By Adding The Cost Parameters Of The Optimal Cvar Derivative Portfolio

The objective of this paper is the CVaR risk measurement for a portfolio of derivatives. We analyze the problem of computing the optimal CVaR portfolios. In order to find out a more reasonable optimal portfolios, a cost parameter is added to the optimal target function, which is also the most important point of this paper.Value at risk (VaR) and conditional value at risk (CVaR) are the most frequently used risk measures in current risk management practice. As an alternative to VaR, CVaR is attractive since it is a coherent risk measure.We illustrate the CVaR minimization problems for derivatives portfolios are typically ill-posed. For example, the VaR and CVaR minimizations based on delta-gamma approximations of the derivative values typically have an infinite number of solutions.We propose to include cost as an additional preference criterion for the CVaR optimization problem. We demonstrate that, with the addition of a proportional cost, it is possible to compute an optimal CVaR derivative investment portfolio with significantly fewer instruments and comparable CVaR and VaR.