Valuation of project portfolios: An endogenously discounted method

Real options analysis (ROA) has been developed to value assets in which managerial flexibilities create significant value. The methodology is ideal for the valuation of projects in which frequent adjustments (e.g. investment deferral, project scope changes, etc) are necessary in response to the realization of market and technological uncertainties. However, ROA has no practical application when valuing portfolios of multiple concurrent projects sharing resources, as the size of the problem grows exponentially with the number of projects and the length of the time horizon. In this paper an extension of ROA suitable for the valuation of project portfolios with substantial technological uncertainty (e.g. R&D portfolios) is proposed. The method exploits the distributed decision making strategy encountered in most organizations to decompose the portfolio valuation problem into a decision-making sub-problem and a set of single project valuation sub-problems that can be sequentially solved. Discrete event simulation is used for the first sub-problem, while a tailored ROA based strategy is used for the set of valuation sub-problems. A case study from the pharmaceutical industry is used to compare the decision tree analysis (DTA) method and the proposed method.     

Real (investment) options with multiple sources of rare events

We value real (investment) options when the underlying asset follows a mixed jump-diffusion process involving various types (sources) of rare events (jumps). These jumps are assumed independent of each other, with each type having a log-normally distributed jump size and a random (Poisson-distributed) arrival time. They may represent uncertainties about the arrival and impact (on the underlying investment) of new information concerning technological innovation, competition, political risk, regulatory effects and other sources. An analytic solution is presented for European claims (call or put options) with multiple sources of jumps. A discrete-time (Markov-chain) methodology (implemented within a finite-difference scheme) is proposed for the valuation of American as well as European options. The approach is also applicable to financial options with multiple types of rare events. The approach is illustrated through valuing complex real options with compound features involving interactions between optimal investment and subsequent operating decisions. Specifically, we value a growth option and an extension option.     

基于模糊集合论的实物期权定价方法

实物期权的定价在风险投资决策过程中具有重要意义.传统的实物期权定价方法忽略标的资产价值和投资成本的模糊性,从而可能导致错误的投资决策.本文主要研究了具有模糊标的的资产价值和投资成本情形时的实物期权定价模型.文中将这些模糊因素分别视为模糊数和模糊变量,然后运用模糊集合论,结合B-S期权定价理论,对实物期权进行定价,得到了基于模糊集合论的实物期权定价模型.     

Insuring a risky investment project

In the standard model for insurance demand, the risk is totally exogenous and the insurance premium is paid for out of riskless wealth. This model yields results that are mostly in contradiction to everyday observation and have been used to question the pertinence of expected utility theory on which the model is based. For some years now, several papers have made attempts to provide foundations for a theory of insurance demand that leads to less provocative comparative statics results. In these papers, the risk for which coverage is sought becomes endogenous, and the decision to purchase insurance is made simultaneously with the decision on how much to invest in insurable assets. All these papers use a standard financial investment framework. This paper offers a contribution to this literature by using a slightly different framework: the case of a firm exposed to an insurable risk affecting return on a real investment project. The model is kept simple by using a two-state environment. It yields results that are both more complete and more general than results in previous work with the same motivation.     

Real options valuation of forest plantation investments in Brazil

In this paper, we consider investments in eucalyptus plantations in Brazil. For such projects, we discuss real options valuation in the place conventional methods such as IRR or NPV, possibly with CAPM. Traditionally, real options valuation assumes complete markets and neglects market imperfections. Yet, market frictions, such as transaction costs, interest rate spreads, and restricted short positions, can play an important role. We extend real options valuation to allow incomplete and imperfect markets. The value is obtained as a competitive price, given markets of competing investment opportunities, such as real and financial assets. Under perfect and complete markets, such valuation method is consistent with conventional real options theory. Stochastic programming and standard software is used for valuation of eucalyptus plantations. We estimate the underlying interdependent diffusion processes of stock market, interest rates, exchange rates and pulpwood price, and derive novel expressions of stochastic integrals to be employed in scenario generation for discrete time stochastic programming.     

On “investment decisions in the theory of finance: Some antinomies and inconsistencies”

In the paper “Investment Decisions in the Theory of Finance: Some antinomies and inconsistencies”, Magni [Eur. J. Operat. Res. 137 (2002) 206] shows that using the net present value rule for making investment decisions can lead to inconsistencies and antinomies. The author claims that the so-called equivalent-risk tenet of finance, whereby an investor needs to compare an investment opportunity with an asset of equivalent risk, is impossible to implement. In this paper, we show that the main thesis of this paper is incorrect, and that finance theory, when applied correctly, can be used to value investment projects by comparing assets of equivalent risk. We point out the fallacies in the author's reasoning and provide an alternative, and correct, methodology for valuing the projects described in the paper.     

