Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.     

ADAPT: An Adaptive Approach to Media Decisions

A firm's market changes under the impact of the firm's advertising. Feedback information on the market response allows the firm to learn about such changes and to adapt its subsequent media decisions accordingly. This paper presents an adaptive media model (ADAPT) that utilizes feedback information to revise certain parameters in a media decision model. Simulation experiments conducted with the ADAPT model demonstrate how different types of feedback information affect the media decisions and thereby the expected net profit contributions from sales. It is shown how the economic value of feedback information depends on the characteristics of the firm's market and also on the revision rules applied for updating the parameters. The value of the information may actually be negative if it is not used "intelligently".     

A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options

We propose a general framework to model equity volatility for a firm financed by equity and additional non-equity sources of funds. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities. Second, we show for the first time in the option literature, that instantaneous equity volatility is a solution of a partial differential equation similar to Black-Scholes', although it is non-linear and in general does not have any analytical solution. However, analytical approximations for equity volatility are proposed for different capital structures: (1) equity and debt, (2) equity and warrants, and (3) equity, debt and warrants. They are shown to be very accurate.     

Optimal allocation and backup of computer resources under asymmetric information and incentive incompatibility

This paper presents the optimal allocation and backup of computing resources in a multidivisional firm in the presence of asymmetric information and incentive incompatibility. A game-theoretic model is developed and transformed to a linear programming problem. The solution to this linear programming problem enables the corporate headquarters to design a resource allocation scheme such that the revelation principle prevails and all divisions tell the truth. To cope with the combinatorial explosion of complexity caused by the resource constraint, a greedy-type algorithm and an averaged version of the original linear programming problem are developed to provide the upper and lower bounds. The greedy-type algorithm generates exact solutions for a wide range of instances. The lower bounds coincide with the exact solutions for the cases where the computer resource is either scarce or abundant. The averaged-version resource allocation model with slight modifications solves the optimal computer backup capacity problem. It determines how much back up capacity the firm should purchase when the firm's computer breaks down.     

委托代理冲突下的企业投融资决策

采用实物期权与均衡定价理论,研究委托-代理冲突下的企业投融资决策问题.考虑管理者拥有企业投融资决策权时,其如何同时选择投资时机、投资规模及资本结构.分析了管理者持股与项目风险(不确定性)对企业非效率投融资的影响.数值分析表明:给定资本结构下,杠杆企业管理者决策的投资时机与投资规模变化呈现出负相关;对比于纯股权融资企业,杠杆企业管理者加速了投资期权的执行并增大了投资规模;财务杠杆率是管理者持股比例的U形函数,且管理者持股比例的增大,会加速投资期权的执行、增大投资规模与债务融资规模,并降低代理成本;项目风险的增大会导致企业投资时机、投资规模、债务融资规模和代理成本增大及财务杠杆率降低.     

Callable risky perpetual debt with protection period

Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection (‘grace’) period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of perpetual debt and barrier options with a time dependent barrier. We also analyze how an issuer’s optimal bankruptcy decision is affected by the existence of the call option by using closed-form approximations. The model quantifies the increased coupon and the decreased initial bankruptcy level caused by the embedded option. Examples indicate that our closed form model produces reasonably precise coupon rates compared to numerical solutions. The credit-spread produced by our model is in a realistic order of magnitude compared to market data.     

Portfolio selection under DEA-based relative financial strength indicators: case of US industries

Fundamental analysis is an approach for evaluating a firm for its investment-worthiness whereby the firm's financial statements are subject to detailed investigation to predict future stock price performance. In this paper, we propose an approach to combine financial statement data using Data Envelopment Analysis to determine a relative financial strength (RFS) indicator. Such an indicator captures a firm's fundamental strength or competitiveness in comparison to all other firms in the industry/market segment. By analysing the correlation of the RFS indicator with the historical stock price returns within the industry, a well-informed assessment can be made about considering the firm in an equity portfolio. We test the proposed indicator with firms from the technology sector, using various US industries and report correlation analyses. Our preliminary computations using RFS indicator-based stock selection within mean–variance portfolio optimization demonstrate the validity of the proposed approach.     

