Why We Have Always Used the Black-Scholes-Merton Option Pricing Formula

Abstract

Derman and Taleb (The Issusions of Dynamic Hedging, 2005) uncover a seeming anomaly in option pricing theory which suggests that static hedging based on put-call parity provides sufficient theoretical support to justify risk-neutral option pricing. From this they suggest that dynamic hedging as a theoretical basis for the celebrated option pricing model of Black and Scholes (1973) and Merton (1973), while correct, is redundant [see also Haug and Taleb (Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula, 2009)]. This paper examines the anomaly and finds that put-call parity does not provide a basis for risk-neutral option pricing.

Keywords: option pricing, put-call parity, dynamic hedging, static hedging, Black-Scholes-Merton

JEL Classification: G12, G13