Optimal Liquidity management and Hedging in the presence of a non-predictable investment opportunity

In this paper, we develop a dynamic model that captures the interaction between a firm’s cash reserves, the risk management policy and the profitability of a non-predictable irreversible investment opportunity. We consider a firm that has assets in place generating a stochastic cash-flow stream. The firm has a non-predictable growth opportunity to expand its operation size by paying a sunk cost. When the opportunity is available, the firm can finance it either by cash or by costly equity issuance. We provide an explicit characterization of the firm strategy in terms of investment, hedging, equity issuance and dividend distribution.     

不确定竞争市场投资决策

本文针对不确定的竞争市场 ,分析现在作一个数量为 I的不可逆投资 ,产生一个生产容量 k,以在将来不确定竞争市场中比潜在进入的竞争对手具有某种占先优势这样一个投资机会的策略投资行为和机会的价值。用博奕论方法分析和给出了基于现在投资可获得将来增长期权价值的决策方法。     

随机环境下技术开发和授权的最优策略

技术创新的价值实现需要后续的商业化投资,在随机不确定的市场环境下,创新企业面对着投资或等待、自身开发或技术授权的策略选择.利用实物期权方法建立了市场不确定时的决策模型,分析开发能力、不确定性等多种因素对企业授权的影响,在多种情况下得到企业的最优决策并对相关现象给出了解释.研究发现不确定性提高了企业投资的临界值,提高了企业的技术授权价格,高度的不确定性减少了技术授权的可能,较高的能力差异会促进技术交易.     

A two-level hedging point policy for controlling a manufacturing system with time-delay,demand uncertainty and extra capacity

This paper focuses on the production control of a manufacturing system with time-delay, demand uncertainty and extra capacity. Time-delay is a typical feature of networked manufacturing systems (NMS), because an NMS is composed of many manufacturing systems with transportation channels among them and the transportation of materials needs time. Besides this, for a manufacturing system in an NMS, the uncertainty of the demand from its downstream manufacturing system is considered; and it is assumed that there exist two-levels of demand rates, i.e., the normal one and the higher one, and that the time between the switching of demand rates are exponentially distributed. To avoid the backlog of demands, it is also assumed that extra production capacity can be used when the work-in-process (WIP) cannot buffer the high-level demands rate. For such a manufacturing system with time-delay, demand uncertainty and extra capacity, the mathematical model for its production control problem is established, with the objective of minimizing the mean costs for WIP inventory and occupation of extra production capacity. To solve the problem, a two-level hedging point policy is proposed. By analyzing the probability distribution of system states, optimal values of the two hedging levels are obtained. Finally, numerical experiments are done to verify the effectiveness of the control policy and the optimality of the hedging levels.     

Optimal dividend strategies in a dual model with capital injections

We study three types of practical optimization problems faced by a firm that can control its liquid reserves by paying dividends and by issuing new equity. In the first problem, we consider the classical dividend problem without equity issuance. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of issuing new equity over strategies associated with positive reserves at all times. The third problem has the same objective as the second one, but with no constraints on the reserves. Under the assumption of proportional transaction costs, we identify the value functions and the optimal strategies. We also present the relationship between three problems.     

Irreversible capital accumulation under interest rate uncertainty

We consider the optimal sequential irreversible investment policy of a value maximizing firm facing decreasing returns to scale and interest rate uncertainty. We characterize the optimal accumulation policy and its value for a broad class of diffusion models of the short interest rate by focusing on the marginal investment decision and deriving the marginal value of capital explicitly. We also state a set of conditions under which there is a maximal capital stock above which the option to expand productive capacity further in the future becomes valueless. Hence, our results indicate that interest rate uncertainty may limit the size of an optimally investing firm.     

Hedging with a correlated asset: Solution of a nonlinear pricing PDE

Hedging a contingent claim with an asset which is not perfectly correlated with the underlying asset results in unhedgeable residual risk. Even if the residual risk is considered diversifiable, the option writer is faced with the problem of uncertainty in the estimation of the drift rates of the underlying and the hedging instrument. If the residual risk is not considered diversifiable, then this risk can be priced using an actuarial standard deviation principle in infinitesimal time. In both cases, these models result in the same nonlinear partial differential equation (PDE). A fully implicit, monotone discretization method is developed for solution of this pricing PDE. This method is shown to converge to the viscosity solution. Certain grid conditions are required to guarantee monotonicity. An algorithm is derived which, given an initial grid, inserts a finite number of nodes in the grid to ensure that the monotonicity condition is satisfied. At each timestep, the nonlinear discretized algebraic equations are solved using an iterative algorithm, which is shown to be globally convergent. Monte Carlo hedging examples are given to illustrate the profit and loss distribution at the expiry of the option.     

