Value-at-risk-based risk management in a jump-diffusion model

This paper investigates optimal portfolio and wealth strategy of an institutional investor with a Value-at-Risk (VaR) constraint in an economy under jump diffusion. The problem is solved in closed form. We show that overlooking or underestimating jump risk resultsin failures to satisfy the VaR constraint. We also find that the presence of jump risk drives the institutional investor to move towards the portfolio insurance strategy, alleviating the problem with VaR identified by Basak and Shapiro (2001) that the VaR risk manager incurs larger losses than non risk manager in worst scenarios. The demand for put options is driven by the risk-and-return tradeoff. Only when jump risk is not compensated or jumpsizes are very large, the investor takes long positions in put options to hedge against jump risk.