Markets never give in: an asset price bubble analysis

Abstract

This thesis aims to analyze asset price bubbles, where we developed, in Chapter I, a brief historical crashes description and a bibliometric analysis of 2,494 articles. In Chapter II, we studied the presence of financial bubbles in fifty stocks that constitute the S&P 500 index, using the generalized augmented Dickey-Fuller (GSADF) test proposed by Phillips et al. (2011, 2015). We found one hundred six bubbles in fifteen assets and detected that in the last decade (2010-2020), there is an increasing pace of this phenomenon. In Chapter III, we developed the ability of the Normal Inverse Gaussian distribution (NIG) to fit the returns of eight stocks where we found in the previous chapter at least one bubble-type behavior in the period from January 3, 2000, to December 31, 2009 (1P), and from January 4, 2010, to April 29, 2020 (2P). For the first period, the NIG could fit the mentioned segment; therefore, we estimate at different levels of confidence the VaR and CVaR for the in-sample-data (1P). We took the maximum expected loss and shortfall values and applied them to the out-of-the-sample (2P). In conclusion, we obtained a good adjustment to the second period (2P) and found the NIG differences compared to the Generalized Hyperbolic (GH) are just marginal. At the same time, we benefit the NIG is close under convolution and minor computational effort evaluation. In Chapter IV, we implemented a model-based clustering method of the Gaussian mixture model to categorize previously identified asset price bubbles and three dropdown scenarios of the S&P 500 index for 2020. We took an approach based on the price-driven identification: bubble size and crash size. We obtained different Gaussian cluster models and concluded that the Gaussian mixture model is a gold standard for further investigations. Finally, in Chapter V, we developed the previous chapters' final remarks that include all supervisors' valuable feedback.