Valuation and Hedging of Options with General Payoff under Transactions Costs

We present the pricing and hedging method for options with general payoffs in the presence of transaction costs. The convexity of the payoff function gamma of the options is an important issue under transaction costs. When the payoff function is convex, Leland-style pricing and hedging method still works. However, if the payoff function is of general form, additional assumptions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payoff is convex as in Leland [11] and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. [10], Avellaneda and Parás [1]. We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payoff into difference of two options each of which has a convex payoff. This method is consistent with a scheme of separating out the seller’s and buyer’s position of an option. In this paper, we first present a simple linear valuation method of general payoff options, and also propose in the last section more efficient hedging scheme which costs less to hedge options.