Financial Engineering 101: What is an Option?

It's been a while since my first post. Since my last blog post I have moved to Tokyo for my summer internship, and this has been a source for many novel experiences. On a bright note, my current internship has given me some new insights on what is happening at the forefront of the financial industry, which I would like to contemplate on and share here.


Today I will discuss the "Option." It is the most basic and fundamental type of product in a class of financial instruments called "Derivatives." Personally, I would consider Robert Merton's 1973 paper deriving the Black-Scholes Equation on pricing derivatives to be the birth of financial engineering. As such, it is the central piece of any education in financial engineering.
While initially the method on how to "price" an option may seem of trivial importance, there is an enormous and extensive literature on how to accomplish this, many of which is covered in a financial engineering education. I will go into some depth on this in my later posts, but first lets go over the key concepts.

Basic Set-Up

An option (in finance) is, just like the name implies, an "option" to either buy or sell a stock at some pre-specified future date. This means that it's a contract that gives whoever is buying the option the right  - but not an obligation - to buy/sell the stock in the future. The two basic types are the call and put, with the call option being the right to buy and the put being the right to sell.

"Call Option" Contract

Example Problem

Forget the Black-Scholes and any other formulas for now - lets think logically how we should "price" this thing. Given that:

• Lets say we are buying a call option on a share of Apple one year from now. 
• Assume that Apple's share price right now is $92.
• The "strike" of the option is also $\$92 $. This means that the option gives us the right to buy Apple stock one year from now for $92. 
• Assume that somehow we know for certain that Apple's stock price one year from now will be $100. 
• Let's say that 1-year treasury rates are 10%.
• What is the most logical price for the Apple call option?

Solution: The No-Arbitrage-Pricing Concept

If we buy the Apple stock today and sell it at $\$100$ one year from now, we know for certain that we will make $\$8$ after one year. Thus from the concept of no-arbitrage-pricing, we would be given that the most logical price for the Apple call option should be the present value of $\$8 $. This is because if we buy the option at $\$8$ and exercise our right to buy the AAPL at $\$92$ one year from now and then sell it immediately for $\$100 $, we would neither make nor lose any money.

\begin{align} \text{Price of this Call} = \frac{8}{1+0.1} \end{align}

Note how the price of the option is dependent on a couple of things. Once we knew the price of the stock for the relevant times - as well as the risk-free interest rate - we were able to find out what the price for the option should be. This is why we say that options are derivative instruments. A derivative (conceptually) doesn't contain any new market information. It's price is (conceptually) solely dependent on the underlying asset, which in this case is the Apple stock. (I say "conceptually" because in the real world, its not quite this simple).

Okay, I hope that the above example gives a good explanation on what an option is, and also an inkling on how we price such financial instruments through the no-arbitrage-pricing concept. Note the many difficulties that we would encounter though, if we didn't make the assumptions that we made. In particular, how do you know the price of the stock one year from now with 100% certainty? What if the treasury rates changed? What if Apple went bankrupt before one year? Yes...indeed these are very important questions that have been asked before.

Why Study Options?

But even before we go into the details of how we price options in real life, lets ask ourselves why we need options at all and why we are even interested in learning how to price them. So far, I can come up with a couple reasons why we want to study options:

1. Options are actually traded in large volumes on exchanges like the Chicago Board Options Exchange (CBOE) and the Chicago Mercantile Exchange (CME). Many traders make a living trading options on these exchanges, pocketing price discrepancies in the market. Therefore, from knowing this theory, you might actually be able to make some profit. Before you start trading options, you need to know the "correct price" so that you can determine whether the price on the market is too expensive or too cheap. 
2. Options can be attractive instruments to keep in portfolios to hedge against certain risks. Some companies and asset management funds will invest in options to protect their portfolios. 
3. The methods employed in pricing options can be transferred over to "price" different types of things. Real options are a tangential concept that stem from ordinary stock options. Such methods of modeling and valuing real options in the same way as stock options is beginning to change the way many companies are planning their businesses. Currently, only a select few companies at the forefront of new technologies have started employing these techniques in their businesses. Basically, it is the "cutting edge" technique for the valuation of companies in M&As, strategic decision making in consulting firms, etc. So if you want a job at a reputable consulting firm or an investment bank, I believe it to be possible that some knowledge on options will improve your chances on landing a gig!