美式回望期权定价的有限元超收敛分析

考虑美式回望看跌期权的有限元方法．在把原问题转化成等价的变分不等式的基础上,研究了半离散格式在L^2和L^∞范数意义下的最优误差估计．此外,为了进一步提高逼近解的精度,借助超收敛分析技术和插值后处理方法,研究了H^1范数意义下的整体超收敛以及后验误差估计。     

基于CEV过程带交易费的脆弱期权定价的数值算法

主要研究基于CEV过程且支付交易费的脆弱期权定价的数值计算问题.首先通过构造无风险投资组合,导出了基于CEV过程且支付交易费用的脆弱期权定价的偏微分方程模型;其次应用有限差分方法将定价模型离散化,并设计数值算法;最后以看跌期权为例进行数值试验,分析各定价参数对看跌期权价值的影响.     

Optimal investment under operational flexibility, risk aversion, and uncertainty

Traditional real options analysis addresses the problem of investment under uncertainty assuming a risk-neutral decision maker and complete markets. In reality, however, decision makers are often risk averse and markets are incomplete. We confirm that risk aversion lowers the probability of investment and demonstrate how this effect can be mitigated by incorporating operational flexibility in the form of embedded suspension and resumption options. Although such options facilitate investment, we find that the likelihood of investing is still lower compared to the risk-neutral case. Risk aversion also increases the likelihood that the project will be abandoned, although this effect is less pronounced. Finally, we illustrate the impact of risk aversion on the optimal suspension and resumption thresholds and the interaction among risk aversion, volatility, and optimal decision thresholds under complete operational flexibility.     

An option-based revenue management procedure for strategic airline alliances

An airline has to decide whether to accept an incoming customer request for a seat in the airplane or to reject it in hope that another customer will request the seat later at a higher price. Capacity control, as one of the instruments of revenue management, gives a solution to this decision problem. In the presence of strategic alliances capacity control changes. For the case of two airlines in the alliance and a single flight leg we propose an option-based capacity control process. The determination of booking limits for capacity control is done with real options. A simulation model is introduced to evaluate the booking process of the partner airlines within the strategic alliance, considering the option-based procedure. In an iterative process the booking limits are improved with simulation-based optimization. The results of the option-based procedure will be compared with the results of the simulation-based optimization, the results of a first-come-first-served (FCFS) approach and ex post optimal solutions.     

Operational asset replacement strategy: A real options approach

This paper analyses the problem of replacement by investigating the optimal moment of investment replacement in a given tax environment with a given depreciation policy. An operation and maintenance cost minimization model, based on the definition of equivalent annual cost, is applied to a real options paradigm. The developed methodology allows for an innovative evaluation of the flexibility of replacement process analysis. A new two-factor evaluation function is introduced to quantify decisions on asset replacement under a unique cycle environment. This study improves upon previous findings in the literature as it accounts for autonomous salvage value processes. Based on partial differential equations, this model achieves a general analytical solution and particular numerical solution. The results differ significantly from those observed in one-factor models by showing evidence of over-evaluation in optimal levels of replacement, and by confirming suspicions that different types of uncertainties produce non-monotonous effects on the optimal replacement level. The scientific contribution of this study lies in new and stronger approaches to equivalent annual cost literature, supplying an algorithm for operation and maintenance cost minimization that is conditioned by autonomous salvage value. This study also contributes to the real options literature by developing a two-factor model with Brownian processes applied to asset replacement.     

跳跃扩散下双障碍期权定价的数值解

提出了一种求解带有跳跃的双障碍期权定价模型的数值方法.算法采用了Crank-Nicolson 有限差分格式和复化梯形公式对模型进行离散,对离散后的线性系统采用GMRES迭代法求解,并且构造了一个新的预处理算子以加速迭代法的收敛.数值实验验证了该方法能快速求解模型并达到二阶收敛精度.     

Valuing the flexibility of investing in security process innovations

In this paper, we develop a decision model of a firm’s optimal strategy for investment in security process innovations (SPIs) when confronted with a sequence of malicious attacks. The model incorporates real options as a methodology to capture the flexibility embedded in such investment decisions. SPIs, when seamlessly integrated with the organization’s overall business dynamics, induce organizational learning and provide the flexibility of switching to more suitable technologies as the environment of malicious attacks changes. The theoretical contribution of this paper is a mathematical model of the invest-to-learn and switching options generated upon early investment in flexible SPIs. The practical significance of the paper is the application of a binomial lattice model to approximate the continuous-time model, resulting in an easy to use decision aid for managers.     

Applying the maximum NPV rule with discounted/growth factors to a flexible production scale model

This study examines the maximum net present value of the market entry and exit thresholds derived by the traditional net present value method and combines the real options approach for the project investment or disinvestment. The discounted and growth factors are incorporated into the proposed entry and exit models, facilitating the complicated calculations required to identify the discounted and growth rates so as to assess and determine the expected present value of uncertain cash flow streams. Consequently, this investigation successfully combines applying the maximum net present value method and the real options approach to decision-making with the simple consideration of the discounted and growth factors in the flexible production scale model.     

The determinant of production entry and exit model on financing behavior

This study seeks for equity/debt values and the relevant potential firm value with financing or not when the real options approach is assessed. The paper deals with the following relative problems: (1) the assessment rule of decision whether to stop production or not; (2) whether the (dis) investment cost or salvage could reflect the production scale; (3) whether the rate of capital cost or the rate of return in different stages could reflect the suitable risk premium; (4) when the investment cost, exit cost, and salvage are the linear functions of production volume and follow the geometric Brownian motion to analyze the optimum external financing behavior and to decide the production thresholds of production entry and exit.     

Processing process: The Gilbreath conjecture

There is one very important aspect of history that is often left out - the process. The development of the Gilbreath conjecture is described as an example of this issue. This includes a theorem that delineates the possible series of integers satisfying the conditions of the conjecture. Those who do not learn from history are destined to have less options. Processing a process can suggest relevant questions, it will increase our options - which is an important part of any exploration.