Five variables are used in calculating the value of real options using the BSOP model as follows:. The following three examples demonstrate how the BSOP model can be used to estimate the value of each of the three types of options.

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Supposing the company does not have to make the decision right now but can wait for two years before it needs to make the decision. The increase in value reflects the time before the decision has to be made and the volatility of the cash flows. Solution: The variables to be used in the BSOP model for the second follow-on project are as follows:. Conventional NPV would probably return a negative NPV for the second project and therefore the company would most likely not undertake the first project either.

However, there are four years to go before a decision on whether or not to undertake the second project needs to be made. A lot could happen to the cash flows given the high volatility rate, in that time. Present value of cash flows approx. It could be recommended that, if only these results are taken into consideration, the company should not proceed with the project.

This would suggest that Duck Co should undertake the project.

## Model risk in real option valuation | SpringerLink

Many of the limitations and assumptions discussed below stem from the fact that a model developed for financial products is used to assess flexibility and choice embedded within physical, long-term investments. The BSOP model is a simplification of the binomial model and it assumes that the real option is a European-style option, which can only be exercised on the date that the option expires.

An American-style option can be exercised at any time up to the expiry date. Most options, real or financial, would, in reality, be American-style options. In many cases the value of a European-style option and an equivalent American-style option would be largely the same, because unless the underlying asset on which the option is based is due to receive some income before the option expires, there is no benefit in exercising the option early. An option prior to expiry will have a time-value attached to it and this means that the value of an option prior to expiry will be greater than any intrinsic value the option may have, if it were exercised.

With real options, a similar situation may occur when the possible actions of competitors may make an exercise of an option before expiry the better decision. In these situations the American-style option will have a value greater than the equivalent European-style option.

Because of these reasons, the BSOP model will either underestimate the value of an option or give a value close to its true value. Nevertheless, estimating and adding the value of real options embedded within a project, to a net present value computation will give a more accurate assessment of the true value of the project and reduce the propensity of organisations to under-invest.

The BSOP model assumes that the volatility or risk of the underlying asset can be determined accurately and readily. Real options would probably be available on large, one-off projects, for which there would be little or no historical data available. Volatility in such situations would need to be estimated using simulations, such as the Monte-Carlo simulation model, with the need to ensure that the model is developed accurately and the data input used to generate the simulations reasonably reflects what is likely to happen in practice.

### Module summary

The BSOP model requires further assumptions to be made involving the variables used in the model, the primary ones being:. In any given situation, one or more of these assumptions may not apply. This article discussed how real options thinking can add to investment appraisal decisions and in particular NPV estimations by considering the value which can be attached to flexibility which may be embedded within a project because of the choice managers may have when making investment decisions.

It then worked through computations of three real options situations, using the BSOP model. The article then considered the limitations of, and assumptions made when, applying the BSOP model to real options computations. The value computed can therefore be considered indicative rather than conclusive or correct. The second article will consider how managers can use real options to make strategic investment appraisal decisions. Written by a member of the Advanced Financial Management examining team.

Investment appraisal and real options. However, if the decision-maker has very high risk tolerance the opposite could occur, i. ROV might actually increase with project size, relative to inital wealth. We have found no previous investigation into these questions and how the answers relate to the structure of the investment costs.

Note that a similar effect can be present for CARA utilities: even though the exponential utility-based option value is independent of initial wealth, as previously noted in Sect. By contrast, in the right-hand Fig. As we move from a variable to a fixed cost structure the main difference is that larger investments are always ranked highest. In general, risk-neutral decision makers attribute higher ranks to larger investments; risk-averse decision makers also tend to prefer larger fixed-strike investments; but when an investment is at market price, smaller investments are ranked more highly even by investors with very low values risk-aversion.

Slade introduces a model with three state variables—price, cost, and reserves, finding that the dynamic models that are selected for these processes greatly affect the ROV. In particular, the option values associated with non-stationary processes are systematically larger than the comparable stationary values. However, with two notable exceptions discussed in more detail below all the real-options literature which examines the sensitivity of real options to assumptions made about the price process employs the risk-neutral paradigm.

## The real options approach to capital investment projects

This problem has been analysed in many previous papers, albeit within a particular real-world application where other basic assumptions are made—typically RNV. So we set our more general results, based on HARA utilities, in the context of this research. The question of model risk has not previously been analysed in this context.

Finally, in Sect. There is some previous literature on this extension, reviewed below, but all the papers that we can find are based on RNV.

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However, the ROV volatility sensitivity is quite different for the fixed-strike option, i. Similar, but less pronounced, effects are present with the logarithmic and other HARA utilities, as can be verified using the downloadable code. Many markets are subject to booms and recessions, or periodically collapsing bubbles. To name a few examples: the price of gold—which underpins associated mining projects—recently reached a peak in , since when it has been generally declining; surges in the price of the cryptocurrency Bitcoin have caused the value of projects based on Initial Coin offering ICOs to rise and fall over long periods during the last few years; and the real-estate market has experienced several booms and busts since the second world war.

However, for intermediate values of n the invest-at-market-price option often has a higher value than the fixed-strike option. Irrespective of cost structure, in this example the preferred investments are those for which boom and bust periods are of roughly equal length.

Increasing the speed of mean-reversion has a similar effect to decreasing volatility.

vandefubackme.tk All other parameter values are the same as in Fig. For each utility we highlight the preferred project in bold. However, once we relax the risk-neutral assumption the ranking of these two investment opportunities may change, depending on the utility of the decision maker. In each case the greater option value is depicted in bold. In all other cases the decision maker would prefer project A. The value of an investment real option is the net present value that, if received with certainty, would give a risk-averse decision maker the same utility value as the expected utility of the uncertain investment.

Such values enable the decision maker to rank opportunities to invest in alternative projects and the process of valuing the option also specifies an optimal time to exercise. The minimum value of zero applies when the project would not be attractive whatever its future value. The special case of RNV, while most commonly employed in the literature, only applies to a real option that is tradable on a secondary market. Therefore, we introduce a general methodology with applications to a wide range of private investment or divestment decisions where project risks are based on a source of uncertainty which cannot be hedged.

It permits risk-averse private companies, publicly-funded entities, or individuals to compute a real option value that is completely tailored to the decision maker, based on a very flexible risk preference model HARA , where views on the dynamics of the project price process can take several forms and with investment costs that have both fixed and variable components. In this paradigm, ROVs can be very different from the risk-neutral price obtained under the standard but typically invalid assumption of perfectly-hedgeable risks.

Likewise, publicly-funded entities may have objectives that are far removed from wealth maximisation under risk-neutrality. The real option price that is obtained using standard RNV assumptions can be very much greater than or less than the value that would be found using a more realistic assumptions about investment costs in an incomplete market, and very often the RNV approach would specify a later investment time. The assumption about the investment cost, whether it is pre-determined or stochastic, has a significant influence on the real option value.

The pre-determined-strike assumption can significantly over-estimate the value of a real option when the more-appropriate assumption is that the investment cost is positively related to the market price, or has both a fixed and variable components. Fixed-strike options may be more realistic for a decision maker having significant market power, who can use this power to influence the investment cost in her favour. Intuitively, real options can be more valuable for those decision makers—less powerful decision makers have to bear more uncertainty in investment costs.

It is important to account for the flexibility of the decision-making process in real option analysis because the real option value increases with the frequency of decision opportunities.