一种无风险利率时变条件下的Black-Scholes期权定价模型

本文研究了无风险利率改进的Black-Scholes期权定价模型问题.利用指数函数和Ito公式的方法,获得了一种改进的Black-Scholes期权定价模型,推广了现有Black-Scholes期权定价模型的结果.     

基于实物期权定价方法的林业碳汇项目投资决策仿真研究

文章针对林业碳汇项目投资决策的复杂性、动态性和不确定性过程,利用林业—碳汇共同经营决策模型计算林业碳汇项目在投资期内的期望价值,采用实物期权定价方法对不同阶段不同策略下的林业碳汇项目价值进行评估,同时提出了多主体仿真建模方法,利用NetLogo仿真软件对林业碳汇项目投资决策过程进行动态模拟。仿真系统中涉及到的主体有林地、CO₂和投资者,投资者主要是作为观察者的身份,在不同阶段会做出不同的投资策略。模拟仿真三种不同状态下投资者的决策变化:一是传统林业投资动态模拟,不包含碳汇和期权因素动态模拟;二是引入碳汇市场后的林业投资动态模拟;三是引入碳汇市场和期权后林业投资动态模拟。NetLogo仿真分析结果表明引入碳汇市场可以提高投资者的收益并改变投资者的经营策略,同时引入期权,不仅增加了投资者的积极性而进行扩张投资,还可以更好地发挥林木碳汇功能,体现林业的生态价值及经济价值。     

资产剥离对风险溢价的影响研究

资产剥离会通过改变在位资产的构成而影响总资产风险收益特征。区别于已有研究将资产剥离看作看跌期权的通常做法,本文考虑企业剥离非核心资产并将资源重新聚焦于核心资产的一般情形,将资产剥离决策视作一种交换期权。运用实物期权方法和定价核技术,本文在连续时间框架下分析了资产剥离影响资产风险溢价的理论机理,并利用沪深A股上市公司数据进行实证检验。研究结果表明:资产剥离对资产风险溢价的影响方向取决于非核心和核心两类资产风险溢价的相对大小,影响程度则由两类资产价值占比的差异和交换期权的价值占比共同决定;进一步,等待剥离的决策灵活性会削弱资产剥离的影响;年轻阶段的资产剥离更加可能对风险溢价具有提升作用。     

私募基金规模、申购赎回机制与动态道德风险

运用动态合约理论与实物期权理论研究了私募基金最优激励相容合约的一般特征,考察了基金规模与申购赎回机制对缓解道德风险的作用。结论表明,私募基金最优激励相容合约由投资人的最大预期收益与管理者的最大预期回报共同决定,且购买私募基金类似于做多一种特殊期权,该期权标的资产价格由管理者后续值度量;投资人为激励管理者努力工作而付出的激励成本随基金初始规模或再申购比例递增,而最优基金规模由其边际激励成本与预期边际业绩决定;赎回成本影响投资人的最大预期收益,但对缓解道德风险不具显著作用;适当的业绩抽成可降低道德风险,且业绩抽成与私募基金初始规模或再申购比例在缓解道德风险方面存在一定的替代性。     

欧式幂期权定价模型中参数及隐含波动率的统计特性

研究了欧式幂期权定价公式中价格的渐近无偏估计和隐含波动率估计的统计特性。利用Chaudhury M.M(1989)提出的研究欧式期极定价公式中渐近无偏估计的方法以及隐含波动率求解方法,研究了两种欧式幂型看涨期权定价公式(欧式看涨期权的价值定义分别为m ax(STα-X,0)和m ax(STα-Xa,0)中的隐含波动率的估计的统计特征、幂函数的幂指数选取以及两种幂函数期权定价公式的优劣。Monte-Carlo统计计算的模拟结果说明。幂期权定价公式中幂指数α取值应为α>0,而且欧式看涨期权的价值定义为m ax(STα-Xα,0)更为合理。     

Wasserstein分布鲁棒期权定价

In this paper, the option pricing problem is formulated as a distributionally robust optimization problem, which seeks to minimize the worst case replication error for a given distributional uncertainty set(DUS) of the random underlying asset returns. The DUS is defined as a Wasserstein ball centred the empirical distribution of the underlying asset returns. It is proved that the proposed model can be reformulated as a computational tractable linear programming problem. Finally, the results of the empirical tests are presented to show the significance of the proposed approach.     

