This study focuses on the usefulness of implied risk neutral distributions. We
compare the empirical performance of the Black and Sholes 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, differences between
each model are not so large, but the Black and Sholes model is better than two
lognormal mixture model, especially in the long term.

