金融资产价格具有“尖峰厚尾”和长期记忆等分形特征,采用具有GARCH结构的时变混合双分数Brown运动可以描述其动态变化过程。首先,构建混合双分数Brown运动下的期权定价模型和时变参数模型;再选取上证50ETF指数、香港恒生指数、日本东...金融资产价格具有“尖峰厚尾”和长期记忆等分形特征,采用具有GARCH结构的时变混合双分数Brown运动可以描述其动态变化过程。首先,构建混合双分数Brown运动下的期权定价模型和时变参数模型;再选取上证50ETF指数、香港恒生指数、日本东证指数的历史收盘价进行实证分析,并与传统的BS模型、混合双分数Brown运动定价等模型进行对比研究。结果发现:时变混合双分数Brown运动下的欧式期权定价模型在期权定价精度方面具有明显优势,特别是在发达证券市场上表现更好,同时具有较强的预测能力。对金融衍生品、风险管理、投资管理等方面都具有一定的参考意义和实用价值。Financial asset prices have fractal characteristics such as “sharp peaks and thick tails” and long-term memory, and its dynamic process can be described by the time-varying mixed double-fractional Brownian motion with GARCH structure. Firstly, the option pricing model and the time-varying parameter model are constructed under the hybrid two-fractional Brown’s motion;then, the historical closing prices of SSE 50 ETF index, Hong Kong Hang Seng index, and Japan TSE index are selected for the empirical analysis, and compared with the traditional BS model and the hybrid two-fractional Brown’s motion pricing model. The results show that the European option pricing model with time-varying hybrid bifractional Brownian motion has obvious advantages in terms of option pricing accuracy, especially in the developed stock markets, and has strong forecasting ability. It has certain reference significance and practical value for financial derivatives, risk management and investment management.展开更多
土壤系统经常表现出复杂的性质并导致溶质迁移的异常扩散。基于Skaggs等人的模型,本文研究开发蒸腾和根系吸水条件下的时间分数阶对流扩散方程(FADE)模型,以模拟根区的异常扩散并进行解析求解。模拟表明,时间分数阶对流扩散模型与整数...土壤系统经常表现出复杂的性质并导致溶质迁移的异常扩散。基于Skaggs等人的模型,本文研究开发蒸腾和根系吸水条件下的时间分数阶对流扩散方程(FADE)模型,以模拟根区的异常扩散并进行解析求解。模拟表明,时间分数阶对流扩散模型与整数阶对流扩散模型的数值结果在表面土壤附近出现偏差,随后随着时间的推移逐渐向下移动,偏差随深度逐渐扩大,较小的α对应较高的浓度曲线,说明土壤中溶质储层较强,导致溶质运移速度较慢,即存在亚扩散。Soil systems often exhibit complex properties and lead to abnormal diffusion of solute transport. Based on the model of Skaggs et al., this paper develops a time fractional advection-diffusion equation (FADE) model under transpiration and root water absorption conditions to simulate abnormal diffusion in the root zone and solves it analytically. The simulation shows that the numerical results of the time fractional advection-diffusion model and the integer advection-diffusion model deviate near the surface soil, and then gradually move downward with time. The deviation gradually expands with depth, and the smaller one corresponds to a higher concentration curve, indicating that the solute reservoir in the soil is strong, resulting in a slower solute migration rate, that is, there is sub-diffusion.展开更多
自Black-Scholes期权定价模型提出以来,大量的期权定价模型被陆续提出并加以研究,成为国内外金融工程和金融数学的研究热点。由于列维过程能够很好地描述资产运动的动力学特征,近年来基于列维过程的期权定价模型吸引了广泛关注,如FMLS(f...自Black-Scholes期权定价模型提出以来,大量的期权定价模型被陆续提出并加以研究,成为国内外金融工程和金融数学的研究热点。由于列维过程能够很好地描述资产运动的动力学特征,近年来基于列维过程的期权定价模型吸引了广泛关注,如FMLS(finite moment log stable)、CGMY和KoBol模型。这些模型最终归结为数值求解一类分数阶偏微分方程。为此提出了求解这类分数阶偏微分方程的数值离散格式,理论分析给出了数值格式稳定的充分条件。数值实验验证数值格式和算法的可行性和有效性。基于上证50与沪深300的股指期权实际交易数据,利用KoBol分数阶模型进行定价并反演计算波动率曲线,进一步验证了KoBol模型在真实市场中的有效性。展开更多
