Options are intriguing financial tools known for their unique convexity, which has both created and erased fortunes. Frequently, we encounter options through an academic perspective, where concepts from heat equations in physics are adapted to form the renowned Black-Scholes model and its associated formulas.

Yet, in the early days of trading these contracts, many pit traders possessed minimal expertise in partial differential equations (PDEs) or stochastic calculus. How did they navigate the intricacies of these derivatives using a blend of mathematical principles and gut instinct? This brief series aims to impart a practical understanding of options theory to you.

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Options 101: an options contract is an insurance

Definition: An options contract is the right, but not the obligation to buy/sell a given underlying asset at a set price with an expiration date.

The strike price is the price at which the owner of the option has the right to buy/sell. If we have a SPY call option with strike 350, this means that we have the right to buy SPY stock at 350. If the spot price of SPY < 350, the call option is not very useful as we would rather just buy the underlying directly. Here we say the option is out of the money (OTM).

Conversely, if SPY were trading at 400 today it is considered in the money (ITM). It would be great to own the 350 call here, as we can buy SPY stock 50 points cheaper than what the market is trading at, if we were to exercise our option.

For an analogy, an options contract can be thought of as a form of insurance. Just as the strike price is the trigger point for where an option’s usefulness comes into play, insurance contracts also have such triggers. Let us consider fire insurance. Every month, you pay an insurance company some premium so that in the event your home catches fire, they will pay out some compensation. This raises some interesting points:

• Is fire insurance more or less expensive given the probability of your house catching on fire? (Think about living in California vs. rainy Seattle)
• Is fire insurance more or less expensive given how varied the intensity of fires are in your community? (Think about places with flammable terrain, arsonists, thunderstorms, weather fluctuation, dry places, etc.)
• Is fire insurance more or less expensive depending on how much time is left on your contract? (Think 1 year of fire insurance coverage vs. 10 years)
• In order for an insurance company to issue fire insurance to its customers, how do they decide how much to charge you? Can this insurance premium change if new information comes to light? What is the worst thing that could happen to a company that issues fire insurance?
  

Let us consider these questions one by one:

• As an insurer, you would charge more for homes in areas with a higher chance of fires.
• If your home were in an area with a wide spread of fire intensity – wildfires, arsonists, weather, etc. an insurer would also charge you more.
• The more time you want to be covered for your insurance, the more expensive it’s going to be.
• An insurance company is a for-profit business. In order to make money, they have to charge more premium than the expected payout they have to make over time to customers whose homes do catch on fire. They may have to adjust the premiums as new information comes to light regarding the risk of their customers, and the worst thing that could happen would be if all their customers' homes simultaneously caught on fire.
  

Now let’s get back to options.

• The probability that an option expires ITM is called ‘moneyness' and for practicality, traders use the greek partial derivative delta to represent this probability. We’ll go more in detail later on, but for now understand that as a probability proxy, delta has magnitude between 0 and 1 and that calls have positive delta, while puts have negative delta.
  

• The most important value that goes into pricing options is its implied volatility. Just like the fire example, if there are a wider spectrum of outcomes (some very good, and some very bad), an option contract written for a volatile underlying is more expensive. Just like the seller of fire insurance, the writer (seller) of an options contract is going to price an option higher if the underlying is volatile.
  

• Imagine you own fire insurance on your home for 10 years and your house never catches on fire. For every day that passes, the capital outlay you pay in insurance premiums can be thought of as a form of decay. At time=0 days, all the money you paid the insurance company is wasted since your home never caught on fire. Options contracts have a similar decay that we call theta, which is the value your options loses as time passes.

• Dealers of options, just like bookies, businesses, currency exchange, etc. all have an incentive to buy low and sell high. An options marketmaker is no different. When we quote a two-sided bid/ask spread or market, we are offering other participants the optionality of transacting with us on either side. In order to sustainably profit from doing this, we have to charge enough edge on each side of what we deem fair value to combat the adverse selection of giving other people optionality.
  

In summary, an options contract is effectively a form of insurance coverage and as traders in the options market, we care deeply about option pricing and dynamics. There is a lot of math and technical knowledge in these topics beyond the scope of this primer (also rarely useful in practice to know how to derive), so instead we will highlight some useful intuition in the next installment.

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