Hedging under generalized good-deal bounds and model uncertainty

We study a notion of good-deal hedging, that corresponds to good-deal valuation and is described by a uniform supermartingale property for the tracking errors of hedging strategies. For generalized good-deal constraints, defined in terms of correspondences for the Girsanov kernels of pricing measures, constructive results on good-deal hedges and valuations are derived from backward stochastic differential equations, including new examples with explicit formulas. Under model uncertainty about the market prices of risk of hedging assets, a robust approach leads to a reduction or even elimination of a speculative component in good-deal hedging, which is shown to be equivalent to a global risk minimization in the sense of Föllmer and Sondermann (1986) if uncertainty is sufficiently large.     

Duopolistic competition under risk aversion and uncertainty

A monopolist typically defers entry into an industry as both price uncertainty and the level of risk aversion increase. By contrast, the presence of a rival typically hastens entry under risk neutrality. Here, we examine these two opposing effects in a duopoly setting. We demonstrate that the value of a firm and its entry decision behave differently with risk aversion and uncertainty depending on the type of competition. Interestingly, if the leader’s role is defined endogenously, then higher uncertainty makes her relatively better off, whereas with the roles exogenously defined, the impact of uncertainty is ambiguous.     

Quantile Hedging in a semi-static market with model uncertainty

With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test, an arbitrage-free discretization of the market is proposed as an approximation. The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and helps numerical calculation of the quantile hedging price. As the discretization becomes finer, the approximate quantile hedging price converges and the hedging strategy is asymptotically optimal in the original market.     

考虑无缺陷退货的在线商品信息发布策略

消费者网络购物面临的不确定性往往导致非质量原因的退货。合理发布产品信息,并提供退货保障,是网络零售商促进消费者购买和提高利润的有效策略。基于消费者效用理论和博弈论,构建了产品信息影响消费者购买和退货模型,研究了零售商在垄断和竞争情形下的产品信息发布决策问题,发现垄断性零售商的最优信息发布策略和竞争性零售商在发布产品信息量和信息内容方面的均衡策略均取决于产品价值和退货成本特征,提出了不同市场结构下基于产品特征的在线商品信息发布策略。     

Supply chain network equilibrium with strategic financial hedging using futures

In this paper, we develop a network equilibrium model for supply chain networks with strategic financial hedging. We consider multiple competing firms that purchase multiple materials and parts to manufacture their products. The supply chain firms’ procurement activities are exposed to commodity price risk and exchange rate risk. The firms can use futures contracts to hedge the risks. Our research studies the equilibrium of the entire network where each firm optimizes its own operation and hedging decisions. We use variational inequality theory to formulate the equilibrium model, and provide qualitative properties. We provide analytical results for a special case with duopolistic competition, and use simulations to study an oligopolistic case. The analytical and simulation studies reveals interesting managerial insights.     

Capacity expansion and forward contracting in a duopolistic power sector

The surge in demand for electricity in recent years requires that power companies expand generation capacity sufficiently. Yet, at the same time, energy demand is subject to seasonal variations and peak-hour factors that cause it to be extremely volatile and unpredictable, thereby complicating the decision-making process. We investigate how power companies can optimise their capacity-expansion decisions while facing uncertainty and examine how expansion and forward contracts can be used as suitable tools for hedging against risk under market power. The problem is solved through a mixed-complementarity approach. Scenario-specific numerical results are analysed, and conclusions are drawn on how risk aversion, competition, and uncertainty interact in hedging, generation, and expansion decisions of a power company. We find that forward markets not only provide an effective means of risk hedging but also improve market efficiency with higher power output and lower prices. Power producers with higher levels of risk aversion tend to engage less in capacity expansion with the result that together with the option to sell in forward markets, very risk-averse producers generate at a level that hardly varies with scenarios.     

Impact of equity and equality on stability and collusion in a decentralized network

We consider a firm that procures a product from a regular supplier whose production is subject to both supply disruption and random yield risks and a backup supplier whose production capacity requires reservation in advance. Under both deterministic and stochastic demand, we study the impact of the two types of supply risks on the firm’s optimal procurement decisions and the importance of correctly identifying the source of supply risks. We find that if the overall supply risk is unchanged but its main source shifts from random yield to supply disruption, the firm should order more from the regular supplier and reserve less capacity from the backup supplier. Ignoring the existence of supply disruption leads to under-utilization of the regular supplier and over-utilization of the backup supplier. Moreover, we examine the option value of the reserved capacity that is affected by the uncertainty of customer demand. We find that the option value increases/decreases in demand uncertainty if the reservation capacity is exercised after/before demand is realized.     