A Multi-Layered Potential Field Method for Multi-Agent Navigation,Searching and Tracking

Collaborating multi-agent systems can handle complex tasks with several or changing mission objectives. We developed a potential field method that allows various information layers to influence the control over a group of vehicles. The gradient of the potential field is the driving force for local action, whereas the global waypoint is determined by the minimum of the agent's potential field. The driving force to the global waypoint is a virtual spring-mass-damper system that pulls the agent towards its waypoint, restricted by the local gradient of the agent's potential field. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Service contracts: A stochastic model

There is a growing trend to outsource maintenance where equipment failures are rectified by an external agent under a service contract. The agent's profit is influenced by many factors—the terms of the contract, equipment reliability, and the number of customers being serviced. The paper develops a stochastic model to study the impact of these on the agent's expected profit and the agent's optimal strategies using a game theoretic formulation.     

A fuzzy attractiveness of market entry (FAME) model for market selection decisions

A Fuzzy Attractiveness of Market Entry (FAME) model is developed to address the decision-making problem of product introduction into alternative markets. FAME is a market entry selection model that is specifically designed to handle situations when information is limited and/or ambiguous, and a high level of uncertainty exists. As such, the FAME model is an easy to implement tool that supports a reasoning approach to market selection decisions. The model uses expert opinions regarding four factors: (1) fit of the firm's marketing mix in each market; (2) the fit of its key competitor's marketing mix in each market; (3) environmental conditions in each market; and (4) the strategic importance of each market to the firm. Application of the model algorithm is conducted for a small, Bulgarian winery's market selection decision. Ease of use is relevant for small to mid-size companies since a spreadsheet is sufficient to complete the algorithmic calculations.     

On the interaction between indirect cost allocations and the firm's objectives

The import of cost allocation procedures are through their ex ante important decision making. Hence, it is important that the allocation issue be placed squarely within the context of those firm's objectives which gave rise to the need for the specific allocation. To that effect, this paper focuses the debate on the identification of the indirect cost allocation method that is best suited to the specific reasons for requiring the cost information. First, it is shown that all existing allocation schemes (i) may be expressed in a common equation, flexible enough to be adapted to whatever decision-making purpose the firm desires; and (ii) fulfil the individual rationality conditions of game theory. Then, in light of the controversy as to whether the US Defense Department indirectly subsidizes the commercial side of its suppliers' operations, necessary and sufficient conditions are provided for allocations which do and do not subsidize. Non-subsidized allocations are shown to belong to the core. Subsidized allocations occur when the players (divisions') rational objectives are superseded by higher priority coordinating objectives of non-players (the firm).     

Investment decisions in the rent-to-own industry in the absence of inventory

This study addresses the product investment decision faced by firms in the rent-to-own industry. In this setting, a customer arrives according to a random process and requests one unit of a product to rent (and eventually own should he/she choose to make all the required payments). At the time of request, if the product is available in inventory, the firm enters into a contractual agreement (by accepting the customer's offer) and rents the merchandise. More interesting and the case considered here, if the requested item is not in inventory, the firm must decide whether to purchase the item in order to rent it out or to simply reject the request. The customer's offer specifies the desired maximum contract length and the payment frequency—from which the firm determines the fixed periodic payment charged. The firm makes its investment decision based on the characteristics of the offer as well as those of the product (eg, initial and resale values, useful life and carrying costs) in essence performing a complicated cost benefit analysis. An extension is also considered whereby instead of simply rejecting the request the firm can adjust the required payment amount. Dynamic programming techniques are used to address the problem and to solve for the firm's optimal decision.     

基于权益再融资与策略性债务支付的公司财务困境纾解研究

为了应对公司财务困境问题,在兼顾股东与债权人利益的基础上,采用激励相容理论,构建了基于权益再融资和策略性债务支付的公司定价模型,厘清了权益再融资、债务重组、财务困境及其伴生的再谈判之间的关系,据此提出了一种公司财务困境纾解方案。特别地,给出了策略性债务支付下进行权益再融资的可行性依据,并辅以再谈判手段及股东、债权人双方利益最大化目标,确定了最优重组边界及最优减记息票。分析结果表明:①将策略性债务支付置于财务困境之后、兼容权益再融资的综合方案,可在一定程度上避免策略性债务支付行为的投机性所导致的对公司定价的高估,产生了在一定条件下增加债务价值、放缓信用价差增长速度的效果;②权益再融资成本与信用价差之间呈现倒U型关系;③基于纳什均衡博弈的策略性债务支付减记息票不受流动性及权益再融资的影响,并可保证其处于公司的支付能力之内。     

NATURAL RESOURCE ECONOMICS UNDER UNCERTAINTY: EFFECT OF FUTURES MARKETS

The effects of hedging and time-dependent price and geological uncertainty on the behavior of a firm exploiting a nonrenewable natural resource are derived. Contrasts in behavior with and without hedging and uncertainty are identified and discussed. Much of the analysis centers on the firm's implicit value of its in situ reserves, marginal user cost. The main result is that time-dependent uncertainty lowers the implicit value of reserves. Hedging ameliorates this effect somewhat. Under some conditions even with risk reducing hedging, the firm tilts its extraction and development paths toward the present and may also shorten its decision-making time horizon.     

