Real Options – Path-Dependent, Path-Independent, Mutually Exclusive, Nonmutually Exclusive, and Complex Combinatorial Nested Options

Sequential Compound Options are path-dependent options, where one phase depends on the success of another, in contrast to path-independent options such as those solved using SLS. These options can be mutually exclusive or nonmutually exclusive. In all these types of options, there might be multiple underlying assets (e.g., Japan has a different risk-return or profitability-volatility profile from the United Kingdom or Australia). You can build multiple underlying asset lattices this way using the SLS, and combine them in many various ways depending on the options. Some examples of path-dependent versus path-independent and mutually exclusive versus nonmutually exclusive options follow:

  • Path-Independent and Mutually Exclusive Options: Use the SLS to solve these types of options by combining all the options into a single valuation lattice. Examples include the option to expand, contract, and expand. They are mutually exclusive if you cannot both expand into a different country while abandoning and selling the company. These are path independent if there are no restrictions on timing (i.e., you can expand, contract, and abandon at any time within the confines of the maturity period).
  • Path-Independent and Nonmutually Exclusive Options: Use the SLS to solve these types of options by running each of the options that are nonmutually exclusive one at a time in SLS. Examples include the option to expand your business into Japan, the United Kingdom, and Australia. These are not mutually exclusive if you can choose to expand to any combinations of countries (e.g., Japan only, Japan and the United Kingdom, United Kingdom and Australia, etc.). They are path independent if there are no restrictions on timing (i.e., you can expand to any country at any time within the maturity of the option). Add the individual option values to obtain the total option value for expansion.
  • Path-Dependent and Mutually Exclusive Options: Use the SLS software to solve these types of options by combining all the options into one valuation lattice. Examples include the option to expand into the three countries: Japan, the United Kingdom, and Australia. However, this time, the expansions are mutually exclusive and path dependent. That is, you can expand into only one country at a time, but at certain periods you can expand only into certain countries (e.g., Japan is optimal only in three years due to current economic conditions, export restrictions, etc., as compared to the United Kingdom expansion, which can be executed right now).
  • Path-Dependent and Nonmutually Exclusive Options: Use the SLS software to solve these. These are typically simple Sequential Compound Options with multiple  If more than one nonmutually exclusive option exists, rerun the SLS for each option. Examples include the ability to enter Japan from Years 0–3, Australia in Years 3–6, and the United Kingdom at any time between Years 0–10. Each entry strategy is not mutually exclusive if you can enter more than one country. The strategies and are path dependent as they are time dependent.
  • Nested Combinatorial Options: These are the most complicated options and can take a combination of any of the four types preceding types. In addition, the options are nested within one another in that the expansion into Japan must come only after Australia, and cannot be executed without heading to Australia first. In addition, Australia and the United Kingdom are okay, but you cannot expand to the United Kingdom and Japan (e.g., certain trade restrictions, antitrust issues, competitive considerations, strategic issues, restrictive agreements with alliances). For such options, draw all the scenarios on a strategy tree and use IF, AND, OR, and MAX statements in SLS to solve the option. That is, if you enter into the United Kingdom, that is it, but if you enter into Australia, you can still enter into Japan or the United Kingdom but not Japan and the United Kingdom.

 

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