Fixed versus flexible production systems: A real options analysis

In this work, we address investment decisions in production systems by using real options. As is standard in literature, the stochastic variable is assumed to be normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. The methodology establishes a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case) and then, computes the project value. We have developed and implemented stochastic dynamic programming models both for fixed and flexible capacity systems. In the former case, we consider three standard options: the option to postpone investment, the option to abandon investment, and the option to temporarily shut-down production. For the latter case, we introduce the option of corrective action, in terms of production capacity, that the management can take during the project by considering the existence of one of the following: (i) a capacity expansion option; (ii) a capacity contraction option; or (iii) an option considering both expansion and contraction. The full flexible capacity model, where both the contraction and expansion options exist, leads, as expected, to a better project predicted value and thus, investment policy. However, we have also found that the capacity strategy obtained from the flexible capacity model, when applied to specific demand data series, often does not lead to a better investment decision. This might seem surprising, at first, but it can be explained by the inaccuracy of the binomial model. The binomial model tends to undervalue future decreases in the stochastic variable (demand), while at the same time tending to overvalue an increase in future demand values.     

Can properly discounted projects follow geometric Brownian motion?

The geometric Brownian motion is routinely used as a dynamic model of underlying project value in real option analysis, perhaps for reasons of analytic tractability. By characterizing a stochastic state variable of future cash flows, this paper considers how transformations between a state variable and cash flows are related to project volatility and drift, and specifies necessary and sufficient conditions for project volatility and drift to be time-varying, a topic that is important for real option analysis because project value and its fluctuation can only seldom be estimated from data. This study also shows how fixed costs can cause project volatility to be mean-reverting. We conclude that the conditions of geometric Brownian motion can only rarely be met, and therefore real option analysis should be based on models of cash flow factors rather than a direct model of project value.     

Discrete-continuous project scheduling with discounted cash inflows and various payment models—a review of recent results

In this work discrete-continuous project scheduling problems with discounted cash flows are considered. These problems are characterized by the fact that activities of a project simultaneously require discrete and continuous resources for their execution. A class of these problems is considered, where the number of discrete resources is arbitrary, and there is one continuous, renewable resource, whose total amount available at a time is limited. Activities are non-preemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. A positive cash flow (cash inflow) is associated with each activity, and the objective is to maximize the net present value (NPV). The discrete-continuous resource-constrained project scheduling problem with discounted cash flows (DCRCPSPDCF) is defined. Four payment models are considered: lump-sum payment at the completion of the project, payments at activity completion times, payments at equal time intervals, and progress payments. Some properties of optimal schedules are proved for two important classes of processing rate functions: all functions not greater than a linear function (including linear and convex functions), and concave processing rate functions.     

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.     

Purchasing decisions under stochastic prices: Approximate solutions for order time, order quantity and supplier selection

This paper analyzes purchasing strategies for retailers regarding the best timing and amount of purchases when operating under combined timing and quantity flexibility contracts in an environment of uncertain prices. To decrease the computational complexity and make the procedure adaptable to the case of multiple suppliers, we introduce, analyze, and compare a ??time strategy?? and a ??target strategy?? and then develop a hybrid ??adaptive target strategy?? to facilitate and improve the purchasing decision for the case of option contracts with generally rising prices. The adaptive target strategy is simpler and more intuitive than the traditional binomial lattice method, while the risk of failing to meet a target profit can also easily be calculated. We then extend the solution procedure to maximize expected profits in an environment of selecting among multiple suppliers with potentially different price processes, and we further provide risk analysis to help determine a good estimate for the number of option contracts from different suppliers to generate in order to create adequate risk protection. Numerical analysis demonstrates how the number of candidate suppliers impacts the expected profit and the risk. Monte Carlo simulation results demonstrate that the developed solution procedures provide satisfying outcomes and that the calculation is fast, even for multiple-dimension and multiple-supplier cases.     

Generalised soft binomial American real option pricing model (fuzzy–stochastic approach)

The stochastic discrete binomial models and continuous models are usually applied in option valuation. Valuation of the real American options is solved usually by the numerical procedures. Therefore, binomial model is suitable approach for appraising the options of American type. However, there is not in several situations especially in real option methodology application at to disposal input data of required quality. Two aspects of input data uncertainty should be distinguished; risk (stochastic) and vagueness (fuzzy). Traditionally, input data are in a form of real (crisp) numbers or crisp-stochastic distribution function. Therefore, hybrid models, combination of risk and vagueness could be useful approach in option valuation. Generalised hybrid fuzzy–stochastic binomial American real option model under fuzzy numbers (T-numbers) and Decomposition principle is proposed and described. Input data (up index, down index, growth rate, initial underlying asset price, exercise price and risk-free rate) are in a form of fuzzy numbers and result, possibility-expected option value is also determined vaguely as a fuzzy set. Illustrative example of equity valuation as an American real call option is presented.     

Optimal dividend strategy in compound binomial model with bounded dividend rates

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.     

