A generalized real option pricing method of R&D investments: jump diffusion and external competition

ABSTRACT

Numerous studies have assessed Research and Development (R&D) investment using the real option pricing approach. This paper proposes a more general real option pricing method that both considers the specificity of R&D investment (such as uncertainty) and the R&D investment opportunity of a business in a market environment with external competitors. Specifically, we adopt a jump diffusion model to evaluate R&D investments that incorporate the uncertainties of these activities. The model values a pioneer's R&D investment opportunity allowing the chance that competitors may enter the market and the project value may vary with time. By construction and analysis of the model, we then analyse the optimal timing to realize profit on an investment. Overall, this model should facilitate a more comprehensive evaluation for R&D investments.     

The option value of advanced R & D

Existing tools for making R&D investment decisions cannot properly capture the option value in R&D. Since many new products are identified as failures during the R&D stages, the possibility of refraining from market introduction may add a significant value to the NPV of the R&D project. This paper presents new theoretical insight by developing a stochastic jump amplitude model in a real setting. The option value of the proposed model depends on the expected number of jumps and the expected size of the jumps in a particular business. The model is verified with empirical knowledge of current research in the field of multimedia at Philips Corporate Research. This way, the gap between real option theory and the practice of decision making with respect to investments in R&D is diminished.     

在折现率大于零的情况下,具有完成时间和残值不确定性的R&D项目的投资策略

利用随机停时理论 ,考虑 R&D项目的连续投资策略 .在折现率大于零的情况下 ,给出了具有建设期和残值的不确定性的 R&D投资模型、放弃 R&D项目投资的临界值和最优决策规则 ,并讨论参数对临界值的影响 .也进一步验证了随机停时理论和实物期权理论在投资决策分析中的一致性 .     

不确定竞争市场的R&D投资决策分析

本文针对不确定的竞争市场 ,分析降低成本的不可逆 R& D投资决策 .考虑到 R& D结果不确定 ,而这种不确定与投资量有关 ,在利用博弈论方法分析和给出了投资结果不确定的投资期权价值后 ,设随机市场需求规模服从均匀分布 ,本文分析了各种因素对 R& D投资的影响 ,发现较大的市场需求预期和较强的成本节约效果鼓励了 R& D投资 ;相反地 ,较大的成功 R& D所需的最大投资量挫败了 R& D投资 ;而投资期望净收益与投资成本之间的权衡使得存在事前最优投资量最大化投资期权价值     

Real R&;D options with time-to-learn and learning-by-doing

We model R&D efforts to enhance the value of a product or technology before final development. Such efforts may be directed towards improving quality, adding new features, or adopting technological innovations. They are implemented as optional, costly and interacting control actions expected to enhance value but with uncertain outcome. We examine the interesting issues of the optimal timing of R&D, the impact of lags in the realization of the R&D outcome, and the choice between accelerated versus staged (sequential) R&D. These issues are also especially interesting since the history of decisions affects future decisions and the distributions of asset prices and induces path-dependency. We show that the existence of optional R&D efforts enhances the investment option value significantly. The impact of a dividend-like payout rate or of project volatility on optimal R&D decisions may be different with R&D timing flexibility than without. The attractiveness of sequential strategies is enhanced in the presence of learning-by-doing and decreasing marginal reversibility of capital effects.     

研究与开发投资的多阶段实物期权分析

本文结合技术不确定性和现金流不确定性及专利保护 ,将 R& D项目划分为 R& D阶段和新产品商业化阶段 ,运用实物期权法 ,对 R& D项目进行分析 .由动态规划方法推倒出有关项目价值评估和投资期权评价的方程式 ,并作相应典型数值分析 .     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

Evaluating pharmaceutical R&D under technical and economic uncertainty

This study sets up a compound option approach for evaluating pharmaceutical R&D investment projects in the presence of technical and economic uncertainties. Technical uncertainty is modeled as a Poisson jump that allows for failure and thus abandonment of the drug development. Economic uncertainty is modeled as a standard diffusion process which incorporates both up-and downward shocks. Practical application of this method is emphasized through a case analysis. We show that both uncertainties have a positive impact on the R&D option value. Moreover, from the sensitivity analysis, we find that the sensitivity of the option with respect to economic uncertainty and market introduction cost decreases when technical uncertainty increases.     

