英文标题：
《Option Pricing Accuracy for Estimated Heston Models》
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作者：
Robert Azencott, Yutheeka Gadhyan, Roland Glowinski
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最新提交年份：
2015
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英文摘要：
  We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$, estimation errors do impact the classical option pricing PDEs. We estimate these option pricing errors by combining numerical evaluation of estimation errors for Heston SDEs parameters with the computation of option price partial derivatives with respect to these SDEs parameters. This is achieved by solving six parabolic PDEs with adequate boundary conditions. To implement this approach, we also develop an estimator $\\hat \\lambda$ for the market price of volatility risk, and we study the sensitivity of option pricing to estimation errors affecting $\\hat \\lambda$. We illustrate this approach by fitting Heston SDEs to 252 daily joint observations of the S\\&P 500 index and of its approximate volatility VIX, and by numerical applications to European options written on the S\\&P 500 index.
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中文摘要：
我们考虑价格$X_t$和波动率平方$Y_t$由Heston联合随机微分方程（SDE）共同驱动的资产。当这些SDE的参数是从$N$次采样数据$（X_{nT}，Y_{nT}）$估计时，估计误差确实会影响经典的期权定价偏微分方程。我们通过结合赫斯顿SDEs参数估计误差的数值评估和关于这些SDEs参数的期权价格偏导数的计算来估计这些期权定价误差。这是通过在充分的边界条件下求解六个抛物线偏微分方程来实现的。为了实现这种方法，我们还开发了波动风险市场价格的估计器$\\hat\\lambda$，并研究了期权定价对影响$\\hat\\lambda$的估计误差的敏感性。我们通过将Heston SDE拟合到标准普尔500指数及其近似波动率VIX的252个每日联合观察值，并通过对标普500指数上的欧洲期权的数值应用来说明这种方法。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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