The Black-Scholes Formula when Traders are (Only) Sufficiently Rational

Abstract

The Black-Scholes-Merton model assumes that investors form perfectly rational expectations. Given the challenges associated with forming perfectly rational expectations, in reality, traders may only be forming sufficiently rational expectations (expectations that deviate from perfection without creating arbitrage opportunities). In this article, by using recent findings from brain sciences, we adjust the Black-Scholes formula for sufficiently rational expectations. We find that a relatively simple adjustment arises in the Black-Scholes formula (a higher rate replaces the risk-free rate in the call option formula). The adjusted formula generates the implied volatility skew and potentially contributes to a number of well-known option pricing puzzles.