Application of the fuzzy–stochastic methodology to appraising the firm value as a European call option

The valuing of a firm equity as a call option is a crucial problem in financial decision-making. There are two basic aspects that are studied; contingent claim features (payoff functions) and risk (stochastic process of underlying assets). However, non-preciseness (vagueness, uncertainty) of input data is often neglected. Thus, a combination of risk (stochastic) and uncertainty (fuzzy instruments) could be a useful approach in calculating a firm value as a call option. The Black–Scholes methodology of appraising equity as a European call option is applied. Fuzzy–stochastic methodology under fuzzy numbers (T-numbers) is proposed and described. Fuzzy–stochastic model of appraising a firm equity is proposed. Input data are in a form of fuzzy numbers and result, firm possibility-expected equity value is also determined vaguely as a fuzzy set. Illustrative example is introduced.     

Living on the edge: how risky is it to operate at the limit of the tolerated risk?

This paper studies some of the implicit risks associated with strategies followed by a risk averse investor who maximizes the expected value of his final wealth, subject to a risk tolerance constraint characterized in terms of a convex risk measure such as Conditional Value-at-Risk. Embedded probability measures are uncovered using duality theory; these are used to assess the probability of surpassing a standard Value-at-Risk threshold. Using one of these embedded probabilities, a closed-form measure of the financial cost of hedging the loss exposure associated to the optimal strategies is derived and shown to be, under certain assumptions, a coherent measure of risk.     

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.     

Valuing the option to invest in an incomplete market

This paper considers the impact of entrepreneurial risk aversion and incompleteness on investment timing and the value of the option to invest. A risk averse entrepreneur faces the irreversible decision of when to pay a cost in order to receive a one-off investment payoff. The uncertainty associated with the investment payoff can be partly offset by hedging, but the remaining unhedgeable risk is idiosyncratic. Nested within our incomplete set-up is the complete model of McDonald and Siegel (Q J Econ 101:707–727, 1986) which assumes investment payoffs are perfectly spanned by traded assets. We find risk aversion and idiosyncratic risk erode option value and lower the investment threshold. Our main finding is that there is a parameter region within which the complete and incomplete models give differing investment signals. In this region, the option is never exercised (and investment never occurs) in the complete model, whereas the entrepreneur exercises the option in the incomplete setting. Strikingly, this parameter region corresponds to a negative implicit dividend yield on the payoff, and so this exercise behavior contrasts with conventional wisdom of Merton (Bell J Econ Manage 4:141–183, 1973) for complete markets. Finally, in this parameter region, increased volatility speeds-up investment and option values are not strictly convex in project value, in sharp contrast to the conclusion of standard real options models. The author thanks George Constantinides, Graham Davis, Jerome Detemple, Avinash Dixit, David Hobson, Stewart Hodges, Bart Lambrecht, Andrew Lyasoff, Robert McDonald, Pierre Mella-Barral, Jianjun Miao, Bob Nau (ES discussant), Gordon Sick, James Smith, Stathis Tompaidis, Elizabeth Whalley and Zvi Wiener for their comments. The author also thanks seminar participants at the University of Texas at Austin (2004), Kings College London, the Cornell Finance Workshop, the Oxford-Princeton Finance Workshop, the BIRS Finance Workshop (2004), the Eighth Annual Real Options conference, the Bachelier Finance Society Third World Congress (2004), Princeton University, Boston University, the Fields Institute Toronto, QMF 2004, Warwick Business School, and the Econometric Society Winter Meetings (2006). First version: July, 2004.     

Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives

For many years, the longevity risk of individuals has been underestimated, as survival probabilities have improved across the developed world. The uncertainty and volatility of future longevity has posed significant risk issues for both individuals and product providers of annuities and pensions. This paper investigates the effectiveness of static hedging strategies for longevity risk management using longevity bonds and derivatives (q-forwards) for the retail products: life annuity, deferred life annuity, indexed life annuity, and variable annuity with guaranteed lifetime benefits. Improved market and mortality models are developed for the underlying risks in annuities. The market model is a regime-switching vector error correction model for GDP, inflation, interest rates, and share prices. The mortality model is a discrete-time logit model for mortality rates with age dependence. Models were estimated using Australian data. The basis risk between annuitant portfolios and population mortality was based on UK experience. Results show that static hedging using q-forwards or longevity bonds reduces the longevity risk substantially for life annuities, but significantly less for deferred annuities. For inflation-indexed annuities, static hedging of longevity is less effective because of the inflation risk. Variable annuities provide limited longevity protection compared to life annuities and indexed annuities, and as a result longevity risk hedging adds little value for these products.