Long before I worked on distributed systems, I spent my summers in college working at an options trading desk in Chicago. I ran different models, proposed different strategies, and sent down different reports to the traders on the floor of the S&P 500 trading pit. These traders used pricing models like Black-Scholes or Binomial Options Pricing Model to find arbitrage opportunities. It was a game of risk. But the lessons I learned on the trading floor had wider usefulness — a group of economists has applied options pricing models to real-world decision-making.

First, a crash course in options. In finance, an option is the right, but not the obligation to buy or sell a stock at a certain price until a certain date. It is a derivative of the underlying stock. There are theoretical models that value options. You can look up the partial differential equation that describes the Black-Scholes model, one of the most well-known models, but most traders just talk about "the Greeks".

The Greeks are the different variables that go into options pricing, named after the Greek symbols used in the equation.

• Delta is the sensitivity to the option's theoretical value with respect to changes. in the underlying asset's price. It is the first derivative of the value of the option with respect to the underlying instrument's price. For example, if the stock goes up by \$1 and the delta is 5, the option's price will increase by \$5. Gamma is the second derivative, or how fast delta changes with underlying price changes.
• Vega is the sensitivity to volatility — how much the stock price fluctuates up or down in a given time.
• Theta is the sensitivity of the value to the derivative in the passage of time. Theoretical option values decay over time because options have an expiration date.
• Rho measures the sensitivity to the risk-free interest rate. Where else could you put your money?

But what does this have to do with the real world?

A real option is the right, but not the obligation to undertake a certain decision.

In business, real options are mostly applied to capital budgeting decisions — should the business invest in a new project, wait a year, or abandon an existing project? It incorporates flexibility into a classic net present value (NPV) decision-making process.

We're doing this in our heads all the time. When I was deciding to go to graduate school, I had real options that could be valued: stay at my job, start a company, or go back to school (I went).

While you can't necessarily use the pricing models to exactly determine the value of real-world options, you can still use it as a conceptual model. Here are some questions you can ask when confronted with a decision:

• Can you hedge your bet?
• What is the time value of the option? How long do I have to act?
• Is the option proprietary or able to be exercised by many people?
• How volatile are the hypothetical outcomes?
• Can the project be contracted out? (a "put" option)
• Can the project be abandoned?
• Can the project be delayed?
• How sensitive are the outcomes to changes in the market? How fast is the sensitivity changing (second derivative)?
• Can I sell the option to undertake the project?
• What is the risk-free alternative?
• Can the project be sequenced?