Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing

The path-breaking work of Black and Scholes (1973) initiated the development of the modern option pricing theory. It is based on the so-called geometric Brownian motion as a model for the underlying price process. This process implies that the log returns - i. e. the difference of the logarithm of consecutive prices-follow a normal distribution features like skewness or heavy tails which cannot be captured by normal distribution.