论文标题
通过解决黑色 - choles方程的解决方案的解决方案来预测股票期权价格
Forecasting Stock Options Prices via the Solution of an Ill-Posed Problem for the Black-Scholes Equation
论文作者
论文摘要
在上一篇论文（反问题，32，015010，2016）中，提出了一种新的启发式数学模型，以准确预测股票期权价格的价格，比目前的股票期间1-2交易天数。这项新技术使用新的间隔提供的黑色 - chleoles方程，用于基础库存以及期权价格的新初始和边界条件。黑色 - choles方程是在时间变量的正方向上求解的，这种不足的初始边界值问题是通过所谓的准可逆性方法（QRM）解决的。该方法具有附加的交易策略的368种股票期权的市场数据，并证明了良好的预测结果。在当前的论文中，我们使用几何布朗运动，使用欧洲呼叫选项的计算模拟数据来解释该效率。我们还为QRM提供了收敛分析。该分析的关键工具是卡尔曼估计。
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the Black-Scholes equation supplied by new intervals for the underlying stock and new initial and boundary conditions for option prices. The Black-Scholes equation was solved in the positive direction of the time variable, This ill-posed initial boundary value problem was solved by the so-called Quasi-Reversibility Method (QRM). This approach with an added trading strategy was tested on the market data for 368 stock options and good forecasting results were demonstrated. In the current paper, we use the geometric Brownian motion to provide an explanation of that effectivity using computationally simulated data for European call options. We also provide a convergence analysis for QRM. The key tool of that analysis is a Carleman estimate.
