Predictive Power of the Volatility Smile
Abstract: The Black-Scholes option pricing formula yield lower volatility than volatility observed in the market when looking at option prices. Several theories have been presented to explain this phenomenon and how the world of finance can use this information. Parameterized volatility smile coefficients have been examined in several recent studies but the findings are inconclusive and the alleged predictive power of the smile has not yet been fully understood or proved. We contribute to the field of forecasting finance by proposing a model where coefficients from a parameterized volatility smile contain information that predict the probability and amplitude of geometric Brownian motion jump diffusion. Using S&P 500 options- and index data from 2006 to 2011 we found a negative relationship between curvature on the volatility smile and jump risk indicating that the smaller curvature on the volatility smile, the higher the probability for positive asset price jumps and vice versa.
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