文摘金融资产价格具有“尖峰厚尾”和长期记忆等分形特征,采用具有GARCH结构的时变混合双分数Brown运动可以描述其动态变化过程。首先,构建混合双分数Brown运动下的期权定价模型和时变参数模型;再选取上证50ETF指数、香港恒生指数、日本东证指数的历史收盘价进行实证分析,并与传统的BS模型、混合双分数Brown运动定价等模型进行对比研究。结果发现:时变混合双分数Brown运动下的欧式期权定价模型在期权定价精度方面具有明显优势,特别是在发达证券市场上表现更好,同时具有较强的预测能力。对金融衍生品、风险管理、投资管理等方面都具有一定的参考意义和实用价值。Financial asset prices have fractal characteristics such as “sharp peaks and thick tails” and long-term memory, and its dynamic process can be described by the time-varying mixed double-fractional Brownian motion with GARCH structure. Firstly, the option pricing model and the time-varying parameter model are constructed under the hybrid two-fractional Brown’s motion;then, the historical closing prices of SSE 50 ETF index, Hong Kong Hang Seng index, and Japan TSE index are selected for the empirical analysis, and compared with the traditional BS model and the hybrid two-fractional Brown’s motion pricing model. The results show that the European option pricing model with time-varying hybrid bifractional Brownian motion has obvious advantages in terms of option pricing accuracy, especially in the developed stock markets, and has strong forecasting ability. It has certain reference significance and practical value for financial derivatives, risk management and investment management.
文摘土壤系统经常表现出复杂的性质并导致溶质迁移的异常扩散。基于Skaggs等人的模型,本文研究开发蒸腾和根系吸水条件下的时间分数阶对流扩散方程(FADE)模型,以模拟根区的异常扩散并进行解析求解。模拟表明,时间分数阶对流扩散模型与整数阶对流扩散模型的数值结果在表面土壤附近出现偏差,随后随着时间的推移逐渐向下移动,偏差随深度逐渐扩大,较小的α对应较高的浓度曲线,说明土壤中溶质储层较强,导致溶质运移速度较慢,即存在亚扩散。Soil systems often exhibit complex properties and lead to abnormal diffusion of solute transport. Based on the model of Skaggs et al., this paper develops a time fractional advection-diffusion equation (FADE) model under transpiration and root water absorption conditions to simulate abnormal diffusion in the root zone and solves it analytically. The simulation shows that the numerical results of the time fractional advection-diffusion model and the integer advection-diffusion model deviate near the surface soil, and then gradually move downward with time. The deviation gradually expands with depth, and the smaller one corresponds to a higher concentration curve, indicating that the solute reservoir in the soil is strong, resulting in a slower solute migration rate, that is, there is sub-diffusion.
文摘自Black-Scholes期权定价模型提出以来,大量的期权定价模型被陆续提出并加以研究,成为国内外金融工程和金融数学的研究热点。由于列维过程能够很好地描述资产运动的动力学特征,近年来基于列维过程的期权定价模型吸引了广泛关注,如FMLS(finite moment log stable)、CGMY和KoBol模型。这些模型最终归结为数值求解一类分数阶偏微分方程。为此提出了求解这类分数阶偏微分方程的数值离散格式,理论分析给出了数值格式稳定的充分条件。数值实验验证数值格式和算法的可行性和有效性。基于上证50与沪深300的股指期权实际交易数据,利用KoBol分数阶模型进行定价并反演计算波动率曲线,进一步验证了KoBol模型在真实市场中的有效性。
