About Trees Again

Whenever you build a quant innovation, I recommend to organize objects, models and methods orthogonally. Why? The right selection of  models and methods is vital, but not obvious.

Example: (binomial) trees are still used valuing "options". This can be a good or bad decision.

Trees may destroy delta-hedging

In To Tree or Not To Tree, Andreas Binder, CEO, of UnRisk 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 the heart of the option theory…delta hedging.

Are Trees good for real options?

Real options are referring to project size, life and timing, and operation. Those determine the option characteristics.

Real options are usually distinguished from financial options in that they, and their underlying, are typically not tradable. So, most real options have a value but not a price. At the other hand option holders 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 creating value through flexibility.

With this objective, insight is more important than computational quality.

To Tree!

You can model real options 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.

Real options help finding competitive game rules

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

You can buy antifragility.  In finance, antifragility needs fragility, because hedgers need speculators as counter party, who accept the fragile side of a contract. "Correct" and transparent 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. They're not a derivative. They're actual options. Walking through trees of decisions under uncertainty by simulation help finding competitive game rules you want to establish.


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 and can be replicated by hedge portfolios.

But this is another story. In such a regime. trees would be devalued as firewood again…

This is a compression of this post at UnRisk Insight