Time series model for GLWB with surrender benefit and stochastic interest rate: Dynamic withdrawal approach

This study investigates the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifetime withdrawal benefit (GLWB) rider. VAs are annuities in which the value is linked to a bond and equity sub-account fund. The guaranteed lifetime withdrawal benefit rider regularly provides a series of payments to the policyholder for the term of the policy while he/she is alive, regardless of portfolio performance. At the time of the policyholder's death, the remaining fund value is given to his nominee. Therefore, proper fund modeling is critical in the pricing of VA products. Several writers in the literature used a GBM model in which variance is considered to be constant to represent the fund value in a variable annuity contract. However, on the other hand, the returns on financial assets are non-normally distributed in real life. A bit much Kurtosis, leverage effect, and Non-zero Skewness characterize the returns. The generalized autoregressive conditional heteroscedastic (GARCH) models are also used for presenting a discrete framework for the pricing of GLWB. Still, the interest rate was kept constant without including the surrender benefit and the static withdrawal approach, which keeps the model far from the real scenario. Thus, in this research, the generalized GARCH models are used with surrender benefit and dynamic withdrawal strategy to develop a time series model for the pricing of annuity that overcomes the constraints of previous models. A numerical illustration and sensitivity analysis are used to examine the suggested model.     

Partial differential integral equation model for pricing American option under multi state regime switching with jumps

In this paper, we consider a two dimensional partial differential integral equation (PDIE) model for pricing American option. A nonlinear rationality parameter function for two asset problems is introduced to deal with the free boundary. The rationality parameter function is added in the PDIEs used for pricing American option problems under multi-state regime switching with jumps. The resulting two dimensional nonlinear system of PDIE is then numerically solved. Based on real poles rational approximation, a strongly stable highly efficient and reliable method is developed to solve such complicated systems of PIDEs. The method is build in a predictor corrector style which makes it linearly implicit, therefore, avoids solving nonlinear systems of equations at each time step in all regimes. The method is seen to maintain the stability and convergence for large jump sizes and high volatility in each regime. The impact of regime switching on option prices corresponding to different values interest rate, volatility, and rationality parameter is computed, illustrated by graphs and given in the tables. Convergence results in each regime are presented and time evolution graphs are given to show the effectiveness and reliability of the method.     

New approach and analysis of the generalized constant elasticity of variance model

Generally, it is well known that the constant elasticity of variance (CEV) model fails to capture the empirical results verifying that the implied volatility of equity options displays smile and skew curves at the same time. In this study, to overcome the limitation of the CEV model, we introduce a new model, which is a generalization of the CEV model, and show that it can capture the smile and skew effects of implied volatility. Using an asymptotic analysis for two small parameters that determine the volatility shape, we obtain approximated solutions for option prices in the extended model. In addition, we demonstrate the stability of the solution for the expansion of the option price. Furthermore, we show the convergence rate of the solutions in Monte-Carlo simulation and compare our model with the CEV, Heston, and other extended stochastic volatility models to verify its flexibility and efficiency compared with these other models when fitting option data from the S&P 500 index.     

带跳过程的亚式期权的定价

本文研究了固定敲定价格亚式期权的定价问题.利用Chen和Lyuu[1]的近似分析,获得了完备市场下亚式期权下界的精确表达,推广了文献[4]中的结果到非时齐Poisson跳的广义Black-Scholes模型中,本文模型更符合实际市场规律.