Thinking by analogy, systematic risk, and option prices

People tend to 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 develop a new option pricing model based on the idea that the market consists of coarse thinkers as well as rational investors when limits to arbitrage (transaction costs) prevent rational investors from profiting at the expense of coarse thinkers. The new formula, which is a closed form solution to the model, is a generalization of the Black-Scholes formula. The new formula potentially provides a unified explanation for various implied volatility puzzles.