Closed-form valuation of American call options on stocks paying multiple dividends

An American call option on a stock paying a single known dividend can be valued using the Roll–Geske–Whaley formula. This paper extends the Roll–Geske–Whaley model to the n dividends case by using the generalized n-fold compound option model. In this way this paper offers a closed-form solution for American options on stocks paying n known discrete dividends. Moreover, the model also offers the critical values of the early exercise boundaries at each ex-dividend date instant, making it easy to define an early exercise strategy. Numerical examples are included to illustrate this approach.     

项目投资评价中期权理论的应用

本文通过引入期权理论和贝叶斯理论,弥补传统的项目投资决策方法的不足之处,提出了种改进的期望净现值法。     

Evaluation of the MEMM, Parameter Estimation and Option Pricing for Geometric Lévy Processes

In this paper, we shall propose a useful approach to evaluate concretely the MEMM (minimal entropy martingale measure) for the typical geometric Lévy processes such as compound Poisson, stable, VG (Variance Gamma), CGMY (Carr-Geman-Madan-Yor), NIG (Normal Inverse Gaussian), etc. In addition, we shall estimate the parameters of geometric Lévy processes and value the European call option and Asian call option using the Nikkei financial data.     

供应链延迟战略价值定量分析——蒙特卡罗下的奇异期权估价

对延迟战略建立两阶段决策模型，分半成品有无残值两种情况，从实物期权的视角运用金融学中期权定价理论对延迟战略的期权价值进行分析。将生产商传统生产方式下的收益类比为购买标的证券的收益，采用延迟战略的收益类比为标的于该证券的期权收益，并假设产品价格随机游走。通过分析发现延迟战略的收益相当于奇异期权的回报，并且半成品没有残值是存在残值的特殊情况。进一步运用蒙特卡罗模拟方法定量地对延迟战略的期权价值进行参数分析和成本一收益分析。文章将动态的风险管理和对灵活性价值的度量引入决策过程，研究结论能给延迟战略投资决策提供借鉴。     

A Discrete‐Time Intertemporal Asset Pricing Model: GE Approach with Recursive Utility

This paper studies the equilibrium characterization of asset pricing in a discrete‐time Lucas exchange economy (Lucas 1978) with the intertemporal recursive utility function of Epstein and Zin (1989). A general formulation of equilibrium asset pricing is presented. It is shown that risk aversion of a certainty equivalent corresponds to risk aversion in the intertemporal asset pricing model. The discrete‐time analogue of Ma's (1993) option pricing formula is derived in an i.i.d. environment, with which we prove an observational nonequivalence theorem in distinguishing the differences of the betweenness recursive utility functions and the expected utility functions. Additionally, when the consumption growth rate follows a first-order Markov process, it is shown that the observational nonequivalence result holds for Kreps–Porteus expected utility. Finally, as by-products, this paper also contains derivations of closed-form formulas for the aggregate equity (with endogenously determined yields), the term structure of interest rates, and European call options on the aggregate equity in a Markov setting.     

实物期权在高科技企业初创期投资决策中的应用研究

从传统NPV方法在评估高科技企业初创期投资项目评价中的弱势出发,引入实物期权评价法,并针对波动率在估计过程中的误差问题进行敏感性分析,得出战略NPV值随波动率变化的趋势,为高科技企业初创期投资决策提供了一种可行的思路和方法。     

A STATE-SPACE PARTITIONING METHOD FOR PRICING HIGH-DIMENSIONAL AMERICAN-STYLE OPTIONS

The pricing of American-style options by simulation-based methods is an important but difficult task primarily due to the feature of early exercise, particularly for high-dimensional derivatives. In this paper, a bundling method based on quasi-Monte Carlo sequences is proposed to price high-dimensional American-style options. The proposed method substantially extends Tilley's bundling algorithm to higher-dimensional situations. By using low-discrepancy points, this approach partitions the state space and forms bundles. A dynamic programming algorithm is then applied to the bundles to estimate the continuation value of an American-style option. A convergence proof of the algorithm is provided. A variety of examples with up to 15 dimensions are investigated numerically and the algorithm is able to produce computationally efficient results with good accuracy.     

Option Pricing in ARCH-type Models

ARCH models have become popular for modeling financial time series. They seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discrete-time models and possess too much variability. We show that completeness of the market holds for a broad class of ARCH-type models defined in a suitable continuous-time fashion. As an example we focus on the GARCH(1,1)-M model and obtain, through our method, the same pricing formula as Duan, who applied equilibrium-type arguments.     

Restoring Wetlands Through Wetlands Mitigation Banks

This paper offers the first economic analysis of wetlands mitigation banks. The banks are a new alternative for restoration of wetlands by developers before receiving regulatory approval for future development of wetlands in the same watershed. A stochastic optimal control model is developed which incorporates ecological uncertainty of wetlands restoration. The model helps in examining the decisions of how much to invest in a wetlands mitigation bank. The model is calibrated with data from California bioeconomic parameters. Numerical simulation of the model provides a sensitivity analysis of how model parameters of restoration costs, stochastic biological growth, interest rate, and the market value of credits affect the trajectory of investment and the optimal stopping state of wetlands quality when the investment ends. The analysis reveals that restoration of the whole site will occur when there is a reduction in restoration costs, an increase in biological uncertainty or an increase in the value of wetlands credits. Continued restoration is harder to justify with a higher interest rate.