The impact of delaying an investment decision on R&D projects in real option game

In a research and development (R&D) investment, the cost and the project value of such an investment are usually uncertain, which thus increases its complexity. Correspondingly, the NPV (Net Present Value) rule fails to evaluate the value of this project exactly, because this method does not take into account the market uncertainty, irreversibility of investment and ability of delay entry. In this paper, we employ the real option theory to evaluate the project value of a R&D investment. Since the cost of a R&D investment is very high and the flow of the information is crowded, an investor cannot make an immediate decision every time. So, the proposed real option model is an exchange option. At the same time, combining the real option and the game theory, we can find the Nash equilibrium which is the optimal strategy. Moreover, we also study how the delayed time influences the price of the project investment and how the different delayed times effect the choice of the optimal strategies.     

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.     

The impact of delivery lags on irreversible investment under uncertainty

We consider the valuation and rational exercise of irreversible investment opportunities in the presence of revenue uncertainty and delivery lags. In order to capture supply side market imperfections in the markets for investment goods, we assume that the lag depends on the revenue process faced by the investor. We show that such imperfections have a pronounced decelerating impact on rational investment demand as they may increase the value of waiting in excess of the exercise payoff even for projects which otherwise would be perceived as highly remunerative. We also consider the comparative static properties of the optimal investment policy and its value, and demonstrate that typically increased uncertainty decreases the investment incentives by increasing the value of waiting.     

我国固定资产投资边际效率问题研究

将回归分析与边际效用理论有机结合,深入研究我国固定资产投资对GDP边际贡献问题.研究结果表明在整个正实数区间内高技术产业固定资产投资对GDP边际贡献高于全社会固定资产投资和城镇房地产开发固定资产投资对GDP边际贡献;在0～349578.8207亿元投资区间内,城镇房地产开发固定资产投资对GDP边际贡献高于全社会固定资产投资边际贡献平均水平;当投资额度大于349578.8207亿元时,城镇房地产开发固定资产投资对GDP边际贡献小于全社会固定资产投资边际贡献平均水平.研究结果印证了科技是第一生产力的论断,同时也与我国当前控制房地产开发投入、鼓励发展高新技术产业等宏观经济政策相吻合.     

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.     

Real options in strategic investment games between two asymmetric firms

This paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strategic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strategic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader’s and follower’s optimal investment thresholds. In a duopoly market with negative externalities, a firm may reduce loss of real options value by selecting appropriate pre-emptive entry. When one firm has a dominant advantage over its competitor, both the dominant firm and dominated firm enter at their respective leader’s and follower’s optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead.     

Stochastic modelling of long-term investment risks

There are many risks that individuals, firms, and societieshave to face, and among them are the uncertainties of futureinvestment variables, which include inflation (both of pricesand earnings), interest rates,exchange rates, and returns onordinary shares (including both dividend income and changesin capital values).These investment risks affect inviduals intheir own financial planning; affect companies in planning investmentprojects and in arrangements for raising capital;affect governmentsand government institutions that have to borrow in the capitalmarkets; and especially affect investment institutions and intermediarieswho take on borrowings, deposits, insurance contracts, or pensionfund liabilities on the one hand and invest assets in loans,ordinary shares, property, or other investments on the other. A great deal of work done by financial economists in recentdecades has established reasonable models for describing movementsof many investment variables in the short run. Typically thesemodels are based on a 'random walk' or Gauss-Wiener continuousdiffusion process. This sort of model has been particularlyvaluable to market-makers and other investment participantswhose time horizon is short. But these short-term models oftendo not provide a satisfactory structure for the long term. Thispresentation will describe some of the author's work in thestatistical analysis of long-term investment series, both inthe United Kingdom and in other countries, based on statisticaltime-series analysis of historical data. Although many of the series could be valued using multivariatemethods, such as vector autoregressive (VAR) models, preliminaryinvestigation showed that many of the series could be investigatedin a 'cascade' fashion, with price inflation being put as theinitial 'driver'. A very long historic series shows long periodswhen changes in prices in successive years could be taken asrandom, with zero drift, and other periods (including most ofthis century) when inflation rates in successive years werecorrelated. A similar pattern has applied in recent years inmany other countries. It is postulated that the prices of ordinary shares in aggregateare closely related to the dividends paid on them, so that theratio between dividend and price, i.e. the dividend yield, isstationary—fluctuating around a constant mean. The dividend-yieldseries can be described by means of a first-order autoregressivetime-series model,while the dividend series can be describedby a model that depends on inflation in the current and precedingyears, with an appropriate time lag. Interest rates, both long-term and short-term, are first decomposedinto an allowance for prospective future inflation and a 'real'rate of interest, comparable to the yield on index-linked stocks.The real rate of interest can also be modelled as a mean-revertingautoregressive model. The allowance for future inflationcanbe derived as a moving average of past inflation rates.In orderto link models for different countries, it is necessary to havea model for currency exchange rates. This can be done by postulatinga hypothetical 'purchasingpower parity' exchange rate, whichexactly allows for changes in inflation, and then by modellingthe deviation of the actual rate from the hypothetical rateby means of yet another autoregressive model. It is necessaryalso to keep an appropriate structure for cross rates betweenany pair of currencies. This series of stochastic models is particularly useful forestimating future scenarios of all the variables in a consistentmanner, and for estimating their likely variability. In some cases this can be done analytically, but in generalit requires ’Monte Carlo‘ simulations. Various possibleapplications of the model in different fields will be described.     

