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How do financial markets switch from states of optimism to pessimism and vice versa? Given that a financial market is currently stable, what is the probability that it will become unstable and crash? We answer those questions in the context of a natural experiment with risk sources of probability judgment error, i.e. source functions, implied by index option prices. Source functions reflect investors (option traders) sentiments about the ranking of index options' attractiveness and the weight they place on each rank. We introduce a novel behavioural process (hereinafter BELLE), constructed from noise in investors probability judgment, that (1) characterizes investor sentiment about tail events in index option prices over time and probability ranks, (2) provides early warning signals of market instability, and (3) crash probability estimates from a closed form expression for the time varying transition probability that a seemingly stable market state will become unstable and crash. The model makes the fatalistic prediction that over time investor sentiment about index option prices characterize market transition from stable to unstable states and crash almost surely.

Market Instability, Investor Sentiment, and Probability Judgment Error in Index Option Prices