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首页> 外文期刊>Frontiers in Applied Mathematics and Statistics >Uncertainty of Volatility Estimates from Heston Greeks
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Uncertainty of Volatility Estimates from Heston Greeks

机译：来自赫斯顿希腊人的波动率估计的不确定性

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摘要

Volatility is a widely recognized measure of market risk. As volatility is not observed it has to be estimated from market prices, i.e. as the implied volatility from option prices. The volatility index VIX making volatility a tradeable asset in its own right is computed from near- and next-term put and call options on the S&P 500 with more than 23 days and less than 37 days to expiration and non-vanishing bid. In the present paper we quantify the information content of the constituents of the VIX about the volatility of the S&P 500 in terms of the Fisher information matrix. Assuming that observed option prices are centred on the theoretical price provided by Heston's model perturbed by additive Gaussian noise we relate their Fisher information matrix to the Greeks in the Heston model. We find that the prices of options contained in the VIX basket allow for reliable estimates of the volatility of the S&P 500 with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value of roughly 3%, inferences from option prices become imprecise because Vega, the derivative of a European option w.r.t. volatility, nearly vanishes.
机译：波动率是公认的市场风险度量。由于未观察到波动率，因此必须根据市场价格进行估算，即根据期权价格的隐含波动率进行估算。波动率指数VIX使得波动率本身成为可交易资产，是根据标准普尔500指数的短期和短期看跌和看涨期权来计算的，该期权的到期日和买入价均超过23天且少于37天。在本文中，我们根据Fisher信息矩阵量化了有关标准普尔500指数波动性的VIX成分的信息内容。假设观察到的期权价格集中在Heston模型提供的理论价格上，该理论价格受到加性高斯噪声的干扰，我们将其Fisher信息矩阵与Heston模型中的希腊人联系起来。我们发现，只要波动率足够大，VIX篮子中包含的期权价格就可以可靠地估计S＆P 500的波动率，而不确定性可以忽略不计。有趣的是，如果波动率跌至大约3％的临界值以下，则期权价格的推论就变得不精确，因为欧洲期权权证的衍生工具Vega。波动性几乎消失。

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