Performance estimations for optimal-on-CC-VaR portfolios in option markets

The paper continues investigations of the author about using continuous VaR-criterion (CC-VaR) in financial markets. The problem of projecting ideas and methods elaborated for investments in the ideal theoretical one-period market and its discrete scenario analog onto a discrete-in-strikes option market is considered. The main focus is on the methods of calculating distribution function of income and return relative, and also their mean for option portfolios optimal on CC-VaR and their randomized versions, both full and partial. A discrete optimization algorithm as the result of projecting the theoretical algorithm based on the Newman–Pearson procedure onto scenario market is suggested. The optimal vector of weights derived from this algorithm is applied to the basis of normalized simplest butterflies. If randomizing portfolios are admissible, then special algorithms based on the ideas of the Monte-Carlo method that determine distribution functions of income and return relative are suggested. The exposition is illustrated by examples with beta-distributed underlier's prices and investor's probability forecast, which deal with the problems of volatility selling and buying. The respective diagrams are adduced.