随机通胀风险下基于半鞅理论的最优投资策略

本文在半鞅理论框架下,构建包括可交易风险资产、不可交易风险资产和未定权益的金融投资模型。在考虑随机通胀风险和获取部分市场信息的情形下,研究投资经理人终端真实净财富指数效用最大化问题。运用滤波理论、半鞅和倒向随机微分方程(BSDE)理论,求解带有随机通胀风险的最优投资策略和价值过程精确解。数值分析结果发现,可交易风险资产最优投资额随着预期通胀率的增加而减少,投资价值呈先增后减态势。当通胀波动率无限接近可交易风险资产名义价格波动率时,通胀风险可完全对冲,投资人会不断追加在可交易风险资产的投资额,以期实现终端真实净财富期望指数效用最大化。研究结果为金融市场的投资决策提供更加科学的理论参考。     

Valuing interdependent multi-stage IT investments: A real options approach

In this paper, we use the market asset disclaimer assumption and develop a binomial lattice based real options model to include cash flow interdependencies between multi-stage information technology (IT) investments. Using a simple two-stage IT investment problem with interdependent cash flows, we apply the binomial lattice based real options model to obtain combined valuation of the two-stage IT investment. In addition to investment valuation, our experience with the two-stage IT investment valuation suggests that the binomial lattice based real options model provides a powerful decision aid tool for appropriate timing, delaying and abandoning of the second-stage IT investment.     

Optimal time-consistent investment and reinsurance policies for mean-variance insurers

This paper investigates the optimal time-consistent policies of an investment-reinsurance problem and an investment-only problem under the mean-variance criterion for an insurer whose surplus process is approximated by a Brownian motion with drift. The financial market considered by the insurer consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. A general verification theorem is developed, and explicit closed-form expressions of the optimal polices and the optimal value functions are derived for the two problems. Economic implications and numerical sensitivity analysis are presented for our results. Our main findings are: (i) the optimal time-consistent policies of both problems are independent of their corresponding wealth processes; (ii) the two problems have the same optimal investment policies; (iii) the parameters of the risky assets (the insurance market) have no impact on the optimal reinsurance (investment) policy; (iv) the premium return rate of the insurer does not affect the optimal policies but affects the optimal value functions; (v) reinsurance can increase the mean-variance utility.     

带投资的时依更新风险模型中破产概率的一致渐近估计

本文考虑索赔额过程与索赔时间过程具有相依性的更新风险模型.假定保险公司将其盈余投资到金融市场中,该投资的价格过程服从几何L′evy过程.当索赔额分布属于L∩D时,本文得到有限时间总索赔额现值尾概率的一致渐近估计,同时也得到有限时间破产概率的一致渐近估计.     

Valuing continuous-installment options

Installment options are path-dependent contingent claims in which the premium is paid discretely or continuously in installments, instead of paying a lump sum at the time of purchase. This paper deals with valuing European continuous-installment options written on dividend-paying assets in the standard Black–Scholes–Merton framework. The valuation of installment options can be formulated as a free boundary problem, due to the flexibility of continuing or stopping to pay installments. On the basis of a PDE for the initial premium, we derive an integral representation for the initial premium, being expressed as a difference of the corresponding European vanilla value and the expected present value of installment payments along the optimal stopping boundary. Applying the Laplace transform approach to this PDE, we obtain explicit Laplace transforms of the initial premium as well as its Greeks, which include the transformed stopping boundary in a closed form. Abelian theorems of Laplace transforms enable us to characterize asymptotic behaviors of the stopping boundary close and at infinite time to expiry. We show that numerical inversion of these Laplace transforms works well for computing both the option value and the optimal stopping boundary.     

甘肃省固定资产投资与经济增长关系的协整分析

运用协整理论和格兰杰检验,对甘肃省1995-2009年间的固定资产投资与GRP的数据进行分析研究,结果表明两者之间存在长期稳定的均衡关系,甘肃省目前的固定资产投资与GRP存在双向因果关系,这说明甘肃省固定资产投资明显拉到了经济增长,而经济增长对投资的发展也起了显著的促进作用.     

Utility Indifference Pricing: A Time Consistent Approach

Abstract

This article considers the optimal portfolio selection problem in a dynamic multi-period stochastic framework with regime switching. The risk preferences are of exponential (CARA) type with an absolute coefficient of risk aversion that changes with the regime. The market model is incomplete and there are two risky assets: tradable and non-tradable. In this context, the optimal investment strategies are time inconsistent. Consequently, the subgame perfect equilibrium strategies are considered. The utility indifference ask price of a contingent claim written on the risky assets is computed through an indifference valuation algorithm. By running numerical experiments, we examine how this price varies in response to changes in model parameters.