论文标题
通过Hermite基础功能对期权价格的非参数估算
Nonparametric estimates of option prices via Hermite basis functions
论文作者
论文摘要
我们认为，基于近似于对数的返回密度的近似定价公式，通过缩放的HERMITE多项式的线性组合近似对数返回的密度。所得模型可以看作是经典黑色 - choles One的扰动，在某种意义上是非参数的，即仅假定在固定时间到成熟的对数回报的分布仅被认为具有正方形的整体密度。我们广泛研究了根据样本外相对定价误差定义的经验绩效，这类近似模型的定义，具体取决于它们的顺序（即大致说明多项式扩展的程度），以及多种方法来校准它们以观察到数据。经验结果表明，与简单的非参数估计值相比，这种近似定价公式是基于插值和在隐含波动率曲线上外推的外推时，仅对于距离观察到的样品的行动价格不远的选择不太遥远，只有相当出色的选择。
We consider approximate pricing formulas for European options based on approximating the logarithmic return's density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as perturbations of the classical Black-Scholes one, are nonpararametric in the sense that the distribution of logarithmic returns at fixed times to maturity is only assumed to have a square-integrable density. We extensively investigate the empirical performance, defined in terms of out-of-sample relative pricing error, of this class of approximating models, depending on their order (that is, roughly speaking, the degree of the polynomial expansion) as well as on several ways to calibrate them to observed data. Empirical results suggest that such approximate pricing formulas, when compared with simple nonparametric estimates based on interpolation and extrapolation on the implied volatility curve, perform reasonably well only for options with strike price not too far apart from the strike prices of the observed sample.
