论文标题
在半锁定选项中集成的数值方面的定价公式，用于随机波动跳跃扩散模型
Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models
论文作者
论文摘要
在数学金融中，校准随机波动率（SV）选项定价模型的过程涉及依赖几个模型参数的积分的数值计算。此优化任务包括大量的积分评估，具有高精度和低计算时间要求。但是，对于某些模型参数，许多数值正交层无法满足这些要求。我们可以观察到功能评估，严重的精确问题以及计算时间的显着增加。在本文中，我们对这些问题进行数值分析，并表明它们尤其是由不准确评估的集成媒体引起的。我们提出了一种快速的制度切换算法，该算法说明它是否足以评估标准双算术中的集成，或者必须使用更高的精度算术。我们对典型的SV模型和不同参数值进行比较并建议数值四倍，尤其是对于有问题的情况。
In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of large number of integral evaluations with high precision and low computational time requirements. However, for some model parameters, many numerical quadrature algorithms fail to meet these requirements. We can observe an enormous increase in function evaluations, serious precision problems and a significant increase of computational time. In this paper we numerically analyse these problems and show that they are especially caused by inaccurately evaluated integrands. We propose a fast regime switching algorithm that tells if it is sufficient to evaluate the integrand in standard double arithmetic or if a higher precision arithmetic has to be used. We compare and recommend numerical quadratures for typical SV models and different parameter values, especially for problematic cases.