Real R&D options and optimal activation of two-dimensional random controls

We value investments under uncertainty with embedded optional costly controls (impulse-type with uncertain outcome) that capture managerial intervention for value enhancement and/or information acquisition (exploration, R&D, advertising, marketing research, etc). Implementing real option models but neglecting such embedded managerial actions can severely underestimate investment opportunities and lead to erroneous investment decisions. Optimal decisions are solutions to a maximization problem where the trade-off between the control's cost and the value added by such actions is explicitly taken into consideration. In this paper, we generalize such a methodology from one dealing with the special case of actions affecting only one state-variable, to one with actions that affect several. Asset values follow geometric Brownian motion or jump-diffusion processes with multiple generating sources of jumps. The Markov-chain numerical methodology we provide can handle sequential controls. Although we report the results with open-loop policies, the approach can be readily extended to accommodate dependency among the controls.     

Climate change and optimal energy technology R&D policy

Public policy response to global climate change presents a classic problem of decision making under uncertainty. Theoretical work has shown that explicitly accounting for uncertainty and learning in climate change can have a large impact on optimal policy, especially technology policy. However, theory also shows that the specific impacts of uncertainty are ambiguous. In this paper, we provide a framework that combines economics and decision analysis to implement probabilistic data on energy technology research and development (R&D) policy in response to global climate change. We find that, given a budget constraint, the composition of the optimal R&D portfolio is highly diversified and robust to risk in climate damages. The overall optimal investment into technical change, however, does depend (in a non-monotonic way) on the risk in climate damages. Finally, we show that in order to properly value R&D, abatement must be included as a recourse decision.     

The impact of investment lags on investment decision

This paper suggests a valuation framework for an investment project through the concept of real options. Generally, in real asset world, decision time and its payment time are not identical. This so-called investment lag problem should be considered when valuing real assets. When investment lags exist, firms’ accommodation capacities play important roles. In this paper, the real effect of investment lag on investment value is tested upon various conditions. We show the valuation process of real assets under the risk-neutral world. The closed-form formula is also provided for valuing real assets, including R&D project.     

HETEROGENEOUS INFORMATION ARRIVAL AND R＆D OPTION PRICING

The paper models the arrival of heterogeneous information during R&D stages as a doubly stochastic Poisson process(DSPP). The new product market introduction is considered as a timing option(an American perpetual option). Investment in R&D can be thought of as option on an option(a compound option). This paper derives an analytic approximation valuation formula for the R&D option, and demonstrates that the accounts for heterogeneous information arrival may reduce the pricing biases. This way, the gap between real option theory and the practice of decision making with respect to investment in R&D is diminished.     

含不动产项目的保险公司再保险-投资策略

站在保险公司管理者的角度, 考虑存在不动产项目投资机会时保险公司的再保险--投资策略问题. 假定保险公司可以投资于不动产项目、风险证券和无风险证券, 并通过比例再保险控制风险, 目标是最小化保险公司破产概率并求得相应最佳策略, 包括: 不动产项目投资时机、 再保险比例以及投资于风险证券的金额. 运用混合随机控制-最优停时方法, 得到最优值函数及最佳策略的显式解. 结果表明, 当且仅当其盈余资金多于某一水平(称为投资阈值)时保险公司投资于不动产项目. 进一步的数值算例分析表明: (a)~不动产项目投资的阈值主要受项目收益率影响而与投资金额无明显关系, 收益率越高则投资阈值越低; (b)~市场环境较好(牛市)时项目的投资阈值降低; 反之, 当市场环境较差(熊市)时投资阈值提高.     

Expenditure patterns and timing of patent protection in a competitive R&D environment

In this paper we consider a stochastic R&D decision model for a single firm operating in a competitive environment. The study focuses on the firm's optimal policy which maximizes the expected discounted net return from the project. The firm's policy is composed of two ingredients: a stopping time which determines when the developed technology should be introduced and protected by a patent, and an investment strategy which specifies the expenditure rate throughout the R&D program. The main findings of the study are:

• (a) 

  Under a constant expenditure rate strategy, the optimal stopping time of the project is a control limit policy of the following form: stop whenever the project's state exceeds a fixed critical value, or when a similar technology is introduced and protected by one of the firm's rivals, whichever occurs first.

