Coarse thinking, implied volatility, and the valuation of call and put options

People think by analogies and comparisons. Such way of thinking, termed coarse thinking by Mullainathan et al [Quarterly Journal of Economics, May 2008] is intuitively very appealing. We derive a new option pricing formula based on the assumption that the market consists of coarse thinkers as well as rational investors. The new formula, called the behavioral option pricing formula is a generalization of the Black-Scholes formula. The new formula not only provides explanations for the implied volatility skew and term structure puzzles in equity index options but is also consistent with the observed negative relationship between contemporaneous equity price shocks and implied volatility.