Cutting costs or enhancing revenues? An example of a multi-product firm with impatient customers illustrates an important choice facing operational researchers

A new dilemma facing the operational researcher with limited resources is, whether to continue the traditional focus on improving the efficiency of the firm or to focus instead on improving the revenue side of the firm's income statement. In this article, we examine this decision using a model of a firm that was published in this journal by Levin et al. We use this model, as applied to a UK-based multi-product manufacturer of wooden furniture, to illustrate the dramatic revenue and profit gains potentially available by applying revenue management concepts in a manufacturing environment.     

A firm's optimizing behaviour under a value-at-risk constraint

In this article, we employ the concept of value-at-risk to model a kind of risk-averse behaviour of a firm which seeks to maximize profit?à?la Greenwald–Stiglitz [5]. It is shown that there exists a unique well-defined solution function, which relates output to the firm's net worth, but that this function is not monotone. The latter is due to the fact that whenever the VaR-constraint is not binding, the firm behaves in a risk-neutral fashion. It is also shown that in this context, the Modigliani–Miller theorem applies only in the special case where there is no risk of bankruptcy.     

Closed Form Approximations for Spread Options

Abstract

Market mechanisms are increasingly being used as a tool for allocating somewhat scarce but unpriced rights and resources, and the European Emission Trading Scheme is an example. By means of dynamic optimization in the contest of firms covered by such environmental regulations, this article generates endogenously the price dynamics of emission permits under asymmetric information, allowing inter-temporal banking and borrowing. In the market, there are a finite number of firms and each firm's pollution emission follows an exogenously given stochastic process. We prove the discounted permit price is a martingale with respect to the relevant filtration. The model is solved numerically. Finally, a closed-form pricing formula for European-style options is derived.     

Optimal input substitution of a firm facing an environmental constraint

In this paper we consider the dynamic behavior of a firm subject to environmental regulation. As a social planner the government wants to reduce the level of pollution. To reach that aim it can, among others, set an upper limit on polluting emissions of the firm. The paper determines how this policy instrument influences the firm's decisions concerning investments, abatement efforts, and the choice whether to leave some capacity unused or not. The abatement process is modeled as input substitution rather than end-of-pipe. Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long run optimal level of capital. In some cases, this equilibrium is reached within finite time, but usually it will be approached asymptotically. Different scenarios are considered, ranging from attractive clean input to unattractive clean input, and from a mild emission limit to a very tight one. It is shown that for large capital stocks and/or when marginal cash flow per unit of emissions is larger for the dirty input than for the clean input, it can be optimal to actually leave some production capacity unused. Also, since the convex installation costs suggest to spread investments over time, it can happen that investment in productive capital is positive although capacity remains unused.     

On the connections among activity-based costing,mathematical programming models for analyzing strategic decisions,and the resource-based view of the firm

This paper examines connections between data-driven models for analyzing a firm's strategic plans, which use activity-based costing and mathematical programming, and the resource-based view of the firm. After brief reviews of the three disciplines, extensions of activity-based costing methods to mathematical programming models for strategic resource planning are discussed. Applications of these models to supply chain planning in a multi-national food manufacturer, a specialty chemicals company, and a wholesaling/retailing company are presented. The paper concludes by using concepts from the resource-based view of the firm to interpret optimal solutions from mathematical programming models. Extensions to strategic planning under uncertainty using stochastic programming are also discussed briefly.     

Evolutionary dynamics of knowledge

This study discusses the evolutionary nature of knowledge acquisition at micro and macro levels, and in particular when the process involves an artificial agent's interpretative devices. In order to accomplish this, we propose using an individual learning model (or inner‐world reconstruction model) that in our view overcomes neoclassic epistemological holdups and may increase the predictive power of computational economics, by letting an artificial agent's knowledge evolve by itself, irrespective of globally specified goals or individual motives of behavior; using simultaneous (or parallel) genetic algorithms (GA) to evolve a single agent's learning strategy, each GA with different general specifications, in a multiagent setting. © 2006 Wiley Periodicals, Inc. Complexity 11: 12–19, 2006