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Using Black-Scholes in software engineering gives a rough lower bound

Derek Jones from The Shape of Code

In the financial world, a call option is a contract that gives the buyer the option (but not the obligation) to purchase an asset, at an agreed price, on an agreed date (from the other party to the contract).

If I think that the price of jelly beans is going to increase, and you disagree, then I might pay you a small amount of money for the right to buy a jar of jelly beans from you, in a month’s time, at today’s price. A month from now, if the price of Jelly beans has gone down, I buy a jar from whoever at the lower price, but if the price has gone up, you have to sell me a jar at the previously agreed price.

I’m in the money if the price of Jelly beans goes up, you are in the money if the price goes down (I paid you a premium for the right to purchase at what is known as the strike price).

Do you see any parallels with software development here?

Let’s say I have to rush to complete implementation some functionality by the end of the week. I might decide to forego complete testing, or following company coding practices, just to get the code out. At a later date I can decide to pay the time needed to correct my short-cuts; it is possible that the functionality is not used, so the rework is not needed.

This sounds like a call option (you might have thought of technical debt, which is, technically, the incorrect common usage term). I am both the buyer and seller of the contract. As the seller of the call option I received the premium of saved time, and the buyer pays a premium via the potential for things going wrong. Sometime later the seller might pay the price of sorting out the code.

A put option involves the right to sell (rather than buy).

In the financial world, speculators are interested in the optimal pricing of options, i.e., what should the premium, strike price and expiry date be for an asset having a given price volatility?

The Black-Scholes equation answers this question (and won its creators a Nobel prize).

Over the years, various people have noticed similarities between financial options thinking, and various software development activities. In fact people have noticed these similarities in a wide range of engineering activities, not just computing.

The term real options is used for options thinking outside of the financial world. The difference in terminology is important, because financial and engineering assets can have very different characteristics, e.g., financial assets are traded, while many engineering assets are sunk costs (such as drilling a hole in the ground).

I have been regularly encountering uses of the Black-Scholes equation, in my trawl through papers on the economics of software engineering (in some cases a whole PhD thesis). In most cases, the authors have clearly failed to appreciate that certain preconditions need to be met, before the Black-Scholes equation can be applied.

I now treat use of the Black-Scholes equation, in a software engineering paper, as reasonable cause for instant deletion of the pdf.

If you meet somebody talking about the use of Black-Scholes in software engineering, what questions should you ask them to find out whether they are just sprouting techno-babble?

  • American options are a better fit for software engineering problems; why are you using Black-Scholes? An American option allows the option to be exercised at any time up to the expiry date, while a European option can only be exercised on the expiry date. The Black-Scholes equation is a solution for European options (no optimal solution for American options is known). A sensible answer is that use of Black-Scholes provides a rough estimate of the lower bound of the asset value. If they don’t know the difference between American/European options, well…
  • Partially written source code is not a tradable asset; why are you using Black-Scholes? An assumption made in the derivation of the Black-Scholes equation is that the underlying assets are freely tradable, i.e., people can buy/sell them at will. Creating source code is a sunk cost, who would want to buy code that is not working? A sensible answer may be that use of Black-Scholes provides a rough estimate of the lower bound of the asset value (you can debate this point). If they don’t know about the tradable asset requirement, well…
  • How did you estimate the risk adjusted discount rate? Options involve balancing risks and getting values out of the Black-Scholes equation requires plugging in values for risk. Possible answers might include the terms replicating portfolio and marketed asset disclaimer (MAD). If they don’t know about risk adjusted discount rates, well…

If you want to learn more about real options: “Investment under uncertainty” by Dixit and Pindyck, is a great read if you understand differential equations, while “Real options” by Copeland and Antikarov contains plenty of hand holding (and you don’t need to know about differential equations).

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Altruistic innovation and the study of software economics

Derek Jones from The Shape of Code

Recently, I have been reading rather a lot of papers that are ostensibly about the economics of markets where applications, licensed under an open source license, are readily available. I say ostensibly, because the authors have some very odd ideas about the activities of those involved in the production of open source.

Perhaps I am overly cynical, but I don’t think altruism is the primary motivation for developers writing open source. Yes, there is an altruistic component, but I would list enjoyment as the primary driver; developers enjoy solving problems that involve the production of software. On the commercial side, companies are involved with open source because of naked self-interest, e.g., commoditizing software that complements their products.

It may surprise you to learn that academic papers, written by economists, tend to be knee-deep in differential equations. As a physics/electronics undergraduate I got to spend lots of time studying various differential equations (each relating to some aspect of the workings of the Universe). Since graduating, I have rarely encountered them; that is, until I started reading economics papers (or at least trying to).

Using differential equations to model problems in economics sounds like a good idea, after all they have been used to do a really good job of modeling how the universe works. But the universe is governed by a few simple principles (or at least the bit we have access to is), and there is lots of experimental data about its behavior. Economic issues don’t appear to be governed by a few simple principles, and there is relatively little experimental data available.

Writing down a differential equation is easy, figuring out an analytic solution can be extremely difficult; the Navier-Stokes equations were written down 200-years ago, and we are still awaiting a general solution (solutions for a variety of special cases are known).

To keep their differential equations solvable, economists make lots of simplifying assumptions. Having obtained a solution to their equations, there is little or no evidence to compare it against. I cannot speak for economics in general, but those working on the economics of software are completely disconnected from reality.

What factors, other than altruism, do academic economists think are of major importance in open source? No, not constantly reinventing the wheel-barrow, but constantly innovating. Of course, everybody likes to think they are doing something new, but in practice it has probably been done before. Innovation is part of the business zeitgeist and academic economists are claiming to see it everywhere (and it does exist in their differential equations).

The economics of Linux vs. Microsoft Windows is a common comparison, i.e., open vs. close source; I have not seen any mention of other open source operating systems. How might an economic analysis of different open source operating systems be framed? How about: “An economic analysis of the relative enjoyment derived from writing an operating system, Linux vs BSD”? Or the joy of writing an editor, which must be lots of fun, given how many have text editors are available.

I have added the topics, altruism and innovation to my list of indicators of poor quality, used to judge whether its worth spending more than 10 seconds reading a paper.