G-期望框架下的指数O-U期权定价模型
Index O-U Option Pricing Model under G-Expectation Framework
摘要: 本文基于G-期望空间理论和指数O-U (Ornstein-Uhlenback)过程模型，将指数O-U过程推广到G-期望空间，在股价预期收益率波动的基础上，使模型更加广泛地适用于概率测度还无法确定的情况，推导出G-期望空间下的O-U过程模型的股票价格公式以及期权定价公式，使股票模型更贴近且反映金融市场实际情况。
Abstract: Based on the G-expectation space theory and the Ornstein-Uhlenback process model, the index O-U process is extended to the G-expectation space. Based on the volatility of stock price expected returns, the model is more widely applicable to situations where probability measures cannot be determined. The stock price formula and option pricing formula of the O-U process model in the G-expectation space are derived, making the stock model closer to and reflecting the actual situation of the financial market.
文章引用：江继祥. G-期望框架下的指数O-U期权定价模型[J]. 理论数学, 2024, 14(4): 91-97. https://doi.org/10.12677/pm.2024.144114

参考文献

[1] Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-654. [Google Scholar] [CrossRef] 
[2] Peters, E.E. (1989) Fractal Structure in the Capital Markets. Financial Analysts Journal, 45, 32-37. [Google Scholar] [CrossRef] 
[3] Torres-Hernandez, A., Brambila-Paz, F. and Torres-Martínez, C. (2021) Numerical Solution Using Radial Basis Functions for Multidimensional Fractional Partial Differential Equations of Type Black-Scholes. Computational and Applied Mathematics, 40, Article No. 245. [Google Scholar] [CrossRef] 
[4] Wang, J., Wen, S., Yang, M. and Shao, W. (2022) Practical Finite Difference Method for Solving Multi-Dimensional Black-Scholes Model in Fractal Market. Chaos, Solitons & Fractals, 157, Article ID: 111895. [Google Scholar] [CrossRef] 
[5] Perelló, J., Sircar, R. and Masoliver, J. (2008) Option Pricing under Stochastic Volatility: The Exponential Ornstein-Uhlenbeck Model. Journal of Statistical Mechanics: Theory and Experiment, 6, P06010. [Google Scholar] [CrossRef] 
[6] Dai, L., Fu, Z. and Huang, Z. (2017) Option Pricing Formulas for Uncertain Financial Market Based on the Exponential Ornstein-Uhlenbeck Model. Journal of Intelligent Manufacturing, 28, 597-604. [Google Scholar] [CrossRef] 
[7] Gao, Y., Yang, X. and Fu, Z. (2018) Lookback Option Pricing Problem of Uncertain Exponential Ornstein-Uhlenbeck Model. Soft Computing, 22, 5647-5654. [Google Scholar] [CrossRef] 
[8] Peng, S. (2007) G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type. Stochastic Analysis and Applications, 2, 541-567. [Google Scholar] [CrossRef] 
[9] Avellaneda, M., Levy, A. and Parás, A. (1995) Pricing and Hedging Derivative Securities in Markets with Uncertain Volatilities. Applied Mathematical Finance, 2, 73-88. [Google Scholar] [CrossRef] 
[10] Epstein, L.G. and Ji, S. (2013) Ambiguous Volatility and Asset Pricing in Continuous Time. The Review of Financial Studies, 26, 1740-1786. [Google Scholar] [CrossRef] 
[11] 陆允生, 刘莹莹. 由G-布朗运动驱动的某些欧式期权的定价[J]. 苏州科技学院学报(自然科学版), 2014, 31(3): 6-9.
[12] 王瑶. G-期望下的比较定理与亚式期权定价问题的研究[D]: [硕士学位论文]. 南京: 南京理工大学, 2018.
[13] Peng, S. (2008) Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation. Stochastic Processes and Their Applications, 118, 2223-2253. [Google Scholar] [CrossRef] 
[14] Hu, M., Ji, S. and Xue, X. (2019) The Existence and Uniqueness of Viscosity Solution to a Kind of Hamilton-Jacobi-Bellman Equation. SIAM Journal on Control and Optimization, 57, 3911-3938. [Google Scholar] [CrossRef] 

为你推荐