Option Implied Tail Index and Volatility Based on Heavy-tailed Distributions: Evidence from KOSPI 200 Index Options Market

Abstract

This paper compares the option implied tail indexes and volatilities from two option pricing formulas based on heavy-tailed distributions: generalized extreme value (GEV) distribution and generalized logistic (GLO) distribution. Option pricing models based on heavy-tailed distributions with three parameters overcome some well-known drawbacks of the Black–Scholes model when the realized underlying asset returns are not normally distributed. Both GEV-based and GLO-based option pricing formulas extract the implied volatilities successfully, indicating that they are compatible with the Black–Scholes formulas. However, GEV-based pricing model shows more unexpected patterns when extracting the implied tail indexes for put options than GLO-based pricing model including the credit crisis in 2008, implying that GEV-based pricing model is less capable of measuring the market sentiment during the extreme crisis events.