• Choi, Hyeong-In (Department of Mathematics Seoul National University) ;
  • Heath, David (Department of Mathematical Sciences Carnegie Mellon University) ;
  • Ku, Hye-Jin (Department of Mathematics & Statistics York University)
  • Published : 2004.05.01


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 Paras 〔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.


  1. Appl. Math. Finance v.1 Dynamic Hedging Portfolios for Derivative Securities in the Presence of Large Transaction Costs M.Avellaneda;A.Paras
  2. Math. Finance v.2 Derivative Asset Pricing with Transaction Costs B.Bensaid;J.Lesne;H.Pages;J.Scheinkman
  3. J. Political Economy v.81 The Pricing of Options and Corporate Liabilities F.Black;M.Scholes
  4. The Journal of Finance v.47 Option Replication in Dscrete Time with Transaction Costs P.Boyle;T.Vorst
  5. Working Paper, Seoul National U. Replication of European Option with Genaral Payoff Function in the Presence of Transactions Costs H.I.Choi;H.Ku
  6. SIAM J. Control Optim. v.31 European Option Pricing with Transaction Costs M.H.A.Davis;V.G.Panas;T.Zariphopoulou
  7. Option Pricing J.Dewynne;S.Howison;P.Wilmott
  8. An Introduction to Probability Theory and its Application W.Feller
  9. The Review of Futures Markets v.8 Optimal Replication of Contingent Claims under Transaction Costs S.D.Hodges;N.Neuberger
  10. Adv. Futures and Options Research v.7 Hedging Option Portfolios in the Presence of Transaction Costs T.Hoggard;A.E.Whalley;P.Wilmott
  11. J. Finance v.40 Option Pricing and Replication with Transaction Costs H.E.Leland
  12. OCIAM Working Paper, Oxford U. A Hedging Strategy and Option Valuation Model with Transaction Costs A.E.Whalley;P.Wilmott