随机波动率跳扩散模型半闭期权定价公式积分的数值问题
Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models
摘要：
在数学金融学中，将随机波动率（SV）期权定价模型校准到真实市场数据的过程涉及依赖于多个模型参数的积分的数值计算。该优化任务由大量的积分评估组成，具有高精度和低计算时间要求。然而，对于某些模型参数，许多数值求积算法不能满足这些要求。我们可以观察到函数求值的大量增加，严重的精度问题和计算时间的显着增加。在本文中，我们数值分析这些问题，并表明，他们特别是造成不准确的评估被积。我们提出了一个快速的政权切换算法，告诉它是否足以评估被积在标准的双重算术，或者如果一个更高的精度算法必须使用。我们比较和推荐典型的SV模型和不同的参数值，特别是有问题的情况下，数值求积。
英文摘要：
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.
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