@article {Li49, author = {Feng Li}, title = {Option Pricing}, volume = {7}, number = {4}, pages = {49--65}, year = {2000}, doi = {10.3905/jod.2000.319134}, publisher = {Institutional Investor Journals Umbrella}, abstract = {We have long understood that the lognormal distribution for stock returns does not adequately capture the way options are priced I the market. The existence of fat tails, a persistent implied volatility smile or skew, and other discrepancies is well-established empirically. One solution is simply to fit a general shape to the implied density function using non-parametric methods. This essentially allows any kind of irregularity in the distribution as dictated by the data, with little input from the user as to what {\textquotedblleft}reasonable{\textquotedblright} shapes might be. Another approach, which puts more structure on the problem while allowing the distribution with different skewness, kurtosis, and higher moments than the lognormal. A variety of alternative distributions have also been explored in the literature. Li presents a horse race among models from a family that nests the common ones and contains a number of more general ones to see which one provides the best and the most reliable fit for options on the S\&P 500 index. Looking at both in-sample fit and out-of-sample forecasting ability, the winners are skewed t distributions, with the most general formulation working best, except for longer-period out-of-sample prediction. Among the {\textquotedblleft}also-rans,{\textquotedblright} Li finds that performance is improved more by fitting the non-lognormal skewness of the implied distribution than its kurtosis.}, issn = {1074-1240}, URL = {https://jod.pm-research.com/content/7/4/49}, eprint = {https://jod.pm-research.com/content/7/4/49.full.pdf}, journal = {The Journal of Derivatives} }