Londoño Jaime A, Sandoval Javier
Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Manizales, Colombia.
Universidad Externado de Colombia, Bogotá, Colombia.
Springerplus. 2015 Dec 9;4:762. doi: 10.1186/s40064-015-1563-9. eCollection 2015.
We propose a family of models for the evolution of the price process [Formula: see text] of a financial market. We model share price and volatility using a two-dimensional system of stochastic differential equations (SDEs) driven by a single Wiener process. We prove that this family of models is well defined and that each model from this family is free of arbitrage opportunities, and it is (state) complete. We use option prices written over the S&P500 from December 2007 to December 2008 to calibrate a model of the proposed family and compare the calibration results with results of the Heston Model for the same data set. The empirical results achieved in both models show similarities for periods of low volatility, but the model studied shows a better performance during the period of higher volatility.
我们提出了一族用于金融市场价格过程[公式：见原文]演变的模型。我们使用由单个维纳过程驱动的二维随机微分方程（SDE）系统对股价和波动率进行建模。我们证明了这族模型定义良好，且该族中的每个模型都不存在套利机会，并且是（状态）完备的。我们使用2007年12月至2008年12月期间基于标准普尔500指数的期权价格来校准所提出族中的一个模型，并将校准结果与同一数据集的赫斯顿模型的结果进行比较。在两个模型中获得的实证结果表明，在低波动率时期两者相似，但所研究的模型在高波动率时期表现更好。