Debt recapitalization and value in waiting to finance a project

This paper shows that an option to recapitalize with debt accelerates the exercise of a real option to start an irreversible project investment. The debt-recapitalization add-on, while not directly affecting project cash flows, influences the timing of the project start by offering an extra gain from tax savings less debt costs. This finding demonstrates that capital structure decisions are closely linked to project investment decisions, a deviation from the standard optimal investment rule of the real option theory.     

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.     

Optimization of a highway project planning using a modified genetic algorithm

This paper proposes an optimization method for a national-level highway project planning based on a modified genetic algorithm. The proposed method adds to the existing methods by integrating various planning elements into a single system. A simulation model is used in order to determine the best investment strategy with regard to net present value, time deviation from the initial plan and discrepancy between available resources and investment costs by taking into account economical, social, traffic and political factors. The outcome is a project schedule with an optimized cash flow. The proposed method was tested using the example of the National Highway Programme in Slovenia.     

Market completeness: A return to order

We investigate market completeness with respect to the topology generated by the order relation on a linear lattice of functions describing, in a two-times economy, the associated cash flow space. The study is leading us towards alternative definitions for market completeness, in terms of trading strategy operators and approximate convergent martingales spanning on such linear lattices.

     

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 .     

独立项目的久期预估与融资优化研究

项目投资与融资匹配程度,不仅关系到项目资金成本的大小,还体现对项目利率风险的对冲。基于债券久期的概念内涵,提出了项目久期与融资结构久期的概念及计算方法。以具体项目的投融资为案例进行研究,对案例公司已拟定的针对独立项目的债券融资方案进行投融资久期匹配、各期现金流匹配评价,并从市场利率曲线中发现融资成本优化空间,从投融资久期差及各期投融资现金流量差中找到优化融资的方案。以此提出结论:项目久期与融资结构久期的匹配是降低项目利率风险的重要手段;应综合融资结构久期与项目久期、现金流大小选择融资结构。     

The American Foreign Exchange Option in Time-Dependent One-Dimensional Diffusion Model for Exchange Rate

The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest rates are constant and the exchange rate follows a log-normal diffusion process. In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent case is the continuity in time argument of the value function of the American put option and the regularity properties of the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for the American puts with different strikes, maturities and volatilities. Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value function of the American foreign exchange put option as the sum of the European put option value function and the early exercise premium. The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise boundary which can be studied by numerical methods.     

Optimal exercise of jointly held real options: A Nash bargaining approach with value diversion

This paper provides a two-stage decision framework in which two or more parties exercise a jointly held real option. We show that a single party’s timing decision is always socially efficient if it precedes bargaining on the terms of sharing. However, if the sharing rule is agreed before the exercise timing decision is made, then socially optimal timing is attained only if there is a cash payment element in the division of surplus. If the party that chooses the exercise timing can divert value from the project, then the first-best outcome may not be possible at all and the second-best outcome may be implemented using a contract that is generally not optimal in the former cases. Our framework contributes to the understanding of a range of empirical regularities in corporate and entrepreneurial finance.     

Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models

In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. A project is represented by an activity-on-node (AoN) network. A positive cash flow is associated with each activity. Four different payment models are considered: lump-sum payment at the completion of the project, payments at activities' completion times, payments at equal time intervals and progress payments. The objective is to maximize the net present value of all cash flows of the project. Local search metaheuristics: simulated annealing and tabu search are proposed to solve this strongly NP-hard problem. A comprehensive computational experiment is described, performed on a set of instances based on standard test problems constructed by the ProGen project generator, where, additionally, the activities' cash flows are generated randomly with the uniform distribution. The metaheuristics are computationally compared, the results are analyzed and discussed and some conclusions are given.     

基于随机活动工期的多模式现金流均衡项目调度优化

承包商在项目执行过程中的现金流均衡是保证项目成功的关键因素。本文研究基于随机活动工期的多模式现金流均衡项目调度问题,旨是在项目工期及鲁棒性阈值约束下合理安排活动执行模式与开始时间,实现承包商现金流均衡。本文通过构建整数规划优化模型对研究问题进行刻画,随后设计模拟退火算法进行求解,最后进行案例分析。结果表明:鲁棒性阈值虽然可以保证基准进度的稳定性,但是提高鲁棒性阈值水平反而不利于承包商的现金流均衡,该值过高时甚至得不到可行解。本文研究可为随机活动工期背景下承包商的现金流控制提供定量化决策支持。     

A moment-based analytic approximation of the risk-neutral density of American options

The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density based on the implied moments of the implicit European contract under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalized Edgeworth expansion, where the moments of the American density are obtained by a reverse engineering application of the least-squares method. The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness and kurtosis swaps.     

Complete discounted cash flow valuation

This paper concerns discounted cash flow valuation of a company. When the company is in trouble, the owners have an option to provide it with a new capital; otherwise it is liquidated. In the absence of capital outflows and inflows, the company’s own funds are modelled by a spectrally negative Lévy process. Within this framework, we look for a strategy of dividend payments and capital injections which maximizes the firm’s value. We provide an optimal strategy as well as the corresponding valuation formula. Illustrative examples are given.     

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.