Optimal Risk Management Using Options

This paper addresses the question of how an institution might optimally manage the market risk of a given exposure. We provide an analytical approach to optimal risk management under the assumption that the institution wishes to minimize its Value-at-Risk (VaR) using options follows a geometric Brownian. The optimal solution specifies the VaR-minimizing level of moneyness of the option as a function of the asset's distribution, the risk-free rate, and the VaR hedging period. We find that the optimal strike of the put is independent of the level of expense the institution is willing to incur for its hedging program