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Options Trading: The Untold Story
Part 3 - How Abusing Derivative Correlations Caused the 2008 GFC
This is the first of a three-part series. Today, you will build an intuitive understanding of options. To do so, we must travel back in time to the 600 B.C. Ancient Greeks...
The Origin Story of Options Trading
Once upon a time, there was a philosopher named Thales.
Thales was annoyed by people taunting him about the uselessness of philosophy. You see, Thales was poor, wholly devoted to philosophy, with zero desire to be rich.
However, his job as a philosopher was to cure the ignorance of these people. There was only one way to do this; to use philosophy to become rich. And so he birthed the option.
That winter, he placed a deposit to hire all of the olive-presses in two cities. He had speculated with his knowledge of astronomy that, when summer came, there would be a bountiful harvest of olives. Because no-one was the wiser, he only had to put down a meagre amount.
Sure enough, when summer came, there was a sudden demand for olive-presses. Not only did he successfully perform the first-recorded options trade (effectively buying a call option), he held a monopoly on these olive-presses. By cornering the market, he could rehire these olive-presses for whatever he liked, making Thales a very rich man.
So what, exactly, is an option?
The term ‘option’ is quite intuitive. To put simply, an option is simply the right, but not the obligation, to buy or sell a particular underlying asset for a particular price within a specified time period.
In Thale’s case, he had placed a deposit on all the olive-presses in Miletus and Chios for the summer, thus securing an option for their hire. He holds the right, but not the obligation, to hire out the olive-presses in the summer.
If the summer harvest was less than expected, Thales could choose to not hire the olive presses, thereby losing only the initial amount, his deposit - this is called the option premium.
On the flip side, if the summer harvest was very bountiful, Thales could choose to hire out all the olive presses at an agreed upon price - this is called the strike price. In this way, he stood to profit greatly by risking only a fraction of the money.
The Universe of Option Contracts
In Aristotle’s account (yes, it’s a real story), Thales had purchased what’s known as a call option. A call option gives one the right to buy an underlying asset in the future for a particular price. Even if olive presses in the summer now cost 10 silver coins to rent, Thales’ call option allows him to rent them per the original agreement for just 1 silver coin!
Conversely, a put option gives on the right to sell an underlying asset in the future at a particular price. Suppose you don’t believe in $DOGECOIN as it is grounded in degenerate speculation. So you decide to buy a put option on it for $1 one year from now. Now suppose that in a year’s time Dogecoin has crashed to just one cent, you are still able to sell it at $1.
While there are many types of exotic options out there such as knockout or barrier options, we will focus our attention to two in particular. American call or put options allow you to exercise your contract at any time up until the expiry date. On the other hand, European call or put options allow you to exercise your contract only on the expiry date.
Sometimes options are referred to as ‘derivatives’, as they derive value from some underlying asset. Derivatives is an umbrella term including not just options, but the beautiful world of futures, swaps, swaptions, convertible bonds, and other exotic contracts.
To recap, all option contracts must include the following three features:
Time of expiry
In addition, there are three other features one must understand before entering a position:
Type of contract - American, European, or some other exotic option
Cash vs physical settled
Most options contracts have a 100 multiplier, meaning that 1 call option contains the right to buy 100 shares of underlying stock. There are exceptions to this rule of course, including cryptocurrency options with multipliers of 1 and crude oil options with multipliers of 1000.
Another facet to be clear about is whether the option is cash or physical settled. Suppose you bought a $100-striked call option on oil, and today is the expiry date. The price of oil is currently $120. You stand to make $20,000 off this contract if we assume there to be a 1000 multiplier.
The difference between cash vs physical settled options is that upon exercising, you obtain a cash payment of the profit vs physical barrels of oil. While the difference may seem subtle, crude oil reached negative prices because people could not physically settle their contracts.
Our discussion of options contracts reveals a variety of different ways to structure it. In order to build an intuition in pricing options, let us consider the following example. Please take a moment to think independently before reading on.
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Suppose the land you bought contains oil. If you purchase the land for $300K, you stand to profit $700K. Similarly if the land contains coal, you stand to profit $200K.
However in the instance the land contains nothing, you don’t want to exercise your option contract. Afterall, why would you pay $300K for land valued at $200K? Unless you are irrational of course. This makes your option worthless.
This is a great opportunity to introduce the concept of “moneyness”.
If the option is currently useless, then it is called “out of the money” (OTM) - such as holding your option when the land contains nothing. Conversely, an option that is currently useful is called “in the money” (ITM) - such as our land option when the land contains oil.
