Multidimensional binary markets and CC-VaR

The work further investigates the problems of using the continuous VaR-criterion (CC VaR) in financial markets. It deals with some technical problems arising in multidimensional markets — markets generated by several stochastically connected underliers. The multidimensional extension of binary markets, a simplified markets variant of traditional options such as calls and puts, is considered. They are also the simplest extension of scenario markets in discrete-on-instruments markets. Based on the supposition that scenario indicators are not fully traded in the market directly, an approach to replicating such indicators by binary instruments is suggested. This approach is based on the parity theorems for one-dimensional markets. It is formed for multidimensional markets and is described in details for two-dimensional markets. The constructions of bases for both single-type versions and the natural mixed version with a fixed market center are given. The theoretical constructions with optimal portfolios representations in these bases are illustrated on the example of a specific two-dimensional market.