Multidimensional butterflies in problems of optimization on CC-VaR

G. A. Agasandyan

Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The work continues studying problems of using continuous VaR-criterion (CC-VaR) in financial markets. Again some technical problems are concerned. However, they emerge this time not in multidimensional relatively simple binary markets but in multidimensional markets that are an extension of one-dimensional traditional markets of options such as calls and puts. In assumption that scenario butterflies are not traded in markets directly, a method of receiving their replication from multidimensional options, i. e., $\alpha$-options, is developed. It is based on options parity theorems and can be applied to markets of arbitrary dimension, but actual realization is conducted for two-dimensional markets. The bases constructions in terms of $\alpha$-options both one-type and natural mixed with selected market center are produced. Theoretical representations of optimal portfolios in these bases accompanied with the payoffs diagram are illustrated by the distinctive example of a two-dimensional market.

Keywords: underliers, multidimensional market, investor's risk preferences function, continuous VaR-criterion, cost and forecast densities, scenario indicators, bases, binary options, one-type portfolio, market center, mixed portfolio.

Received: 09.03.2022

DOI: 10.14357/19922264230114