*“[Certainty can] seem like a good idea, but actually lead us into trouble… The story here revolved primarily around the stochastic nature of product development… Succeeding in product development requires the discovery and exploitation of options where there is an asymmetry to the payoff function.” […]*

Editor’s Commentary:

I had stumbled on this page a while ago, but lost the link. For some reason, this post stood out to me as an elegant graphical example of applied expected measure theory. The intuitions which resulted in Black-Scholes’ and Merton’s methods for finding a “not wrong” price are thus: an unconditional expectation is the entire range of possible outcomes; a conditional expectation is a more limited range of outcomes (e.g., given an event has occurred; bounded over an interval, etc…)

I find the broad implications of measure theory morally appealing. For example, the striking parallels between many natural and probabilistic phenomena: the likelihood of any given event is inversely proportional to its magnitude. Because of close linkages between reality and uncertainty, the closest thing to unified field of inquiry into stochastic phenomena is known as “real analysis”.

However, I also think it’s important to realize the limitations of models in which actual outcomes and their corresponding probabilities can never be known a priori. Thus, it is likely that real options analysis has failed to become a standard business tool because real-world pay-off conditions are usually ill-defined. I.e., there is no “risk-neutral measure” which defines the “correct” distribution in most situations.

Bridging this divide between real options analysis and the standard tools of capital budgeting (i.e., discounted cash flow analyses) will likely require the development and/or re-discovery of different mathematical constructs than those which currently fall under the canonical umbrella.

Blog Post Source: Black Swan Farming. *Product Development Payoff Asymmetry*. Black Swan Farming. 16 Sep 2014. Original content accessible: http://blackswanfarming.com/product-development-payoff-asymmetry/

*Updates to the Read List are meant to keep readers informed of stories and analytical highlights from third party sources that I find particularly relevant and worth sharing. Content that was recommended prior to 2017 is accessible through the Read List Archives*.

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