We considered theoretically Levy Feller distribution function, which is one of the functions that explains anomalous diffusion in statistical physics, including normal diffusion.
As a applicaion of this, we applied it to the stock price return distribution. Especially, we fitted log return distribution of Kospi index which was stored every 1 minimute, during 1995~2000 years, using Levy Feller distribution function. And we obtained α, γ, and the length ,where truncation begins, l, which characterize Levy Feller distribution function. We also found more accurate fitting function of distribution, which explains not only Levy tail, but also truncated tail. Using this, we calculated Kospi 200 index Call option price at 7.7.1997 with varing times to maturity, and strike prices. As a result, we obtained much better result ,when we set the ratio, which changes price to the present value of it, 0 instead of stock price return when stock price return is smaller than 0. And pricing method using AR+GARCH option showed much better performance than Black Scholes option pricing method.
