Option pricing and uncertainties in the Black-Scholes model

Abstract

The pricing of European call options traded on the Chicago Board of Options Exchange (CBOE) is studied in the Black-Scholes model. A method for treating uncertainties in option prices based on the propagation of uncertainties is presented. Practically implementable formulas for the uncertainties are derived. The Black-Scholes prices with uncertainties are compared to SPX options, where the underlying asset is the Standard\&Poor 500 index consisting of 500 large US based companies, sold on the CBOE. Possible arbitrage opportunities for certain strike prices and maturities are found, showing that real markets may have pricing issues.