A call option is ITM when the stock price is greater than the strike price. Similarly, a call option is OTM when the stock price is less than the strike price. The opposite holds true for puts. Lastly, if the strike price is roughly equal to the stock price, then the option is “at the money” (ATM).
Taking the expected value of the above figures, it gives us an option value of $130K. (The mathematical equation is 10% * $700K + 30% * $200K + 60% * 0 = $130K)
The Three Musketeers of an Option’s Price
There is a huge misnomer among casual finance forums, that a call option is simply a bet on the stock moving upwards. Yes, it is certainly possible for you to lose money on a call option, even if the stock moves up!
This is because there are three components to an option’s price! In addition to the stock price, there are also two other elements - volatility and the cost of carry.
Volatility can be loosely defined as the expected fluctuation of a market. There are parallels to it being a gauge for fear, as we typically see elevated volatility levels in market crashes.
Cost of carry can be thought of as the cost you incur in holding the underlying asset. It is usually represented as the interest rate minus the dividend payments you receive. Interest rates are present here because holding any asset incurs an opportunity cost.
The easiest way to visualise the relationship between option prices and these three components is through the Put-Call Parity. This relationship between puts and calls is rooted in the idea of zero arbitrage.
(An arbitrage is a situation where it is possible to exploit mispricings in a risk-free manner - imaging if you could buy an apple for $1 and then sell it back at $2, instantly.)
A rough construction of the proof is worth going over, as it helps build basic understanding.
Put-Call Parity and Payoff Diagrams
Imagine constructing two portfolios, each with the same payoff structure.
The payoff function for an option is its value at expiry - this is important as option values change with increasing time to expiry. We can visualise the payoff for a (long) call below. Recall that a call is worthless if it is OTM (stock value < strike value). Only when it is ITM, does the option linearly increase in value with the stock price.
If you are stuck, imagine a $30-strike call option. What is the option’s value at expiry if the stock is worth $29? How about $30? Or $31?
A similar argument can be made to construct a (long) put payoff diagram. Take time to think this through, and digest this - it will become extremely important later on. Short positions can be thought of as taking the opposite bet. Graphically, this just involves flipping the payoff function about the x-axis.
Suppose now you want to take a long call and a short put position together. What would the resulting payoff structure be? Luckily all you have to do is graphically superimpose the payoff functions of a long call and a short put together.
The resulting payoff resembles a linear line, which is equivalent to that of long stock.
Here is the more mathematically involved part - I have handwaved some of the details.
Suppose we want to construct two portfolios with zero arbitrage opportunities. In portfolio 1, we can construct a long call (+C) and short put (-P). This will be equivalent to the price of the stock in the future at the date of expiry (F), less the option strike price in cash (K). Therefore in portfolio 2, we can effectively replicate portfolio 1 with some stock and cash.
As we are considering payoffs that are happening sometime in the future, we must discount (D) it back to the present. Don’t worry if this part is confusing.
With some hand waving, we obtain one of the most important relationships for option traders. The Put-Call Parity not only expresses the price of a call to the three price components, but it also allows one to quickly infer the price of other option structures.
You might notice the price of a put as the volatility component. This is because all options are effectively a form of insurance, or a bet on volatility - more on this in pt2.
To recap, the three components in all options pricing is:
Cost of carry (the present value of interest less dividends)
To tie this all together, let us consider buying $TSLA call to bet on earnings. Before earnings stock options typically have elevated volatility, as it is a catalyst for a potential move - this is called earnings volatility.
When earning results are released, volatility typically gets crushed as there is now no more uncertainty. If $TSLA ends up trading flat after the earnings report, the drop in volatility results will still cause the price of our call option to plummet.
Always remember to be considering not just the price of the stock, but also the volatility of the option. Usually the cost of carry is negligible, unless there are dividend considerations, or the threat of a potential short squeeze.
We will pick up next week with the famous Black Scholes paper that was the first to price options reasonably accurately. Of course, there are flaws with it, that were unsurprisingly abused, leading to traders getting wiped out in the 1987 Black Monday.
Part 2 (click here) will discuss some of the strategies behind options trading, and the legendary rise of the unknown options juggernaut, Susquehanna International Group.
Quantitative Finance Quiz
Every week, I will post a real question asked in real Wall Street interviews. These are great for improving your critical thinking ability, regardless if you are into quantitative finance.
Click on the Tweet to submit your answer, and for solutions the following week.