INFERRING THE PROBABILITY OF THE FINANCIAL CRISIS: A RISK-NEUTRAL DENSITY APPROACH

Abstract

Option prices reflect the market expectations and uncertainty regarding the future outcomes of the underlying asset. This information can be extracted in the form of a probability distribution known as the risk-neutral density (RND). RND is popularly used to forecast market events and gauge market sentiments The financial crisis in 2007 and 2008 and others before it highlight the importance of early detection of crash risk in financial systems and institutions. In this thesis, we explore the effectiveness of RNDs of S&P 500 index option (SPX) and major financial institutions stock options as a forecasting tool in the context of the recent financial crisis. Specifically, we want to determine if the RNDs could have helped to anticipate the financial crisis and by studying the bankruptcy event of Lehman Brothers, we want to compare the forecasting abilities of the RNDs of the index option and the individual stock options. We find that the RNDs of the SPX and the financial institutions stock options showed heightened uncertainty from July 2007 onwards. We also observe that the RNDs of the options of Lehman Brothers and similar financial institutions appear to forecast the bankruptcy event earlier than the SPX RND. The results indicate that the RNDs are able to capture the tail risks as the financial crisis approached, and it is useful to analyse RNDs at the individual stock option level.