A Closed-form Pricing Solution for Options on Assets with Pricing Errors

Abstract

This paper examines the effects that pricing errors in the underlying asset have on options prices, their Greeks, and their implied risk neutral densities. Pricing errors can be viewed as a random proportional transaction cost. When pricing errors are information-unrelated, options prices are unambiguously higher than the Black-Scholes case and increasing in the pricing error variance. Hedging volatility is higher and the optimal exercise price for American put options is decreased. The option implied risk-neutral density and option Greeks are materially affected, which leads to suboptimal risk management and hedging when pricing errors are not accounted for.

Keywords: Pricing errors, options prices, mathematical finance

JEL Classification: G13