Theoretical Prediction of the Real Options Pricing Model

Introduction 

For each decision that a company makes concerning investment, it usually revolves around the capital project worth pursuing together with the time for performing it. The kind of flexibility attributed to investment decisions’ timing delivers value to a company, while the value is mostly understood as the real option value. Real options serve as vital elements within a macro economy while practicing them has attained considerable recognition in the theory literature revolving around corporate finance. Nonetheless, irrespective of the value accorded to real options, empirical proof on the micro-level concerning application performance is insufficient (Décaire, Gilje, & Taillard, 2018) . Here, it is vital to focus on direct proof attributed to the application performance of real options among companies while contracting with the behaviors that theory applies.

Characterizing how companies practice real options pose empirical problems. Firstly, it is not possible to come across comprehensive data when it comes to scheduling the flexibility attributed to capital projects. Secondly, to facilitate in characterizing how firms practice real options fully, it is essential to gather data related to the different projects that a company anticipates pursuing. These should comprise of the projects it opts to perform together with the ones it disregards. This from of visibility is usually inaccessible. Thirdly, having the capacity for noting the major inputs that would lead to performing decisions is crucial. This facilitates in contradicting the forecasted behavior from the real one. The major inputs in this case comprise of cash flows from anticipated initiatives and the task cash flows’ instability. Lastly, issues emerge when it comes to recognizing the forces that contribute to a company altering its real options’ behavior in a plausible manner (Décaire, Gilje, & Taillard, 2018) . For this paper, therefore, it discusses empirical work that has been done, which tests the prediction of the real options pricing model while confirming the theoretical findings.

Real Options Pricing Model 

The decision for delaying drilling while emphasizing on an assessment to invest in well based on evidenced reserves might be regarded as an owner possessing an American call opportunity on the evidenced reserves. One major approaches created for option-pricing models entails the utilization of reproducing portfolios. The key argument regarding the method is forthright (Décaire, Gilje, & Taillard, 2018) . If individuals were capable of developing portfolios that can duplicate options’ payoffs always, the option and the portfolio would fetch similar value based on arbitrage.

The decision by an organization for infilling drill matches with the need for advancing the evidenced reserves for natural gas further in a particular area. Two major ways prevail for duplicating an asset. The first approach entails developing evidenced developed segment while the other is via a non-developing evidenced developed segment. The overall return realized on the reserves created for the purposes of producing are possible to decompose into two key elements. The first one relates to profits attained from manufacturing γ unit (the total for the matching depletion) while the second one revolves around capital gains realized by holding the outstanding reserves (Décaire, Gilje, & Taillard, 2018) . In this vein, it becomes evident that with the extracted resource’s value being higher as opposed to the one on the ground, the anticipated returns on the reserves meant for production purposes is higher, unlike the case of the non-producing reserves’ anticipated returns.

In the event that different assets attain an equilibrium state, the anticipated return from the producing reserve, which has been proved (μP) need to serve as equal to the threat that it poses. In this sense, the anticipated non-producing reserve, which has been proved (μ) needs to fetch a lower value as opposed to the case of μP. Nevertheless, studies reveal that the replication approach while having an asset whose earnings are less than the returns realized at equilibrium are wasteful. As such, it is crucial to refrain from utilizing them when pricing the option. In the event of the equilibrium state, utilizing an asset capable of earning returns while at the equilibrium serves as the ideal replicating approach. This is usually the producing evidenced reserve. In this vein, it is probable to reveal that the appropriate pricing normally matches with a call option’s value on the primary asset (Décaire, Gilje, & Taillard, 2018) . This is particularly the case when stream is divided while matching with the production of oil from proved reserves that do not accumulate to the holder of the option.

When considering real options pricing model, it is crucial to have understanding of the optimal moment for creating the proved reserves. The ideal time for performing a real option resembles the best time for practicing a stock option while it revolves around the principal asset. In the event that the natural resource that remained on the ground fetched more value as opposed to the case of the extracted resource, the principle asset associated with the repeating portfolio would serves as the non-producing evidenced reserve while the actual option would match with the call option of America on paying stock that does not feature dividends. Here, the stock would serve as the non-producing evidenced reserves (Smith, Matthews, & Driver, 2017) . In this sense, it is understood that performing an early option is not optimal.

