VALUATION AND HEDGING OF OPTIONS WITH GENERAL PAYOFF UNDER TRANSACTIONS COSTS

We present the pricing and hedging method for op- tions with general payofis in the presence of transaction costs. The convexity of the payofi function - gamma of the options - is an im- portant issue under transaction costs. When the payofi function is convex, Leland-style pricing and hedging method still works. How- ever, if the payofi function is of general form, additional assump- tions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payofi is convex as in Le- land (11) and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. (10), Avellaneda and Paras (1). We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payofi into difierence of two options each of which has a convex payofi. This method is consistent with a scheme of separating out the seller's and buyer's position of an option. In this paper, we flrst present a simple linear valuation method of general payofi options, and also propose in the last section more e-cient hedging scheme which costs less to hedge options.