Pathwise superhedging for time-dependent barrier options on càdlàg paths—Finite or infinite tradeable European,One-Touch,lookback or forward starting options

We establish pathwise duality using simple predictable trading strategies for the robust hedging problem associated with a barrier option whose payoff depends on the terminal level and the infimum of a càdlàg strictly positive stock price process, given tradeable European options at all strikes at a single maturity. The result allows for a significant dimension reduction in the computation of the superhedging cost, via an alternate lower-dimensional formulation of the primal problem as a convex optimization problem, which is qualitatively similar to the duality which was formally sketched using linear programming arguments in Duembgen and Rogers [10] for the case where we only consider continuous sample paths. The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn–Banach theorem. We later adapt this result to include additional tradeable One-Touch options using the Kertz and Rösler (1990) condition. We also compute the superhedging cost when in the more realistic situation where there is only finite tradeable European options; for this case we obtain the full duality in the sense of quantile hedging as in Soner (2015), where the superhedge works with probability $1?\epsilon$ where $\epsilon$ can be arbitrarily small), and we obtain an upper bound for the true pathwise superhedging cost. In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes. This set up is designed to approximate the more realistic situation where we have a finite number of tradeable Europeans at both maturities plus a finite number of tradeable forward starting options.¹     

时间敏感选项依赖下的基础设施恢复决策研究

突发事件发生后,基础设施之间的恢复依赖为恢复过程带来了严重挑战。为了能够在突发事件后高效而有序的实现基础设施恢复运行,根据相互之间的恢复依赖关系制定合理的恢复决策非常关键。本文基于网络流理论,以累积恢复效能最大化为目标,建立了时间敏感选项依赖下的恢复设计与调度决策混合整数规划模型。然后,讨论了模型在完全中心化、完全分散和信息共享决策环境下的应用方法。最后,通过真实基础设施数据集测试了模型,结果表明:(1)该模型在突发事件后的基础设施恢复决策中具有应用可行性;(2)决策环境显著影响存在恢复依赖的基础设施网络整体累积恢复效能;(3)与完全分散决策环境相比,在信息共享决策环境下独立决策的整体累积恢复效能可以得到大幅提升。     

Socially responsible merchant operations: Comparison of shutdown-averse CVaR and anticipated regret policies

Commodity and energy production assets are managed as real options on market uncertainties. Social impacts of plant shutdowns incentivize balancing asset value with shutdown probability. We propose new shutdown-averse policies based on the popular dynamic conditional value-at-risk (CVaR). We analytically and numerically compare these policies to known shutdown-averse policies based on anticipated regret (AR). Our findings support the use of AR over CVaR to embed shutdown-aversion and the consideration of hybrid policies that are asymptotically time-consistent but easily interpretable.     

基于非对称漂移双gamma跳-扩散过程的创新幂型期权定价模型

针对假设股价的对数收益率布朗运动在期权定价时产生的无法解释股价对数收益率的尖峰厚尾和序列相关性的缺陷,采用了Zhang提出的非对称漂移双gamma跳-扩散过程来描述资产(股价)的对数收益率运动形态(该过程是kou提出的双指数跳-扩散过程的推广),并利用Esscher风险中性变换,研究了幂型期权的定价公式.还设计了两种创新的幂型期权,在非对称漂移双gamma跳-扩散过程下给出了相应的定价公式.     

非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

Arithmetic Brownian motion and real options

We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.     

Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

基于加权可能性均值的亚式期权模糊定价

主要探讨不确定环境下用模糊集理论处理亚式期权的定价问题.运用梯形模糊数来表示标的资产价格、无风险利率、红利率和波动率,建立了亚式期权的加权可能性均值模糊定价模型,得到连续几何和算术亚式期权的模糊价格公式.最后通过数值例子表明:亚式期权的加权可能性均值模糊定价模型具有很大的灵活性,更符合现实的不确定情况,具有较强的实用价值.     

Hurst指数属于(1/3,1/2)的分数模型的期权定价

本文建立了由一类分数Brown运动驱动的新的随机微分方程模型,当基础资产价格运动服从该随机微分方程时,推导出了欧式期权的解析公式.