Nevertheless, it is essential to realize that since extracted natural assets fetch increased value as opposed to the ones that remain in the ground, the dominant resources utilized for the purposes of replication emerge as the producing evidenced reserves. The manufacturing that originated from the resource matches with dividends, which the holder of the option relinquishes by failing to perform the option. In this perspective, the primary assets matches with a stock that pays dividends while a compromise emerges between the charges for relinquishing the present revenues associated with the extracted natural assets. This is due to the delay that prevails when performing the option and the advantages of waiting for the primary asset to fetch greater prices. The tradeoff prevailing between failures to perform (continuation) and performing (hindering) might result to an ideal stopping time before realizing maturity (Smith, Matthews, & Driver, 2017) . In the same manner as conventional financial options, in increased volatility of the key asset, waiting leads the options value to become great (delayed performance).

Methodology, Data, and Results 

An amazing feature of the study revolves around the capacity for acquiring the distinct inputs required for computing the decision model for the real option in the case of companies adopting the typical real option structure. The vital elements worth considering for the data comprise of cash flows, costs of drilling, prices of natural gas, and the indirect volatility of natural gas. The background for the investigation is shale development at Arkoma Woodford (Décaire, Gilje, & Taillard, 2018) . This serves as an institutional setting that has the different required resources prevalent during the period of the study between 2005and 2015.

In acquiring information regarding what every well cost, Oklahoma Corporation Commission avails the information. All companies that initiate the drilling of the initial well disclose this information. Other companies use the information having ownership stakes to guide them on whether to take part in well drilling. The costs of drilling normally fluctuate because of the demand and supply for completion and drilling services. These also differ across geography and operators within the shale basin during certain periods. However, they vary considerably as additional time passes (Décaire, Gilje, & Taillard, 2018) . The data detailed in the investigation relates to 996 wells, which facilitates in approximating the costs of well infilling.

The wells’ cash flows revolve around prices, production, costs of loyalty, and the costs for operating lease. The comprehensive data on production was obtained a monthly basis for each well the sample. Overall, the data made 1,776,811 observations within a month. The data revolves around reports, which corporations make to regulatory institutions of states regarding production. The study also utilizes comprehensive data on a monthly basis to acquire information on the rate of depletion, which serves as a major area of focus on typical real option models. The prices of natural gas together with its implicit volatility are acquired from the data that Bloomberg offers concerning the futures contracts of the prices of natural gas. For the key specifications in the hazard model, the study uses a futures price of 18 months for natural gas while it revolves around natural gas’s implicit volatility. These are measured in the form of overall prices of gas together with their implicit volatility during the lifetime of a well. The operating costs for lease revolve around approximations acquired from 10-Ks. Approximates on loyalty revolve around percentages of royalty gathered from DrillingInfo. This was on 71,120 leases on gas and oil, which were signed in the shale basin of Arkoma Woodford (Smith, Matthews, & Driver, 2017) . When merged together, the Arkoma Woodford’s institutional setting makes it possible to calculate the different major inputs, which are essential when it comes to calculating “trigger value” together with the performed decisions as the typical real option frameworks forecasted.

The major hazard framework assessment revolve s around the development of panel data decision for performing infilling in drilling decision for wells. The observation segment within the panel revolves around the idea of option-mouth framework. Overall, there exist approximately 54,208 open-mouths before the performance of the sample. For every observation of open-mouth, the study incorporates futures price of natural of natural gas, which is acquired from Bloomberg. It also avails information regarding natural gas’s implicit volatility of 18 months. For the two variables, they offer clear forecast on ways in which they would influence performance depending on typical decisional framework. Here, volatility correlates in a negative manner with performance whereas the prices of natural gas relate positively. In addition, the study includes information pertaining to the nominal interest rates during the development of the panel. To substitute for the total reserve’s quality, which the drilling option depends on, the study incorporate the production of the initial well during the first year (Décaire, Gilje, & Taillard, 2018) . This serves as a variable that facilitates explanation since the initial well is the first before practicing the infill decision.

The major event utilized in determining the performance of the option revolves around the infill well’s “spud date.” This refers to a date through which capital spending on drilling commences while the subsequent well’s drilling starts (Décaire, Gilje, & Taillard, 2018) . Since an option is available for practicing with the drilling of the initial well, the option’s number prevalent during a sample period differs with time.

Confirming Theoretical Findings 

Concerning the study, it focuses on an environment that provides individuals with the opportunity of realizing tremendous progress for the distinct challenges realized. The study assesses approximately $31.6 billion worth of capital project revolving around performed and non-performed investments in wells of natural gas in a key sector for developing shale in North America. The organizational state of the environment makes it possible to realize optimal visibility concerning timing flexibility in which companies have when deciding on drilling. Generally, it is possible to identify the actual dates companies opt to practice their actual options (drilling wells), together with the duration that they would take in the event that they opted to wait prior to commencing drilling. Secondly, owing to the lease’s organizational structure regarding the contract terms, it is possible to recognize non-performed options during any period. Thirdly, since natural gas’s price serves as the major influencer of the cash flow of the project, it serves as an element whose implicit volatility and anticipated price it possible to observe from financial derivatives. As such, the study institutes the needed approximation to the optimal time for stopping, which is the performance time (Décaire, Gilje, & Taillard, 2018) . Lastly, it is probable to leverage on organizational characteristics to acquire exogenous variation in the forces that might influence the time for performing the options.

