Managing Value at Risk Using Put Options

A natural approach to reducing the risk of a position in stock, is by buying put options on the underlying. We consider a model where the Value at Risk is taken as measure of risk, in the framework of the BlackScholes model. We show a method for the choice of the optimal strike price of the options, and provide an analytic formula for the optimal Value at Risk, for arbitrary hedging expenditure. We show that hedging with put options is more effective than hedging with forward contracts. We also investigate the impact of the position on Value at Risk if one is to terminate the investment prior to the maturity of the options. We demonstrate that American options do not provide better protection throughout the life span of the investment than European options.