• (b) 

  For a R&D race model in which the winner-takes-all competition and the loser's return is zero, we show that the firm's optimal expenditure rate throughout the R&D program increases monotonically as a function of the project's state.

In order to gain a better insight regarding optimal R&D programs in competitive markets we examine the effect of key economic parameters on the firm's optimal policy.     

A model of R&D valuation and the design of research incentives

We develop a real options model of R&D valuation that takes into account the uncertainty in the quality (or efficacy) of the research output, the time and cost to completion, and the market demand for the R&D output. The model is then applied to study the problem of pharmaceutical under-investment in R&D for vaccines to treat diseases affecting the developing regions of the world. To address this issue, world organizations and private foundations are willing to sponsor vaccine R&D, but there is no consensus on how to administer the sponsorship effectively. Different research incentive contracts are examined using our valuation model. Their effectiveness is measured in the following five dimensions: expected cost to the sponsor, probability of development success, consumer surplus generated, expected number of successful vaccinations and expected cost per person successfully vaccinated. We find that, in general, purchase commitment plans (pull subsidies) are more effective than cost subsidy plans (push subsidies). Moreover, we find that a hybrid subsidy plan constructed from a purchase commitment combined with a sponsor research cost-sharing subsidy is the most effective.     

A model of R&D valuation and the design of research incentives

We develop a real options model of R&D valuation that takes into account the uncertainty in the quality (or efficacy) of the research output, the time and cost to completion, and the market demand for the R&D output. The model is then applied to study the problem of pharmaceutical under-investment in R&D for vaccines to treat diseases affecting the developing regions of the world. To address this issue, world organizations and private foundations are willing to sponsor vaccine R&D, but there is no consensus on how to administer the sponsorship effectively. Different research incentive contracts are examined using our valuation model. Their effectiveness is measured in the following five dimensions: expected cost to the sponsor, probability of development success, consumer surplus generated, expected number of successful vaccinations and expected cost per person successfully vaccinated. We find that, in general, purchase commitment plans (pull subsidies) are more effective than cost subsidy plans (push subsidies). Moreover, we find that a hybrid subsidy plan constructed from a purchase commitment combined with a sponsor research cost-sharing subsidy is the most effective.     

Multi-stage IT project evaluation: The flexibility value obtained by implementing and resolving Berk, Green and Naik (2004) model

In this paper, we evaluate a multi-stage information technology investment project, by implementing and resolving Berk, Green and Naik’s (2004) model, which takes into account specific features of IT projects and considers the real option to suspend investment at each stage. We present a particular case of the model where the project value is the solution of an optimal control problem with a single state variable. In this case, the model is more intuitive and tractable. The case study confirms the practical potential of the model and highlights the importance of the real-option approach compared to classical discounted cash flow techniques in the valuation of IT projects.     

Step by step. The benefits of stage-based R&D licensing contracts

We examine how a licensor can optimally design licensing contracts for multi-phase R&D projects when he does not know the licensee’s project valuation, leading to adverse selection, and cannot enforce the licensee’s effort level, resulting in moral hazard. We focus on the effect of the phased nature typical of such projects, and compare single-phase and multi-phase contracts. We determine the optimal values for the upfront payment, milestone payments and royalties, and the optimal timing for outlicensing. Including multiple milestones and accompanying payments can be an effective way of discriminating between licensees holding different valuations, without having to manipulate the royalty rate, which induces licensees to invest less, resulting in lower project values and socially suboptimal solutions. Interestingly, we also find that multiple milestone payments are beneficial even when the licensor is risk-averse, contrary to standard contract theory results, which recommend that only an upfront payment should be used. In terms of licensing timing, we show that the optimal time depends on the licensor’s risk aversion, the characteristics of the licensee and the project value.     

Optimal Expenditure Patterns of a Double-Path Engineering Project

The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.     

Strategic optimization in R&D investment

We use d'Aspremont and Jacquemin's strategic optimal R&D investment in a duopoly Cournot competition model to construct myopic optimal discrete and continuous R&D dynamics. We show that for some high initial production costs, the success or failure of a firm is very sensitive to small variations in its initial R&D investment strategies.