Asset Price Bubbles: An Option-based Indicator
Asset Price Bubbles: An Option-based Indicator
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资产价格泡沫：基于期权的指标
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Simon
中科院分区：
文献类型：
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作者：
Petteri Piiroinen;L. Roininen;Tobias Schoden;M. Simon
本文基于普通看跌期权和看涨期权的买入和卖出报价信息量，构造了一个短期资产价格泡沫检测的统计指标。我们的构造利用了资产价格泡沫的鞅理论，以及资产价格超过其基本价值的情况原则上可以通过分析隐含波动率表面的渐近行为来检测的事实。为了外推隐含波动率，我们选择SABR模型，主要是因为它非常适合真实的期权市场报价，适用于各种到期日，并且易于校准。作为主要的理论结果，我们表明，在对数正态SABR动力学，我们可以计算一个简单而强大的封闭形式的鞅亏损指标通过解决一个不适定的逆校准问题。为了科普不适定性和量化的不确定性，这是固有的这样一个指标，我们采用贝叶斯统计参数估计的角度来看。我们探测后验密度与优化和自适应马尔可夫链蒙特卡罗方法的组合，从而提供了一个全面的不确定性估计的所有基本参数和鞅缺陷指标。最后，我们提供了对拟议的基于期权的指标的真实市场测试，重点是科技股，因为人们越来越担心科技泡沫2.0。
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale theory of asset price bubbles and the fact that such scenarios where the price for an asset exceeds its fundamental value can in principle be detected by analysis of the asymptotic behavior of the implied volatility surface. For extrapolating this implied volatility, we choose the SABR model, mainly because of its decent fit to real option market quotes for a broad range of maturities and its ease of calibration. As main theoretical result, we show that under lognormal SABR dynamics, we can compute a simple yet powerful closed-form martingale defect indicator by solving an ill-posed inverse calibration problem. In order to cope with the ill-posedness and to quantify the uncertainty which is inherent to such an indicator, we adopt a Bayesian statistical parameter estimation perspective. We probe the resulting posterior densities with a combination of optimization and adaptive Markov chain Monte Carlo methods, thus providing a full-blown uncertainty estimation of all the underlying parameters and the martingale defect indicator. Finally, we provide real-market tests of the proposed option-based indicator with focus on tech stocks due to increasing concerns about a tech bubble 2.0.