This book describes existing approaches that estimate risk-neutral density functions (RND)implied by option prices and provides an empirical comparison of some of these methods on illustrative basis. The theoretical option-pricing background is well introduced in Chapter 2 and used as foundation for the ongoing discussion of the different estimation procedures in the following chapters. The literature review is comprehensive with respect to the inclusion and discussion of a large number of different estimation procedures. Moreover, this work offers an adequate contribution by applying and comparing existing RND estimation procedures for Euro Stoxx 50 index options.