  In this paper we employ deep learning techniques to detect financial asset
bubbles by using observed call option prices. The proposed algorithm is widely
applicable and model-independent. We test the accuracy of our methodology in
numerical experiments within a wide range of models and apply it to market data
of tech stocks in order to assess if asset price bubbles are present. Under a
given condition on the pricing of call options under asset price bubbles, we
are able to provide a theoretical foundation of our approach for positive and
continuous stochastic asset price processes. When such a condition is not
satisfied, we focus on local volatility models. To this purpose, we give a new
necessary and sufficient condition for a process with time-dependent local
volatility function to be a strict local martingale.