The decision for drilling the prevailing reserves for natural gas might serve as an option for regarding the primary asset by America. When emphasizing on the ideal time for performing the option, just as with stocks that pay dividends among American options, the organization should refrain from waiting to reach maturity in an effort to perform the option. The reason for this is that natural gas generation from reserves resembles the dividends that stocks pay, while a tradeoff prevails between benefits affiliated with probable optimal future prices as well as the opportunity cost that emanates because of deferring incomes (Smith, Matthews, & Driver, 2017) . The traditional derivations attributed to ideal stopping time realize a rule that can facilitate in the computation of the rigger value in such a manner that in the event that the existing asset surpasses the trigger value, it becomes ideal to perform the option.

From the findings, it becomes apparent that whereas aspects of performing investment decisions rhyme with the theory of real options, the performance behavior that companies portray shifts from the typical one that real option frameworks support in economic and systematic ways. For instance, it becomes evident that the propensity for performing an option relies on the subjectivity of the prices of natural gas, based on what theory forecasts. Nevertheless, systematic proof prevails whereby organizations perform their options at significantly early periods, which leads them to miss considerable value of their options. The value that the options deliver revolves around the capacity for delaying investments. This leads the process of performing the options to become costly since this entails losing the waiting requirement for an option. As such, the chances of realizing increased prices of natural gas are foregone during the future (Décaire, Gilje, & Taillard, 2018) . Generally, companies usually focus on performing their options at values that are less than the ideal “trigger point.”

In quantifying the vital role that the derivations play, various inputs are utilized in data to facilitate in solving the trigger values that companies would require to calculate in the event that they utilized typical actual options models. It is realized that companies perform averagely in the event that the net present value (NPV) of a project is 52 percent less the trigger value. In particular, organizations usually perform at a time when the NPV of a project is approximately $1.25 million. This serves as the time through which the value attributed to holding an option would be worth around $2.60 million. A sensitivity analysis is carried out on the parameters of the input, which leads to the realization that several parameters linked to option value are inevitable while they fluctuate from between 35.5 percent and 76.2 percent (Décaire, Gilje, & Taillard, 2018) . The significant value of an option rhymes with the extended time for maturity. When it comes to natural gas’s considerable volatile state, two forces would lead to a rise in the value of option holding. Corporations usually perform projects upon realizing that a project’s IRR (internal rate of return) has attained 18 percent, irrespective of the option theory arguing that organizations should consider waiting. Averagely, for samples of projects that companies practices, corporations usually wait for a period of about 22.3 months prior to performing. This is irrespective of having the capacity for waiting up to a period of approximately 240 months (Smith, Matthews, & Driver, 2017) . Existing knowledge suggests that this is the initial empirical quantification on a macro level on the value distinctions between real performance behavior and the performance behavior, which the typical actual option frameworks portray in the absence of information externalities.

Questions prevail as to why companies commence performing their options early. The real option theories surrounding corporate finance offer solid forecasts regarding the reasons as to why companies might consider diverging from the forecasted practice of typical real option frameworks in the absence of information externalities or even frictions. Certain theories argue that companies might influence their individual investment timings because of performing the behaviors that their rivals portray. The decisions that organizations make in an effort to respond to rivalry has received major emphasis in finance and economics literature (Décaire, Gilje, & Taillard, 2018) . The theories are usually reliant on the critical role that information plays to influencing the decisions that companies make. As opposed to the case of financial options, real options feature vital externalities that relate to information. In this sense, it is crucial to direct emphasis on the evaluation of certain channels that relate with the information externalities while learning the manner in which companies invest to deal with the performance decisions by the competitors. The data utilized is granular to an extent that it can facilitate in the observation of key drilling units companies have together with the units surrounding their assets. All the units utilized in the sample are surrounded by an additional eight units offering considerable variations when it comes to exploiting. For instance, in case a company realizes that a rival is performing an option surrounding a drilling unit it possesses, the company gains new insight concerning its individual reserves’ quality. In this manner, it would end up claiming that its individual option has reached the trigger value. On the other hand, organizations might experience pressure when it comes to signaling to their supporters that their project’s quality resemble the ones of the rivals in the accompanying vicinity (Smith, Matthews, & Driver, 2017) . The prevailing conflict, which results to this form of practice, would revolve around agencies. The two prevailing conflicts offer theoretical backing for evaluating the important role that the activities of the rivals play in coercing companies to perform early.

