On the Rate of Convergence of Discrete‐Time Contingent Claims

This paper characterizes the rate of convergence of discrete‐time multinomial option prices. We show that the rate of convergence depends on the smoothness of option payoff functions, and is much lower than commonly believed because option payoff functions are often of all‐or‐nothing type and are not continuously differentiable. To improve the accuracy, we propose two simple methods, an adjustment of the discrete‐time solution prior to maturity and smoothing of the payoff function, which yield solutions that converge to their continuous‐time limit at the maximum possible rate enjoyed by smooth payoff functions. We also propose an intuitive approach that systematically derives multinomial models by matching the moments of a normal distribution. A highly accurate trinomial model also is provided for interest rate derivatives. Numerical examples are carried out to show that the proposed methods yield fast and accurate results.     

A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets

This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-variance hedging in a class of stochastic volatility models. We explain the theory for both hedging approaches in a general framework, specialize to a Markovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical results are obtained mainly by PDE and simulation methods. In addition, we take special care to check that all of our examples do satisfy the conditions required by the general theory.     

试论股票期权激励的有效性条件

股票期权虽然是美国企业普遍采用的激励经理人员的模式，但是在不同的行业和不同的组织中具有不同的特点。我国企业在推行股票期权激励过程中，应该注意到这只是激励经理人员的一种模式，注意到股票期权的采用是对经理人员薪酬结构的调整，特别要考虑到我国企业所面临的现实环境中还存在着许多不利于股票期权激励模式发挥效率的限制条件。否则，股票期权激励就难以产生预期的效果。     

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.     

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。     

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.     

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.     

Valuing and hedging fixed rate mortgage commitments

A fixed rate loan commitment that is binding on the lender but not on the loan applicant is equivalent to a put option. This article uses the Black-Scholes option pricing model to establish a value for fixed rate loan commitments and to derive the hedge ratio for the lending institution to hedge the interest rate risk associated with the commitments in the FHLMC forward market for mortgages. The effectiveness of the resulting hedge is tested in a simulation, where it is found that the result is a 71% reduction in the variance of the value of the lender's gain or loss associated with the commitment period.     

试论我国上市公司实行经理股票期权的动因及策略

作为薪酬制度的经理股票期权是一种长期激励机制，它将期权长期激励与工资、福利、津贴等短期激励相结合，以使经理人员利益与股东、企业利益相一致。当前我国上市公司推行经理股票期权是必要而可行的，但同时也面临不少障碍。应进一步完善上市公司内部治理结构，建立科学的绩效评价体系，完善法律、政策环境，推进我国上市公司经理股票期权制度的实施。     

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.