This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions...

Let W denote a family of probability distributions with parameter space Τ, and WG be a subfamily of W depending on a mapping G:Θ - Τ. Extremum estimations of the parameter vector ν ∈ Θ are considered. Some sufficient conditions are presented to ensure the uniqueness with probability one....