Derivative Portfolio Hedging Based on CVaR

The use of derivatives can lead to higher yields and lower funding costs. In addition, derivatives are indispensable tools for risk management. We analyze the derivative portfolio hedging problems based on value at risk (VaR) and conditional value at risk (CVaR). We show that these derivative portfolio optimization problems are often ill-posed and the resulting optimal portfolios frequently incur large transaction and management costs. In addition, the optimal portfolio may perform poorly under a slight model error. A CVaR optimization model including a proportional cost is proposed to produce optimal portfolios with fewer instruments and smaller transaction cost with similar expected returns and a small compromise in risk. In addition, we illustrate the importance of sensitivity testing of the hedging performance with respect to model error; the optimal portfolio under a suitable cost consideration performs much more robustly with respect to model error. Finally, we discuss computational issues for large scale CVaR optimization problems and consider a smoothing technique which solves a CVaR optimization problem more eÆciently than the standard linear programming methods.