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The problem of stock hedging is reconsidered in this paper, where a putoption is chosen from a set of available put options to hedge the market riskof a stock. A formula is proposed to determine the probability that thepotential loss exceeds a predetermined level of Value-at-Risk, which is used tofind the optimal strike price and optimal hedge ratio. The assumptions that thechosen put option finishes in-the-money and the constraint of hedging budget isbinding are relaxed in this paper. A hypothesis test is proposed to determinewhether the failure rate of hedging strategy is greater than the predeterminedlevel of risk. The performances of the proposed method and the method withthose two assumptions are compared through simulations. The results ofsimulated investigations indicate that the proposed method is much more prudentthan the method with those two assumptions.

Hedging strategies with a put option and their failure rates