Can option pricing models catch the difference?

Abstract

This paper compares alternative options pricing models`` performance and their implications. Stochastic volatility, stochastic interest rate, returns-jump, and volatility jump are added to the BS model. We examine i) In-sample fitting performance with numerical and graphical methods 2) Out-sample performance with the implied volatility consistency and pricing errors 3) Delta hedge performance. Additionally we find that KOSPI 200 index based options had abnormal price gap between call options and put options from year 2000 to 2002. Call options have on average lower implied volatility compared to put options. We investigate if different models can find abnormal price and implied volatility structure with results that doubt the use of put-call parity.