Value-at-Risk-Based Risk Management Using Options

This paper investigates optimal portfolio and wealth strategy of an institutional investor under the Value-at-Risk (VaR) constraint in an economy under jump diffusion. We show that overlooking or underestimating jump risk factor could be the cause of failure to satisfy the VaR constraint in the recent financial crisis for many financial institutions. We also find that the introduction of the jump risk factor drives the institutional investor to move towards the portfolio insurance strategy, alleviating the problem with VaR identified by Basak and Shapiro (2001) that VaR risk manager incurs larger losses than non risk manager in worst scenarios.