Mean-Reverting Process in Real Option Valuation

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What does the mean reversion of asset price have to do with options pricing? We have explored this topic previously for financial options. However, the mean-reverting property of an asset affects not only the values of financial options but also real options.

A real option is the right – but not the obligation – to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, real options valuation could examine the opportunity to invest in the expansion of a firm’s factory and the alternative option to sell the factory. The real option valuation framework is a relatively new method of investment valuation. In its beginnings, the method was used for projects in the energy industry and capital budgeting decisions involving oil refineries. Recently, however, the application of real-options analysis has been extended to cover other types of investments as well.  Although the real-options valuation method has clear benefits to companies, it is important to note that, like any model, it is based on certain assumptions. One of the most important assumptions is the asset dynamics: mean-reverting (MR) or Geometric Brownian Motion (GBM).

Reference [1] explored how the mean-reverting process affects the prices of real options.

This paper compares the investment decision of an option to build a gas-fired power plant using a geometric Brownian motion and a mean reverting process as stochastic process. The option setting has stochastic costs and will be solved using a Least-Squares Monte Carlo Simulation. The results show that a mean-reverting model results in higher optimal threshold prices compared with a geometric Brownian motion. The difference between the investment decision is relatively small for small maturities, however, as maturity increases the difference in the investment decision becomes very significant. Therefore, it can be concluded that neglecting mean-reverting characteristics could lead to overly conservative investment decisions.

The paper concluded,

Consistent with existing literature, the volatility of the mean-reverting model was substantially lower compared with the GBM that had important implications for the investment decision. .. For the designed real option setting, the MR model resulted in significantly lower option values than with the geometric Brownian motion. Consequently, the threshold price of the MR model was significantly higher than with the GBM, implying that with the MR model the investment would optimally be undertaken earlier. The difference between the threshold price from both models differs over time. When the maturity of the option is small(<3 months), the threshold prices of the models are relatively similar and also close to the threshold price of the NPV approach. As the maturity of the option increases, the threshold price of the GBM decreases much faster than the threshold price of the MR model.

Mean reversion is a process that affects not only prices of financial options, but also prices of real options. By understanding and considering the effects of mean reversion in the analysis of your real options, you can make more informed capital budgeting decisions for your business.

References

[1] C. Dik, Real Option Valuation – The Implication of Mean Reversion on The Investment Decision, University of Groningen.

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