Title: Asset Price Bubbles: An Option-based Indicator,
Abstract: 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.