a market maker may have taken down a big order earlier and is now looking to reduce her net risk by subsequently trading in the other direction.

Watching a market in motion is fascinating, it is the aggregation of many different participants, each with different aims, priorities, and goals, expressed in the dynamics of four numbers: the bid and ask price, and the size of the quote on both sides, the volume of contracts / shares / currencies available at those prices.

Option volumes are expressed in contracts. An option contract is for 100 shares, the same size as a round-lot of shares on stock exchanges. Despite this, contracts are quoted as if only 1 share of underlying is involved. I assume this is historical as that is how futures contracts are traded. It is also the most natural unit for pricing the option, and gives the exchange flexibility in terms of how contracts are standardised - contract sizes could be changed without requiring any change in how they quote the prices.

Thus, if you buy 1 call for 1.25 USD, you will pay 125 USD, as an option contract is for 100 shares, but the price is quoted in terms of 1 share.9

Exchanges standardise the expiration date and strike prices for options. This makes things manageable, only a finite number of contracts are available for trade.

• Until 2012, options expired on a monthly basis, and then weekly options for the large indexes were added. These additional expirations proved hugely popular, so weekly expirations were added for large single stock options in the last few years. There are now expirations every Friday in almost all liquid options.

• Strike prices are also set by the exchanges, largely according to demand. Large equity index exchange-traded funds (ETFs) offer shares in funds that mirror the composition of the large indexes. ETFs are so liquid that there are strikes every 50c close to the stock price, despite underlying prices over 150 USD per share. The demand is there so the exchange provides those contracts.

It is worth giving a concrete example of this. Consider the stock symbol SPY, the ETF based on the famous S&P-500 index of large US public companies. At the time of writing, this ETF is around 205 USD per share, and for the closest expiration date in a few days time, there are strikes every 50c from at least 190 to 220, i.e. the current price plus/minus 15 USD.

For less liquid stocks, strikes are relatively further apart. For a lot of stocks in the range of 40-80 USD per share, strike may be still be 50c apart, possibly even 1 USD.

# Conclusion

We have discussed the trading environment and infrastructure involved in trading, as well as how the markets themselves are structured, focusing on options in particular.

In the next article I will discuss the basic assumptions of option prices and the most common methodologies for pricing them, then discuss some of the consequences of those models.

We will also discuss some price behaviour, and talk about effective ways for using options. Hopefully this will provide some insights to how focused firms make so much money trading them.

1. A futures contract (future) is a simple type of derivative that allows you to buy or sell an asset today and take delivery of the asset at a future point in time. Futures differ from options in that entering into a futures contract obligates you to trade and so it functions in many ways like stock. I will not really discuss futures much in this article but a lot of the idiosyncratic nature of options contracts seems related to the fact that the first options exchanges were offshoots of futures exchanges. Please let me know if I am wrong about this.

2. This term does make sense, and you will understand it by the end of this series.

3. American options will always be at least as valuable as the European equivalent as you can always decide to hold the option to expiration. Thus, it is sometimes useful to price an option as if it were European purely to obtain a lower bound on the price.

4. My inner cynic also insists that the consequent erection of competitive barriers to entry plays a non-trivial role too.

5. I've tried a few times and have never been wholly satisfied - it is a concept that tends to mean different things in different contexts, but you can usually determine some measure that is close to what you are after.

6. If this surprises you, think about the expense in time and fees involved in the buying or selling of a house or piece of commercial property. It is not something you can do in a few minutes or even days, and the price is always prone to uncertainty. In contrast, you can trade a few billion USD or EUR in the currency markets in seconds or minutes without much problem.

7. There are stories of traders on the New York Stock Exchange in the 1800s carrying revolvers with them when they went to settle trades with counterparties. Similarly, in the early days of poker-playing in US a lot of players were armed to ensure they left the card-rooms with their winnings.

8. Of course, like all risk mitigation strategies, this means there is now a massive systemic risk of the clearing system failing. However were that to occur, it is likely you are now looking for a shotgun, a 4x4, and a stock of canned food, rather than worrying about those call options you bought.

9. Back in the days of floor trading, order sizes of 10 contracts or less were often met with a derisive "would you like a lollipop with that?"