A general framework for hedging and speculating with options (Q2703111)

The Black-Scholes formula is derived from considering the problem of an agent who wants to hold an option for hedging purposes, i.e. to insure against risk. This paper extends this framework by allowing agents to hold options also for speculation purposes, i.e. in the hope that the options price will rise before it expires. The latter agents will necessarily hold the option only when their subjective valuation is higher than its market value. The authors derive the optimal investment behavior of the agent given his subjective valuation. One of the applications of this approach is for an investor to evaluate if the current price of an option justify holding an option, given his intended use.