## Real options binomial lattice model

- (PDF) Using Binomial Decision Trees to Solve Real-Option
- Real Options: Calculating the option to switch use using

The typical solution for this kind of issue involves the computation of replicating portfolios at each node that, of course, involves the concept of complete markets where the payoff of traded securities can replicate the behaviour of the underlying asset at different times.

## (PDF) Using Binomial Decision Trees to Solve Real-Option

The Company’s value, “regulated” by a red square node, is instead assessed taking the maximum value between the two outcomes of the two branches that were born in such node.

### Real Options: Calculating the option to switch use using

The binomial lattices involve several paths that conduct to the same outcome, and that reduces the number of nodes in the lattice. Unfortunately, a process that involves binomial lattices could be non-intuitive, especially for more complex investment decisions that involve real assets with many simultaneous options.

In most of the cases, a closed-form of mathematical solutions is not suitable for the calculation. Numerical processes, such as the Monte Carlo simulation or Variance Reduction Techniques, are implied instead. For a better understanding of a “real process”, we should discretise the stochastic models through, for example, binomial lattices. A binomial lattice is a probability tree with binary decision branches, where the underlying price (in our case the project value) can go up (by factor 𝑢) or down (by factor 𝑑).

However “Real Options” differ from “Financial Options”. The latter are simply traded securities. Their parameters rely on a stochastic process of the underlying price where only the market has the capability to affect it.

Node 6: the founder decides to run the Seed Round. If the market (pool of investors) approves his project, the fundraising will go well and the startup continues its life. In the opposite case, the investors will not back the company and so it fails.

Where 𝑝6 represents the probability to build an “Extremely Successful” Business 𝑝7 stands for the probability that includes all the risks affecting the founders that are in the process to build a “Successful” Business. 6 − 𝑝6 − 𝑝7 is the probability of failure.

An opportunity gets undertaken if market trends, industry movements and startup metrics run in the desired direction it gets discarded if the feeling about the future is not crystal clear or if it predicts unfavourable performance.

The model, assessing the probabilities, will automatically calculate the investment sought levels that you should be entitled to receive at each round and the post-money valuations as well.