To Tree is The Answer, Provided …..

you want to perform a valuation of certain real options.

Trees may destroy delta-hedging

In To Tree or Not To Tree, Andreas has pointed out that binomial trees are good, because they are  insightful, but they have a really bad computational behavior. So bad, that they may destroy delta-hedging (the heart of the option theory), when applied to the analytics of options of more complexity.

Real options are different

A real option is the right to perform certain business initiatives in a capital investment project. There are real options referring to project size (expand or contract), life and timing (defer, abandon, sequence or parallelize), and operation (product or process flexibility). Those determine the option characteristics.

Real options are usually distinguished from financial options in that they, and their underlying, are typically not tradable. Most real options have a value but not a price. At the other hand option holders (management) can influence the underlying project.

Whilst financial options can help optimizing the risk of a portfolio, real options can help maximizing the value of a project by managing uncertainty and create value through flexibility.

Real option valuation

Real options can be the underlying principle of agile practices. With this objective insight is more important than computational quality. In real option valuation you have to deal with a co-evolution.  You need to take in account the uncertain development of the parameters that determine the value of your project and the management of decisions that influence them.

So, in general real options, are more complex than financial options. Consequently, they are more challenging in valuing inputs (factors) and define the option characteristics.

To Tree

You can model them by PDEs, apply forward techniques with (Least Square) Monte Carlo methods, but, most of the practitioners use binomial trees as they allow for implementing rules (up and down probabilities under conditions, ..) at each node. Although, they cannot handle problems with higher dimension.

Real option analytics as sparring partner

One can see investment projects as cash conversion cycle - with many decision points. Real option analytics can be a kind of sparring partner, telling the management, what if ...

The return is characterized by the investment, time and the distribution of the cash flows. You need to know the cash drivers, volatilities, formulate possible actions (their options) and know their influences on the cash flows.

If your project is innovative you don't have a history. So, you might need to simulate the project to get insight into quantitative aspects of possible decisions. Trees are of good nature for this purpose, right?


You can buy antifragility.  In finance, antifragility needs fragility, because hedgers need speculators as counter party, who accept the fragile side of a contract.  The difficult thing about this is transparency: who has what fragile/antifragile position and how do those positions cross-connect to fragility concentration or fragility diffusion and buffering. "Correct" pricing, valuation and risk analytics is vital to make the market a "fair" play.

Real options usually pertain to tangible assets such as capital equipment, rather than financial instruments. They are not a derivative instrument, but an actual option - that have a value and you gain from knowing which and when. In a tree of possible decisions in an uncertain world. If you compare this to a traditional Discounted Cashflow Method, you cannot lose ...


the real economy could learn from the innovations of the financial systems. They could maybe adopt the "fiction" that the option and the underlying are tradable, or "replicate" the cash flows on the option by a risk free bond and proportions of the underlying?

But this is another story. Trees would be devalued as firewood again?

I am not a RO expert, so I have compiled info from Wikipedia and long discussions with Hermann Fuchs, a RO expert, running a financial controlling advisory firm here. But, I understand that we offer attractive options for a build-an-advanced-risk-management-system project.