On the usefulness of implied risk-neutral distributions – evidence from the Korean KOSPI 200 Index options market

In Joon Kim and Sol Kim

Abstract

ABSTRACT

This study focuses on the usefulness of implied risk-neutral distributions. We compare the empirical performance of the Black and Scholes model, which assumes single lognormal distribution, with that of the option pricing model, which assumes a mixture of two lognormal distributions using three metrics: (1) in-sample performance, (2) out-of-sample performance, and (3) hedging performance. We find that the option pricing formula using the two-lognormal mixture distributions model shows the best in-sample and out-of-sample pricing performance for short-term and long-term forecasting periods. For hedging, the differences between each model are not so large, but the Black and Scholes model is better than the two-lognormal mixture model, especially in the long term.