For the design of the empirical findings in evaluating the reasons as to why companies perform at points below the trigger value, it undertakes a duration assessment while utilizing a hazard framework. The key goal behind utilizing the hazard empirical model revolves around the idea that it creates room for calculating ways in which distinct forces influence chances for performing an option as a given time. The data prevalent in the sample is ideal for this form of assessment since every option comprises of an ideal commencement point. In this case, it is possible to note instances through which an option is performed while comprehensive data prevails on ways through which covariates differ up to the performance time (Smith, Matthews, & Driver, 2017) . For this form of framework, it rhymes with others that have been utilized in devising the decisions for drilling.

By utilizing a duration analysis, it becomes possible to identify a number of traits of performing behavior in directional manner, which rhymes with the typical real options model. Generally, it becomes evident that a single standard deviation rise in the price volatility of the price of natural gas reduces the chances of performing an option by around 28.5 percent compared to the rate of hazard at the baseline. A rise in the prices of natural gas by $1 leads to an increase in the chances for performing an option by 11 percent because of the comparative rise in the NPV of a project when likened to trigger value (Décaire, Gilje, & Taillard, 2018) . Nonetheless, whereas the influences are consistent in a directional manner with the forecasts of the option theory, they fail to close the gap that exists at NPV levels, which is the area of performing the projects.

When assessing the role that the behavior of rivals has on performing an option directly, it becomes essential to determine whether the non-performed options neighboring the options that competitors perform have higher chances of exercising. Here, it becomes apparent that for every adjacent option that a rival performs, the chances of a company performing its individual drilling decision grows by around 29.8 percent (Décaire, Gilje, & Taillard, 2018) . Nonetheless, concerns prevail when utilizing direct approximation of the influence of utilizing the hazard framework, which revolves around a typical environment subject to time force. These might lead both an organization together with the rival to perform the options. Avoiding this endogeneity requires utilizing the remains of the activities of the rivals after controlling the geography and time effects (Smith, Matthews, & Driver, 2017) . Here, it becomes evident that utilizing the residual from the rival companies might lead to increased chances of performing the options. While it is not probable to assess the measure’s exogeneity directly, it exerts control of the key endogeneity issues, which reserve time influences and the quality of geography, which influence performing of an option.

For the empirical findings, overall, they add to literature in various perspectives. Firstly, it offers new proof on a micro-level regarding the behaviors that companies portray when practicing options relative to typical actual options. It also facilitates in the calculation of value distinctions that exist between real behavior for investment and the behavior that theory predicts. This depicts a crucial transformation in the area of calculating the performance behavior of companies when vital forces influencing option value change, such as volatility. The findings from the study also create room for empirical assessments for the influences that various hypothetical approach might have toward performance behavior (Smith, Matthews, & Driver, 2017) . Generally, whereas the prevailing literature argues that influences by peers are crucial for various decisions that companies make, such as the structure of capital, the effects also have major influence on the timing decisions related to investment.

Conclusion 

In conclusion, the paper focuses on comprehensive data on various real options, which companies adopt with the goal of characterizing them via empirical means to understand the approaches that they deploy. It reveals that whereas behavioral performance aspects correlate with forecasts of typical real option models, organizations also stray in a considerable manner from the forecasts. The paper mostly finds that corporations usually perform options at values, which are less than the trigger values. In this sense, theory would forecast doing without considerable option value. As such, questions arise as to why companies perform their options early. After researching actions by competitors, their behaviors serve as major drivers for early practice. For these results, they rhyme with results from real options’ agency properties as well as information externalities, which are regarded as vital avenues for performing behavior. Up until today, empirical literature on real options has remained insufficient mostly due to data restrictions. The paper offers vital proof on a micro-level regarding means of practicing real options together with ways that the identified behavior is distinct from typical forecasts of real option model. Additional work would facilitate in closing the gap between the present comprehensions of real performance of real options.

References

Décaire, P. H., Gilje, E. P., & Taillard, J. P. (2018). Real option exercise: Empirical evidence. Pennsylvania: The Wharton School.

Smith, M., Matthews, W., & Driver, R. (2017). Capital asset pricing model and the real options binomial lattice. Proceedings of 12th Annual London Business Research Conference (pp. 1-13). London: Imperial College.